bump to 2.6.7

(grafted from 971cfbb480614229b5f48b040ef9d5dd18a4ab44)

CMakeLists.txt

@@ -301,7 +301,7 @@ if(EIGEN_INCLUDE_INSTALL_DIR)
   )
 else()
   set(INCLUDE_INSTALL_DIR
-    "${CMAKE_INSTALL_PREFIX}/include/eigen3"
+    "include/eigen3"
     CACHE INTERNAL
     "The directory where we install the header files (internal)"
   )
@@ -404,7 +404,7 @@ if(cmake_generator_tolower MATCHES "makefile")
   message(STATUS "make install  | Install to ${CMAKE_INSTALL_PREFIX}. To change that:")
   message(STATUS "              |     cmake . -DCMAKE_INSTALL_PREFIX=yourpath")
   message(STATUS "              |   Eigen headers will then be installed to:")
-  message(STATUS "              |     ${INCLUDE_INSTALL_DIR}")
+  message(STATUS "              |     ${CMAKE_INSTALL_PREFIX}/${INCLUDE_INSTALL_DIR}")
   message(STATUS "              |   To install Eigen headers to a separate location, do:")
   message(STATUS "              |     cmake . -DEIGEN_INCLUDE_INSTALL_DIR=yourpath")
   message(STATUS "make doc      | Generate the API documentation, requires Doxygen & LaTeX")

CTestConfig.cmake

@@ -4,14 +4,10 @@
 ## # The following are required to uses Dart and the Cdash dashboard
 ##   ENABLE_TESTING()
 ##   INCLUDE(CTest)
-set(CTEST_PROJECT_NAME "Eigen")
+set(CTEST_PROJECT_NAME "Eigen3.2")
 set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC")
 
 set(CTEST_DROP_METHOD "http")
 set(CTEST_DROP_SITE "manao.inria.fr")
-set(CTEST_DROP_LOCATION "/CDash/submit.php?project=Eigen")
+set(CTEST_DROP_LOCATION "/CDash/submit.php?project=Eigen3.2")
 set(CTEST_DROP_SITE_CDASH TRUE)
-set(CTEST_PROJECT_SUBPROJECTS
-Official
-Unsupported
-)

Eigen/Core

@@ -95,7 +95,7 @@
     extern "C" {
       // In theory we should only include immintrin.h and not the other *mmintrin.h header files directly.
       // Doing so triggers some issues with ICC. However old gcc versions seems to not have this file, thus:
-      #ifdef __INTEL_COMPILER
+      #if defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 1110
         #include <immintrin.h>
       #else
         #include <emmintrin.h>
@@ -123,7 +123,7 @@
     #undef bool
     #undef vector
     #undef pixel
-  #elif defined  __ARM_NEON__
+  #elif defined  __ARM_NEON
     #define EIGEN_VECTORIZE
     #define EIGEN_VECTORIZE_NEON
     #include <arm_neon.h>
@@ -165,7 +165,7 @@
 #endif
 
 // required for __cpuid, needs to be included after cmath
-#if defined(_MSC_VER) && (defined(_M_IX86)||defined(_M_X64))
+#if defined(_MSC_VER) && (defined(_M_IX86)||defined(_M_X64)) && (!defined(_WIN32_WCE))
   #include <intrin.h>
 #endif
 

Eigen/SparseCore

@@ -14,7 +14,7 @@
 /** 
   * \defgroup SparseCore_Module SparseCore module
   *
-  * This module provides a sparse matrix representation, and basic associatd matrix manipulations
+  * This module provides a sparse matrix representation, and basic associated matrix manipulations
   * and operations.
   *
   * See the \ref TutorialSparse "Sparse tutorial"

Eigen/src/Cholesky/LDLT.h

@@ -235,6 +235,11 @@ template<typename _MatrixType, int _UpLo> class LDLT
     }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
 
     /** \internal
       * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
@@ -274,30 +279,13 @@ template<> struct ldlt_inplace<Lower>
       return true;
     }
 
-    RealScalar cutoff(0), biggest_in_corner;
-
     for (Index k = 0; k < size; ++k)
     {
       // Find largest diagonal element
       Index index_of_biggest_in_corner;
-      biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
+      mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
       index_of_biggest_in_corner += k;
 
-      if(k == 0)
-      {
-        // The biggest overall is the point of reference to which further diagonals
-        // are compared; if any diagonal is negligible compared
-        // to the largest overall, the algorithm bails.
-        cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
-      }
-
-      // Finish early if the matrix is not full rank.
-      if(biggest_in_corner < cutoff)
-      {
-        for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
-        break;
-      }
-
       transpositions.coeffRef(k) = index_of_biggest_in_corner;
       if(k != index_of_biggest_in_corner)
       {
@@ -328,15 +316,20 @@ template<> struct ldlt_inplace<Lower>
 
       if(k>0)
       {
-        temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
+        temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
         mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
         if(rs>0)
           A21.noalias() -= A20 * temp.head(k);
       }
-      if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
+      
-        A21 /= mat.coeffRef(k,k);
+      // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
-
+      // was smaller than the cutoff value. However, soince LDLT is not rank-revealing
+      // we should only make sure we do not introduce INF or NaN values.
+      // LAPACK also uses 0 as the cutoff value.
       RealScalar realAkk = numext::real(mat.coeffRef(k,k));
+      if((rs>0) && (abs(realAkk) > RealScalar(0)))
+        A21 /= realAkk;
+
       if (sign == PositiveSemiDef) {
         if (realAkk < 0) sign = Indefinite;
       } else if (sign == NegativeSemiDef) {
@@ -446,6 +439,8 @@ template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
 template<typename MatrixType, int _UpLo>
 LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
 {
+  check_template_parameters();
+  
   eigen_assert(a.rows()==a.cols());
   const Index size = a.rows();
 
@@ -454,6 +449,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
   m_transpositions.resize(size);
   m_isInitialized = false;
   m_temporary.resize(size);
+  m_sign = internal::ZeroSign;
 
   internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign);
 
@@ -468,7 +464,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
   */
 template<typename MatrixType, int _UpLo>
 template<typename Derived>
-LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename NumTraits<typename MatrixType::Scalar>::Real& sigma)
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma)
 {
   const Index size = w.rows();
   if (m_isInitialized)
@@ -514,16 +510,21 @@ struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
     using std::abs;
     using std::max;
     typedef typename LDLTType::MatrixType MatrixType;
-    typedef typename LDLTType::Scalar Scalar;
     typedef typename LDLTType::RealScalar RealScalar;
-    const Diagonal<const MatrixType> vectorD = dec().vectorD();
+    const typename Diagonal<const MatrixType>::RealReturnType vectorD(dec().vectorD());
-    RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
+    // In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon
-				 RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
+    // as motivated by LAPACK's xGELSS:
+    // RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() *NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
+    // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
+    // diagonal element is not well justified and to numerical issues in some cases.
+    // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
+    RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest();
+    
     for (Index i = 0; i < vectorD.size(); ++i) {
       if(abs(vectorD(i)) > tolerance)
-	dst.row(i) /= vectorD(i);
+        dst.row(i) /= vectorD(i);
       else
-	dst.row(i).setZero();
+        dst.row(i).setZero();
     }
 
     // dst = L^-T (D^-1 L^-1 P b)
@@ -576,7 +577,7 @@ MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
   // L^* P
   res = matrixU() * res;
   // D(L^*P)
-  res = vectorD().asDiagonal() * res;
+  res = vectorD().real().asDiagonal() * res;
   // L(DL^*P)
   res = matrixL() * res;
   // P^T (LDL^*P)

Eigen/src/Cholesky/LLT.h

@@ -174,6 +174,12 @@ template<typename _MatrixType, int _UpLo> class LLT
     LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     /** \internal
       * Used to compute and store L
       * The strict upper part is not used and even not initialized.
@@ -283,7 +289,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
         return k;
       mat.coeffRef(k,k) = x = sqrt(x);
       if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
-      if (rs>0) A21 *= RealScalar(1)/x;
+      if (rs>0) A21 /= x;
     }
     return -1;
   }
@@ -384,6 +390,8 @@ template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
 template<typename MatrixType, int _UpLo>
 LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a)
 {
+  check_template_parameters();
+  
   eigen_assert(a.rows()==a.cols());
   const Index size = a.rows();
   m_matrix.resize(size, size);

Eigen/src/Cholesky/LLT_MKL.h

@@ -60,7 +60,7 @@ template<> struct mkl_llt<EIGTYPE> \
     lda = m.outerStride(); \
 \
     info = LAPACKE_##MKLPREFIX##potrf( matrix_order, uplo, size, (MKLTYPE*)a, lda ); \
-    info = (info==0) ? Success : NumericalIssue; \
+    info = (info==0) ? -1 : info>0 ? info-1 : size; \
     return info; \
   } \
 }; \

Eigen/src/CholmodSupport/CholmodSupport.h

@@ -78,7 +78,7 @@ cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
   {
     res.itype = CHOLMOD_INT;
   }
-  else if (internal::is_same<_Index,UF_long>::value)
+  else if (internal::is_same<_Index,SuiteSparse_long>::value)
   {
     res.itype = CHOLMOD_LONG;
   }
@@ -395,7 +395,7 @@ class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimpl
     CholmodSimplicialLLT(const MatrixType& matrix) : Base()
     {
       init();
-      compute(matrix);
+      Base::compute(matrix);
     }
 
     ~CholmodSimplicialLLT() {}
@@ -442,7 +442,7 @@ class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimp
     CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
     {
       init();
-      compute(matrix);
+      Base::compute(matrix);
     }
 
     ~CholmodSimplicialLDLT() {}
@@ -487,7 +487,7 @@ class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSuper
     CholmodSupernodalLLT(const MatrixType& matrix) : Base()
     {
       init();
-      compute(matrix);
+      Base::compute(matrix);
     }
 
     ~CholmodSupernodalLLT() {}
@@ -534,7 +534,7 @@ class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecom
     CholmodDecomposition(const MatrixType& matrix) : Base()
     {
       init();
-      compute(matrix);
+      Base::compute(matrix);
     }
 
     ~CholmodDecomposition() {}

Eigen/src/Core/Array.h

@@ -124,6 +124,21 @@ class Array
     }
 #endif
 
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
+    Array(Array&& other)
+      : Base(std::move(other))
+    {
+      Base::_check_template_params();
+      if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)
+        Base::_set_noalias(other);
+    }
+    Array& operator=(Array&& other)
+    {
+      other.swap(*this);
+      return *this;
+    }
+#endif
+
     /** Constructs a vector or row-vector with given dimension. \only_for_vectors
       *
       * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,

Eigen/src/Core/ArrayBase.h

@@ -46,9 +46,6 @@ template<typename Derived> class ArrayBase
 
     typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
 
-    using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
-                typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
-
     typedef typename internal::traits<Derived>::StorageKind StorageKind;
     typedef typename internal::traits<Derived>::Index Index;
     typedef typename internal::traits<Derived>::Scalar Scalar;
@@ -56,6 +53,7 @@ template<typename Derived> class ArrayBase
     typedef typename NumTraits<Scalar>::Real RealScalar;
 
     typedef DenseBase<Derived> Base;
+    using Base::operator*;
     using Base::RowsAtCompileTime;
     using Base::ColsAtCompileTime;
     using Base::SizeAtCompileTime;

Eigen/src/Core/ArrayWrapper.h

@@ -29,6 +29,11 @@ struct traits<ArrayWrapper<ExpressionType> >
   : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
   typedef ArrayXpr XprKind;
+  // Let's remove NestByRefBit
+  enum {
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+    Flags = Flags0 & ~NestByRefBit
+  };
 };
 }
 
@@ -149,6 +154,11 @@ struct traits<MatrixWrapper<ExpressionType> >
  : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
   typedef MatrixXpr XprKind;
+  // Let's remove NestByRefBit
+  enum {
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+    Flags = Flags0 & ~NestByRefBit
+  };
 };
 }
 

Eigen/src/Core/Assign.h

@@ -439,19 +439,26 @@ struct assign_impl<Derived1, Derived2, SliceVectorizedTraversal, NoUnrolling, Ve
   typedef typename Derived1::Index Index;
   static inline void run(Derived1 &dst, const Derived2 &src)
   {
-    typedef packet_traits<typename Derived1::Scalar> PacketTraits;
+    typedef typename Derived1::Scalar Scalar;
+    typedef packet_traits<Scalar> PacketTraits;
     enum {
       packetSize = PacketTraits::size,
       alignable = PacketTraits::AlignedOnScalar,
-      dstAlignment = alignable ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
+      dstIsAligned = assign_traits<Derived1,Derived2>::DstIsAligned,
+      dstAlignment = alignable ? Aligned : int(dstIsAligned),
       srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
     };
+    const Scalar *dst_ptr = &dst.coeffRef(0,0);
+    if((!bool(dstIsAligned)) && (size_t(dst_ptr) % sizeof(Scalar))>0)
+    {
+      // the pointer is not aligend-on scalar, so alignment is not possible
+      return assign_impl<Derived1,Derived2,DefaultTraversal,NoUnrolling>::run(dst, src);
+    }
     const Index packetAlignedMask = packetSize - 1;
     const Index innerSize = dst.innerSize();
     const Index outerSize = dst.outerSize();
     const Index alignedStep = alignable ? (packetSize - dst.outerStride() % packetSize) & packetAlignedMask : 0;
-    Index alignedStart = ((!alignable) || assign_traits<Derived1,Derived2>::DstIsAligned) ? 0
+    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, innerSize);
-                       : internal::first_aligned(&dst.coeffRef(0,0), innerSize);
 
     for(Index outer = 0; outer < outerSize; ++outer)
     {

Eigen/src/Core/Block.h

@@ -66,8 +66,9 @@ struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprTyp
                          : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
                          : int(traits<XprType>::MaxColsAtCompileTime),
     XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
-    IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+    IsDense = is_same<StorageKind,Dense>::value,
-               : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+    IsRowMajor = (IsDense&&MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+               : (IsDense&&MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
                : XprTypeIsRowMajor,
     HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
     InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
@@ -81,7 +82,7 @@ struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprTyp
                        && (InnerStrideAtCompileTime == 1)
                         ? PacketAccessBit : 0,
     MaskAlignedBit = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
-    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 || (InnerPanel && (traits<XprType>::Flags&LinearAccessBit))) ? LinearAccessBit : 0,
     FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
     FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
     Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) |

Eigen/src/Core/CommaInitializer.h

@@ -43,6 +43,17 @@ struct CommaInitializer
     m_xpr.block(0, 0, other.rows(), other.cols()) = other;
   }
 
+  /* Copy/Move constructor which transfers ownership. This is crucial in 
+   * absence of return value optimization to avoid assertions during destruction. */
+  // FIXME in C++11 mode this could be replaced by a proper RValue constructor
+  inline CommaInitializer(const CommaInitializer& o)
+  : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
+    // Mark original object as finished. In absence of R-value references we need to const_cast:
+    const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
+    const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();
+    const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;
+  }
+
   /* inserts a scalar value in the target matrix */
   CommaInitializer& operator,(const Scalar& s)
   {

Eigen/src/Core/CwiseBinaryOp.h

@@ -81,7 +81,8 @@ struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
         )
      ),
     Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
-    CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + functor_traits<BinaryOp>::Cost
+    Cost0 = EIGEN_ADD_COST(LhsCoeffReadCost,RhsCoeffReadCost),
+    CoeffReadCost = EIGEN_ADD_COST(Cost0,functor_traits<BinaryOp>::Cost)
   };
 };
 } // end namespace internal

Eigen/src/Core/CwiseUnaryOp.h

@@ -47,7 +47,7 @@ struct traits<CwiseUnaryOp<UnaryOp, XprType> >
     Flags = _XprTypeNested::Flags & (
       HereditaryBits | LinearAccessBit | AlignedBit
       | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
-    CoeffReadCost = _XprTypeNested::CoeffReadCost + functor_traits<UnaryOp>::Cost
+    CoeffReadCost = EIGEN_ADD_COST(_XprTypeNested::CoeffReadCost, functor_traits<UnaryOp>::Cost)
   };
 };
 }

Eigen/src/Core/DenseBase.h

@@ -40,15 +40,14 @@ static inline void check_DenseIndex_is_signed() {
   */
 template<typename Derived> class DenseBase
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-  : public internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+  : public internal::special_scalar_op_base<Derived, typename internal::traits<Derived>::Scalar,
-                                     typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>
+                                            typename NumTraits<typename internal::traits<Derived>::Scalar>::Real,
+                                            DenseCoeffsBase<Derived> >
 #else
   : public DenseCoeffsBase<Derived>
 #endif // not EIGEN_PARSED_BY_DOXYGEN
 {
   public:
-    using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
-                typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
 
     class InnerIterator;
 
@@ -63,8 +62,9 @@ template<typename Derived> class DenseBase
     typedef typename internal::traits<Derived>::Scalar Scalar;
     typedef typename internal::packet_traits<Scalar>::type PacketScalar;
     typedef typename NumTraits<Scalar>::Real RealScalar;
+    typedef internal::special_scalar_op_base<Derived,Scalar,RealScalar, DenseCoeffsBase<Derived> > Base;
 
-    typedef DenseCoeffsBase<Derived> Base;
+    using Base::operator*;
     using Base::derived;
     using Base::const_cast_derived;
     using Base::rows;
@@ -183,10 +183,6 @@ template<typename Derived> class DenseBase
     /** \returns the number of nonzero coefficients which is in practice the number
       * of stored coefficients. */
     inline Index nonZeros() const { return size(); }
-    /** \returns true if either the number of rows or the number of columns is equal to 1.
-      * In other words, this function returns
-      * \code rows()==1 || cols()==1 \endcode
-      * \sa rows(), cols(), IsVectorAtCompileTime. */
 
     /** \returns the outer size.
       *
@@ -266,11 +262,13 @@ template<typename Derived> class DenseBase
     template<typename OtherDerived>
     Derived& operator=(const ReturnByValue<OtherDerived>& func);
 
-#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal Copies \a other into *this without evaluating other. \returns a reference to *this. */
-    /** Copies \a other into *this without evaluating other. \returns a reference to *this. */
     template<typename OtherDerived>
     Derived& lazyAssign(const DenseBase<OtherDerived>& other);
-#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** \internal Evaluates \a other into *this. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const ReturnByValue<OtherDerived>& other);
 
     CommaInitializer<Derived> operator<< (const Scalar& s);
 
@@ -462,8 +460,10 @@ template<typename Derived> class DenseBase
     template<int p> RealScalar lpNorm() const;
 
     template<int RowFactor, int ColFactor>
-    const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+    inline const Replicate<Derived,RowFactor,ColFactor> replicate() const;
-    const Replicate<Derived,Dynamic,Dynamic> replicate(Index rowFacor,Index colFactor) const;
+    
+    typedef Replicate<Derived,Dynamic,Dynamic> ReplicateReturnType;
+    inline const ReplicateReturnType replicate(Index rowFacor,Index colFactor) const;
 
     typedef Reverse<Derived, BothDirections> ReverseReturnType;
     typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;

Eigen/src/Core/DenseStorage.h

@@ -24,6 +24,14 @@ namespace internal {
 
 struct constructor_without_unaligned_array_assert {};
 
+template<typename T, int Size> void check_static_allocation_size()
+{
+  // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit
+  #if EIGEN_STACK_ALLOCATION_LIMIT
+  EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+  #endif
+}
+
 /** \internal
   * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
   * to 16 bytes boundary if the total size is a multiple of 16 bytes.
@@ -38,12 +46,12 @@ struct plain_array
 
   plain_array() 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 
   plain_array(constructor_without_unaligned_array_assert) 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 };
 
@@ -76,12 +84,12 @@ struct plain_array<T, Size, MatrixOrArrayOptions, 16>
   plain_array() 
   { 
     EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(0xf);
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 
   plain_array(constructor_without_unaligned_array_assert) 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 };
 
@@ -114,33 +122,41 @@ template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseSt
 {
     internal::plain_array<T,Size,_Options> m_data;
   public:
-    inline DenseStorage() {}
+    DenseStorage() {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+    DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()) {}
-    inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+    DenseStorage(const DenseStorage& other) : m_data(other.m_data) {}
-    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }
+    DenseStorage& operator=(const DenseStorage& other)
-    static inline DenseIndex rows(void) {return _Rows;}
+    {
-    static inline DenseIndex cols(void) {return _Cols;}
+      if (this != &other) m_data = other.m_data;
-    inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+      return *this;
-    inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    }
-    inline const T *data() const { return m_data.array; }
+    DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
-    inline T *data() { return m_data.array; }
+    void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }
+    static DenseIndex rows(void) {return _Rows;}
+    static DenseIndex cols(void) {return _Cols;}
+    void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+    void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    const T *data() const { return m_data.array; }
+    T *data() { return m_data.array; }
 };
 
 // null matrix
 template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
 {
   public:
-    inline DenseStorage() {}
+    DenseStorage() {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert) {}
+    DenseStorage(internal::constructor_without_unaligned_array_assert) {}
-    inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+    DenseStorage(const DenseStorage&) {}
-    inline void swap(DenseStorage& ) {}
+    DenseStorage& operator=(const DenseStorage&) { return *this; }
-    static inline DenseIndex rows(void) {return _Rows;}
+    DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
-    static inline DenseIndex cols(void) {return _Cols;}
+    void swap(DenseStorage& ) {}
-    inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+    static DenseIndex rows(void) {return _Rows;}
-    inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    static DenseIndex cols(void) {return _Cols;}
-    inline const T *data() const { return 0; }
+    void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
-    inline T *data() { return 0; }
+    void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    const T *data() const { return 0; }
+    T *data() { return 0; }
 };
 
 // more specializations for null matrices; these are necessary to resolve ambiguities
@@ -160,18 +176,29 @@ template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic
     DenseIndex m_rows;
     DenseIndex m_cols;
   public:
-    inline DenseStorage() : m_rows(0), m_cols(0) {}
+    DenseStorage() : m_rows(0), m_cols(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+    DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
-    inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) : m_rows(nbRows), m_cols(nbCols) {}
+    DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_rows(other.m_rows), m_cols(other.m_cols) {}
-    inline void swap(DenseStorage& other)
+    DenseStorage& operator=(const DenseStorage& other)
+    {
+      if (this != &other)
+      {
+        m_data = other.m_data;
+        m_rows = other.m_rows;
+        m_cols = other.m_cols;
+      }
+      return *this;
+    }
+    DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) : m_rows(nbRows), m_cols(nbCols) {}
+    void swap(DenseStorage& other)
     { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
-    inline DenseIndex rows() const {return m_rows;}
+    DenseIndex rows() const {return m_rows;}
-    inline DenseIndex cols() const {return m_cols;}
+    DenseIndex cols() const {return m_cols;}
-    inline void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
+    void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
-    inline void resize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
+    void resize(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) { m_rows = nbRows; m_cols = nbCols; }
-    inline const T *data() const { return m_data.array; }
+    const T *data() const { return m_data.array; }
-    inline T *data() { return m_data.array; }
+    T *data() { return m_data.array; }
 };
 
 // dynamic-size matrix with fixed-size storage and fixed width
@@ -180,17 +207,27 @@ template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Si
     internal::plain_array<T,Size,_Options> m_data;
     DenseIndex m_rows;
   public:
-    inline DenseStorage() : m_rows(0) {}
+    DenseStorage() : m_rows(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+    DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
-    inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex) : m_rows(nbRows) {}
+    DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_rows(other.m_rows) {}
-    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    DenseStorage& operator=(const DenseStorage& other)
-    inline DenseIndex rows(void) const {return m_rows;}
+    {
-    inline DenseIndex cols(void) const {return _Cols;}
+      if (this != &other)
-    inline void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+      {
-    inline void resize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+        m_data = other.m_data;
-    inline const T *data() const { return m_data.array; }
+        m_rows = other.m_rows;
-    inline T *data() { return m_data.array; }
+      }
+      return *this;
+    }
+    DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex) : m_rows(nbRows) {}
+    void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    DenseIndex rows(void) const {return m_rows;}
+    DenseIndex cols(void) const {return _Cols;}
+    void conservativeResize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+    void resize(DenseIndex, DenseIndex nbRows, DenseIndex) { m_rows = nbRows; }
+    const T *data() const { return m_data.array; }
+    T *data() { return m_data.array; }
 };
 
 // dynamic-size matrix with fixed-size storage and fixed height
@@ -199,17 +236,27 @@ template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Si
     internal::plain_array<T,Size,_Options> m_data;
     DenseIndex m_cols;
   public:
-    inline DenseStorage() : m_cols(0) {}
+    DenseStorage() : m_cols(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+    DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
-    inline DenseStorage(DenseIndex, DenseIndex, DenseIndex nbCols) : m_cols(nbCols) {}
+    DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_cols(other.m_cols) {}
-    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    DenseStorage& operator=(const DenseStorage& other)
-    inline DenseIndex rows(void) const {return _Rows;}
+    {
-    inline DenseIndex cols(void) const {return m_cols;}
+      if (this != &other)
-    inline void conservativeResize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+      {
-    inline void resize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+        m_data = other.m_data;
-    inline const T *data() const { return m_data.array; }
+        m_cols = other.m_cols;
-    inline T *data() { return m_data.array; }
+      }
+      return *this;
+    }
+    DenseStorage(DenseIndex, DenseIndex, DenseIndex nbCols) : m_cols(nbCols) {}
+    void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    DenseIndex rows(void) const {return _Rows;}
+    DenseIndex cols(void) const {return m_cols;}
+    void conservativeResize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+    void resize(DenseIndex, DenseIndex, DenseIndex nbCols) { m_cols = nbCols; }
+    const T *data() const { return m_data.array; }
+    T *data() { return m_data.array; }
 };
 
 // purely dynamic matrix.
@@ -219,18 +266,35 @@ template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynam
     DenseIndex m_rows;
     DenseIndex m_cols;
   public:
-    inline DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
+    DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+    DenseStorage(internal::constructor_without_unaligned_array_assert)
        : m_data(0), m_rows(0), m_cols(0) {}
-    inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
+    DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
       : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows), m_cols(nbCols)
     { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
-    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
-    inline void swap(DenseStorage& other)
+    DenseStorage(DenseStorage&& other)
+      : m_data(std::move(other.m_data))
+      , m_rows(std::move(other.m_rows))
+      , m_cols(std::move(other.m_cols))
+    {
+      other.m_data = nullptr;
+    }
+    DenseStorage& operator=(DenseStorage&& other)
+    {
+      using std::swap;
+      swap(m_data, other.m_data);
+      swap(m_rows, other.m_rows);
+      swap(m_cols, other.m_cols);
+      return *this;
+    }
+#endif
+    ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
+    void swap(DenseStorage& other)
     { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
-    inline DenseIndex rows(void) const {return m_rows;}
+    DenseIndex rows(void) const {return m_rows;}
-    inline DenseIndex cols(void) const {return m_cols;}
+    DenseIndex cols(void) const {return m_cols;}
-    inline void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
+    void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
     {
       m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);
       m_rows = nbRows;
@@ -250,8 +314,11 @@ template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynam
       m_rows = nbRows;
       m_cols = nbCols;
     }
-    inline const T *data() const { return m_data; }
+    const T *data() const { return m_data; }
-    inline T *data() { return m_data; }
+    T *data() { return m_data; }
+  private:
+    DenseStorage(const DenseStorage&);
+    DenseStorage& operator=(const DenseStorage&);
 };
 
 // matrix with dynamic width and fixed height (so that matrix has dynamic size).
@@ -260,15 +327,30 @@ template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Ro
     T *m_data;
     DenseIndex m_cols;
   public:
-    inline DenseStorage() : m_data(0), m_cols(0) {}
+    DenseStorage() : m_data(0), m_cols(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
+    DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
-    inline DenseStorage(DenseIndex size, DenseIndex, DenseIndex nbCols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(nbCols)
+    DenseStorage(DenseIndex size, DenseIndex, DenseIndex nbCols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(nbCols)
     { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
-    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
-    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    DenseStorage(DenseStorage&& other)
-    static inline DenseIndex rows(void) {return _Rows;}
+      : m_data(std::move(other.m_data))
-    inline DenseIndex cols(void) const {return m_cols;}
+      , m_cols(std::move(other.m_cols))
-    inline void conservativeResize(DenseIndex size, DenseIndex, DenseIndex nbCols)
+    {
+      other.m_data = nullptr;
+    }
+    DenseStorage& operator=(DenseStorage&& other)
+    {
+      using std::swap;
+      swap(m_data, other.m_data);
+      swap(m_cols, other.m_cols);
+      return *this;
+    }
+#endif
+    ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
+    void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    static DenseIndex rows(void) {return _Rows;}
+    DenseIndex cols(void) const {return m_cols;}
+    void conservativeResize(DenseIndex size, DenseIndex, DenseIndex nbCols)
     {
       m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);
       m_cols = nbCols;
@@ -286,8 +368,11 @@ template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Ro
       }
       m_cols = nbCols;
     }
-    inline const T *data() const { return m_data; }
+    const T *data() const { return m_data; }
-    inline T *data() { return m_data; }
+    T *data() { return m_data; }
+  private:
+    DenseStorage(const DenseStorage&);
+    DenseStorage& operator=(const DenseStorage&);
 };
 
 // matrix with dynamic height and fixed width (so that matrix has dynamic size).
@@ -296,15 +381,30 @@ template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dyn
     T *m_data;
     DenseIndex m_rows;
   public:
-    inline DenseStorage() : m_data(0), m_rows(0) {}
+    DenseStorage() : m_data(0), m_rows(0) {}
-    inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
+    DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
-    inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows)
+    DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows)
     { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
-    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
-    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    DenseStorage(DenseStorage&& other)
-    inline DenseIndex rows(void) const {return m_rows;}
+      : m_data(std::move(other.m_data))
-    static inline DenseIndex cols(void) {return _Cols;}
+      , m_rows(std::move(other.m_rows))
-    inline void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex)
+    {
+      other.m_data = nullptr;
+    }
+    DenseStorage& operator=(DenseStorage&& other)
+    {
+      using std::swap;
+      swap(m_data, other.m_data);
+      swap(m_rows, other.m_rows);
+      return *this;
+    }
+#endif
+    ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
+    void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    DenseIndex rows(void) const {return m_rows;}
+    static DenseIndex cols(void) {return _Cols;}
+    void conservativeResize(DenseIndex size, DenseIndex nbRows, DenseIndex)
     {
       m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);
       m_rows = nbRows;
@@ -322,8 +422,11 @@ template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dyn
       }
       m_rows = nbRows;
     }
-    inline const T *data() const { return m_data; }
+    const T *data() const { return m_data; }
-    inline T *data() { return m_data; }
+    T *data() { return m_data; }
+  private:
+    DenseStorage(const DenseStorage&);
+    DenseStorage& operator=(const DenseStorage&);
 };
 
 } // end namespace Eigen

Eigen/src/Core/Diagonal.h

@@ -190,18 +190,18 @@ MatrixBase<Derived>::diagonal() const
   *
   * \sa MatrixBase::diagonal(), class Diagonal */
 template<typename Derived>
-inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<DynamicIndex>::Type
+inline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType
 MatrixBase<Derived>::diagonal(Index index)
 {
-  return typename DiagonalIndexReturnType<DynamicIndex>::Type(derived(), index);
+  return DiagonalDynamicIndexReturnType(derived(), index);
 }
 
 /** This is the const version of diagonal(Index). */
 template<typename Derived>
-inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<DynamicIndex>::Type
+inline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType
 MatrixBase<Derived>::diagonal(Index index) const
 {
-  return typename ConstDiagonalIndexReturnType<DynamicIndex>::Type(derived(), index);
+  return ConstDiagonalDynamicIndexReturnType(derived(), index);
 }
 
 /** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this

Eigen/src/Core/DiagonalProduct.h

@@ -34,8 +34,9 @@ struct traits<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
     _Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && _SameTypes && (_ScalarAccessOnDiag || (bool(int(DiagonalType::DiagonalVectorType::Flags)&PacketAccessBit))),
     _LinearAccessMask = (RowsAtCompileTime==1 || ColsAtCompileTime==1) ? LinearAccessBit : 0,
 
-    Flags = ((HereditaryBits|_LinearAccessMask) & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0) | AlignedBit,//(int(MatrixType::Flags)&int(DiagonalType::DiagonalVectorType::Flags)&AlignedBit),
+    Flags = ((HereditaryBits|_LinearAccessMask|AlignedBit) & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0),//(int(MatrixType::Flags)&int(DiagonalType::DiagonalVectorType::Flags)&AlignedBit),
-    CoeffReadCost = NumTraits<Scalar>::MulCost + MatrixType::CoeffReadCost + DiagonalType::DiagonalVectorType::CoeffReadCost
+    Cost0 = EIGEN_ADD_COST(NumTraits<Scalar>::MulCost, MatrixType::CoeffReadCost),
+    CoeffReadCost = EIGEN_ADD_COST(Cost0,DiagonalType::DiagonalVectorType::CoeffReadCost)
   };
 };
 }

Eigen/src/Core/Functors.h

@@ -259,6 +259,47 @@ template<> struct functor_traits<scalar_boolean_or_op> {
   };
 };
 
+/** \internal
+  * \brief Template functors for comparison of two scalars
+  * \todo Implement packet-comparisons
+  */
+template<typename Scalar, ComparisonName cmp> struct scalar_cmp_op;
+
+template<typename Scalar, ComparisonName cmp>
+struct functor_traits<scalar_cmp_op<Scalar, cmp> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = false
+  };
+};
+
+template<ComparisonName Cmp, typename Scalar>
+struct result_of<scalar_cmp_op<Scalar, Cmp>(Scalar,Scalar)> {
+  typedef bool type;
+};
+
+
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_EQ> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+  EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a==b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LT> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+  EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LE> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+  EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<=b;}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_UNORD> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+  EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return !(a<=b || b<=a);}
+};
+template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_NEQ> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+  EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a!=b;}
+};
+
 // unary functors:
 
 /** \internal
@@ -589,7 +630,7 @@ struct linspaced_op_impl<Scalar,true>
 
   template<typename Index>
   EIGEN_STRONG_INLINE const Packet packetOp(Index i) const
-  { return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(i),m_interPacket))); }
+  { return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(Scalar(i)),m_interPacket))); }
 
   const Scalar m_low;
   const Scalar m_step;
@@ -609,7 +650,7 @@ template <typename Scalar, bool RandomAccess> struct functor_traits< linspaced_o
 template <typename Scalar, bool RandomAccess> struct linspaced_op
 {
   typedef typename packet_traits<Scalar>::type Packet;
-  linspaced_op(const Scalar& low, const Scalar& high, DenseIndex num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/(num_steps-1))) {}
+  linspaced_op(const Scalar& low, const Scalar& high, DenseIndex num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1))) {}
 
   template<typename Index>
   EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }

Eigen/src/Core/GeneralProduct.h

@@ -232,7 +232,7 @@ EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest&
   // FIXME not very good if rhs is real and lhs complex while alpha is real too
   const Index cols = dest.cols();
   for (Index j=0; j<cols; ++j)
-    func(dest.col(j), prod.rhs().coeff(j) * prod.lhs());
+    func(dest.col(j), prod.rhs().coeff(0,j) * prod.lhs());
 }
 
 // Row major
@@ -243,7 +243,7 @@ EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest&
   // FIXME not very good if lhs is real and rhs complex while alpha is real too
   const Index rows = dest.rows();
   for (Index i=0; i<rows; ++i)
-    func(dest.row(i), prod.lhs().coeff(i) * prod.rhs());
+    func(dest.row(i), prod.lhs().coeff(i,0) * prod.rhs());
 }
 
 template<typename Lhs, typename Rhs>
@@ -257,7 +257,7 @@ template<typename Lhs, typename Rhs>
 class GeneralProduct<Lhs, Rhs, OuterProduct>
   : public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
 {
-    template<typename T> struct IsRowMajor : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
+    template<typename T> struct is_row_major : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
     
   public:
     EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
@@ -281,22 +281,22 @@ class GeneralProduct<Lhs, Rhs, OuterProduct>
     
     template<typename Dest>
     inline void evalTo(Dest& dest) const {
-      internal::outer_product_selector_run(*this, dest, set(), IsRowMajor<Dest>());
+      internal::outer_product_selector_run(*this, dest, set(), is_row_major<Dest>());
     }
     
     template<typename Dest>
     inline void addTo(Dest& dest) const {
-      internal::outer_product_selector_run(*this, dest, add(), IsRowMajor<Dest>());
+      internal::outer_product_selector_run(*this, dest, add(), is_row_major<Dest>());
     }
 
     template<typename Dest>
     inline void subTo(Dest& dest) const {
-      internal::outer_product_selector_run(*this, dest, sub(), IsRowMajor<Dest>());
+      internal::outer_product_selector_run(*this, dest, sub(), is_row_major<Dest>());
     }
 
     template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
     {
-      internal::outer_product_selector_run(*this, dest, adds(alpha), IsRowMajor<Dest>());
+      internal::outer_product_selector_run(*this, dest, adds(alpha), is_row_major<Dest>());
     }
 };
 

Eigen/src/Core/MapBase.h

@@ -123,7 +123,7 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
       return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
     }
 
-    inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+    explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
     {
       EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
       checkSanity();
@@ -157,7 +157,7 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
                                         internal::inner_stride_at_compile_time<Derived>::ret==1),
                           PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);
       eigen_assert(EIGEN_IMPLIES(internal::traits<Derived>::Flags&AlignedBit, (size_t(m_data) % 16) == 0)
-                   && "data is not aligned");
+                   && "input pointer is not aligned on a 16 byte boundary");
     }
 
     PointerType m_data;
@@ -168,6 +168,7 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
 template<typename Derived> class MapBase<Derived, WriteAccessors>
   : public MapBase<Derived, ReadOnlyAccessors>
 {
+    typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
   public:
 
     typedef MapBase<Derived, ReadOnlyAccessors> Base;
@@ -230,13 +231,17 @@ template<typename Derived> class MapBase<Derived, WriteAccessors>
 
     Derived& operator=(const MapBase& other)
     {
-      Base::Base::operator=(other);
+      ReadOnlyMapBase::Base::operator=(other);
       return derived();
     }
 
-    using Base::Base::operator=;
+    // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
+    // see bugs 821 and 920.
+    using ReadOnlyMapBase::Base::operator=;
 };
 
+#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS
+
 } // end namespace Eigen
 
 #endif // EIGEN_MAPBASE_H

Eigen/src/Core/MathFunctions.h

@@ -294,7 +294,7 @@ struct hypot_impl
     RealScalar _x = abs(x);
     RealScalar _y = abs(y);
     RealScalar p = (max)(_x, _y);
-    if(p==RealScalar(0)) return 0;
+    if(p==RealScalar(0)) return RealScalar(0);
     RealScalar q = (min)(_x, _y);
     RealScalar qp = q/p;
     return p * sqrt(RealScalar(1) + qp*qp);

Eigen/src/Core/Matrix.h

@@ -211,6 +211,21 @@ class Matrix
       : Base(internal::constructor_without_unaligned_array_assert())
     { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
 
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
+    Matrix(Matrix&& other)
+      : Base(std::move(other))
+    {
+      Base::_check_template_params();
+      if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)
+        Base::_set_noalias(other);
+    }
+    Matrix& operator=(Matrix&& other)
+    {
+      other.swap(*this);
+      return *this;
+    }
+#endif
+
     /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
       *
       * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,

Eigen/src/Core/MatrixBase.h

@@ -159,13 +159,11 @@ template<typename Derived> class MatrixBase
     template<typename OtherDerived>
     Derived& operator=(const ReturnByValue<OtherDerived>& other);
 
-#ifndef EIGEN_PARSED_BY_DOXYGEN
     template<typename ProductDerived, typename Lhs, typename Rhs>
     Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
 
     template<typename MatrixPower, typename Lhs, typename Rhs>
     Derived& lazyAssign(const MatrixPowerProduct<MatrixPower, Lhs,Rhs>& other);
-#endif // not EIGEN_PARSED_BY_DOXYGEN
 
     template<typename OtherDerived>
     Derived& operator+=(const MatrixBase<OtherDerived>& other);
@@ -215,7 +213,7 @@ template<typename Derived> class MatrixBase
 
     typedef Diagonal<Derived> DiagonalReturnType;
     DiagonalReturnType diagonal();
-	typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
+    typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
     ConstDiagonalReturnType diagonal() const;
 
     template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
@@ -223,16 +221,12 @@ template<typename Derived> class MatrixBase
 
     template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
     template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
+    
+    typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
+    typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
 
-    // Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
+    DiagonalDynamicIndexReturnType diagonal(Index index);
-    // On the other hand they confuse MSVC8...
+    ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
-    #if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
-    typename MatrixBase::template DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
-    typename MatrixBase::template ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
-    #else
-    typename DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
-    typename ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
-    #endif
 
     #ifdef EIGEN2_SUPPORT
     template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
@@ -446,6 +440,15 @@ template<typename Derived> class MatrixBase
     template<typename OtherScalar>
     void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
 
+///////// SparseCore module /////////
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
+    cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
+    {
+      return other.cwiseProduct(derived());
+    }
+
 ///////// MatrixFunctions module /////////
 
     typedef typename internal::stem_function<Scalar>::type StemFunction;

Eigen/src/Core/PermutationMatrix.h

@@ -250,6 +250,35 @@ class PermutationBase : public EigenBase<Derived>
     template<typename Other> friend
     inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
     { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
+    
+    /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.
+      *
+      * This function is O(\c n) procedure allocating a buffer of \c n booleans.
+      */
+    Index determinant() const
+    {
+      Index res = 1;
+      Index n = size();
+      Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
+      mask.fill(false);
+      Index r = 0;
+      while(r < n)
+      {
+        // search for the next seed
+        while(r<n && mask[r]) r++;
+        if(r>=n)
+          break;
+        // we got one, let's follow it until we are back to the seed
+        Index k0 = r++;
+        mask.coeffRef(k0) = true;
+        for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
+        {
+          mask.coeffRef(k) = true;
+          res = -res;
+        }
+      }
+      return res;
+    }
 
   protected:
 
@@ -555,7 +584,10 @@ struct permut_matrix_product_retval
       const Index n = Side==OnTheLeft ? rows() : cols();
       // FIXME we need an is_same for expression that is not sensitive to constness. For instance
       // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.
-      if(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))
+      if(    is_same<MatrixTypeNestedCleaned,Dest>::value
+          && blas_traits<MatrixTypeNestedCleaned>::HasUsableDirectAccess
+          && blas_traits<Dest>::HasUsableDirectAccess
+          && extract_data(dst) == extract_data(m_matrix))
       {
         // apply the permutation inplace
         Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(m_permutation.size());

Eigen/src/Core/PlainObjectBase.h

@@ -437,6 +437,36 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
     }
 #endif
 
+#ifdef EIGEN_HAVE_RVALUE_REFERENCES
+    PlainObjectBase(PlainObjectBase&& other)
+      : m_storage( std::move(other.m_storage) )
+    {
+    }
+
+    PlainObjectBase& operator=(PlainObjectBase&& other)
+    {
+      using std::swap;
+      swap(m_storage, other.m_storage);
+      return *this;
+    }
+#endif
+
+    /** Copy constructor */
+    EIGEN_STRONG_INLINE PlainObjectBase(const PlainObjectBase& other)
+      : m_storage()
+    {
+      _check_template_params();
+      lazyAssign(other);
+    }
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE PlainObjectBase(const DenseBase<OtherDerived> &other)
+      : m_storage()
+    {
+      _check_template_params();
+      lazyAssign(other);
+    }
+
     EIGEN_STRONG_INLINE PlainObjectBase(Index a_size, Index nbRows, Index nbCols)
       : m_storage(a_size, nbRows, nbCols)
     {
@@ -573,6 +603,8 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
                  : (rows() == other.rows() && cols() == other.cols())))
         && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
       EIGEN_ONLY_USED_FOR_DEBUG(other);
+      if(this->size()==0)
+        resizeLike(other);
       #else
       resizeLike(other);
       #endif

Eigen/src/Core/ProductBase.h

@@ -85,7 +85,14 @@ class ProductBase : public MatrixBase<Derived>
 
   public:
 
+#ifndef EIGEN_NO_MALLOC
+    typedef typename Base::PlainObject BasePlainObject;
+    typedef Matrix<Scalar,RowsAtCompileTime==1?1:Dynamic,ColsAtCompileTime==1?1:Dynamic,BasePlainObject::Options> DynPlainObject;
+    typedef typename internal::conditional<(BasePlainObject::SizeAtCompileTime==Dynamic) || (BasePlainObject::SizeAtCompileTime*int(sizeof(Scalar)) < int(EIGEN_STACK_ALLOCATION_LIMIT)),
+                                           BasePlainObject, DynPlainObject>::type PlainObject;
+#else
     typedef typename Base::PlainObject PlainObject;
+#endif
 
     ProductBase(const Lhs& a_lhs, const Rhs& a_rhs)
       : m_lhs(a_lhs), m_rhs(a_rhs)
@@ -180,7 +187,12 @@ namespace internal {
 template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
 struct nested<GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
 {
-  typedef PlainObject const& type;
+  typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
+};
+template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
+struct nested<const GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
+{
+  typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
 };
 }
 

Eigen/src/Core/Redux.h

@@ -247,8 +247,9 @@ struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
   }
 };
 
-template<typename Func, typename Derived>
+// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
-struct redux_impl<Func, Derived, SliceVectorizedTraversal, NoUnrolling>
+template<typename Func, typename Derived, int Unrolling>
+struct redux_impl<Func, Derived, SliceVectorizedTraversal, Unrolling>
 {
   typedef typename Derived::Scalar Scalar;
   typedef typename packet_traits<Scalar>::type PacketScalar;

Eigen/src/Core/Ref.h

@@ -101,14 +101,15 @@ struct traits<Ref<_PlainObjectType, _Options, _StrideType> >
   template<typename Derived> struct match {
     enum {
       HasDirectAccess = internal::has_direct_access<Derived>::ret,
-      StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),
+      StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),
       InnerStrideMatch = int(StrideType::InnerStrideAtCompileTime)==int(Dynamic)
                       || int(StrideType::InnerStrideAtCompileTime)==int(Derived::InnerStrideAtCompileTime)
                       || (int(StrideType::InnerStrideAtCompileTime)==0 && int(Derived::InnerStrideAtCompileTime)==1),
       OuterStrideMatch = Derived::IsVectorAtCompileTime
                       || int(StrideType::OuterStrideAtCompileTime)==int(Dynamic) || int(StrideType::OuterStrideAtCompileTime)==int(Derived::OuterStrideAtCompileTime),
       AlignmentMatch = (_Options!=Aligned) || ((PlainObjectType::Flags&AlignedBit)==0) || ((traits<Derived>::Flags&AlignedBit)==AlignedBit),
-      MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch
+      ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,
+      MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch && ScalarTypeMatch
     };
     typedef typename internal::conditional<MatchAtCompileTime,internal::true_type,internal::false_type>::type type;
   };
@@ -172,8 +173,12 @@ protected:
     }
     else
       ::new (static_cast<Base*>(this)) Base(expr.data(), expr.rows(), expr.cols());
-    ::new (&m_stride) StrideBase(StrideType::OuterStrideAtCompileTime==0?0:expr.outerStride(),
+    
-                                 StrideType::InnerStrideAtCompileTime==0?0:expr.innerStride());    
+    if(Expression::IsVectorAtCompileTime && (!PlainObjectType::IsVectorAtCompileTime) && ((Expression::Flags&RowMajorBit)!=(PlainObjectType::Flags&RowMajorBit)))
+      ::new (&m_stride) StrideBase(expr.innerStride(), StrideType::InnerStrideAtCompileTime==0?0:1);
+    else
+      ::new (&m_stride) StrideBase(StrideType::OuterStrideAtCompileTime==0?0:expr.outerStride(),
+                                   StrideType::InnerStrideAtCompileTime==0?0:expr.innerStride());    
   }
 
   StrideBase m_stride;
@@ -183,7 +188,11 @@ protected:
 template<typename PlainObjectType, int Options, typename StrideType> class Ref
   : public RefBase<Ref<PlainObjectType, Options, StrideType> >
 {
+  private:
     typedef internal::traits<Ref> Traits;
+    template<typename Derived>
+    inline Ref(const PlainObjectBase<Derived>& expr,
+               typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0);
   public:
 
     typedef RefBase<Ref> Base;
@@ -195,17 +204,20 @@ template<typename PlainObjectType, int Options, typename StrideType> class Ref
     inline Ref(PlainObjectBase<Derived>& expr,
                typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
     {
-      Base::construct(expr);
+      EIGEN_STATIC_ASSERT(static_cast<bool>(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+      Base::construct(expr.derived());
     }
     template<typename Derived>
     inline Ref(const DenseBase<Derived>& expr,
-               typename internal::enable_if<bool(internal::is_lvalue<Derived>::value&&bool(Traits::template match<Derived>::MatchAtCompileTime)),Derived>::type* = 0,
+               typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
-               int = Derived::ThisConstantIsPrivateInPlainObjectBase)
     #else
     template<typename Derived>
     inline Ref(DenseBase<Derived>& expr)
     #endif
     {
+      EIGEN_STATIC_ASSERT(static_cast<bool>(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+      EIGEN_STATIC_ASSERT(static_cast<bool>(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+      enum { THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY = Derived::ThisConstantIsPrivateInPlainObjectBase};
       Base::construct(expr.const_cast_derived());
     }
 
@@ -224,13 +236,23 @@ template<typename TPlainObjectType, int Options, typename StrideType> class Ref<
     EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
 
     template<typename Derived>
-    inline Ref(const DenseBase<Derived>& expr)
+    inline Ref(const DenseBase<Derived>& expr,
+               typename internal::enable_if<bool(Traits::template match<Derived>::ScalarTypeMatch),Derived>::type* = 0)
     {
 //      std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch << "," << match_helper<Derived>::InnerStrideMatch << "\n";
 //      std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n";
 //      std::cout << int(StrideType::InnerStrideAtCompileTime) << " - " << int(Derived::InnerStrideAtCompileTime) << "\n";
       construct(expr.derived(), typename Traits::template match<Derived>::type());
     }
+    
+    inline Ref(const Ref& other) : Base(other) {
+      // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
+    }
+
+    template<typename OtherRef>
+    inline Ref(const RefBase<OtherRef>& other) {
+      construct(other.derived(), typename Traits::template match<OtherRef>::type());
+    }
 
   protected:
 

Eigen/src/Core/Replicate.h

@@ -135,7 +135,7 @@ template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
   */
 template<typename Derived>
 template<int RowFactor, int ColFactor>
-inline const Replicate<Derived,RowFactor,ColFactor>
+const Replicate<Derived,RowFactor,ColFactor>
 DenseBase<Derived>::replicate() const
 {
   return Replicate<Derived,RowFactor,ColFactor>(derived());
@@ -150,7 +150,7 @@ DenseBase<Derived>::replicate() const
   * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
   */
 template<typename Derived>
-inline const Replicate<Derived,Dynamic,Dynamic>
+const typename DenseBase<Derived>::ReplicateReturnType
 DenseBase<Derived>::replicate(Index rowFactor,Index colFactor) const
 {
   return Replicate<Derived,Dynamic,Dynamic>(derived(),rowFactor,colFactor);

Eigen/src/Core/ReturnByValue.h

@@ -72,6 +72,8 @@ template<typename Derived> class ReturnByValue
     const Unusable& coeff(Index,Index) const { return *reinterpret_cast<const Unusable*>(this); }
     Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }
     Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }
+    template<int LoadMode>  Unusable& packet(Index) const;
+    template<int LoadMode>  Unusable& packet(Index, Index) const;
 #endif
 };
 
@@ -83,6 +85,15 @@ Derived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
   return derived();
 }
 
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::lazyAssign(const ReturnByValue<OtherDerived>& other)
+{
+  other.evalTo(derived());
+  return derived();
+}
+
+
 } // end namespace Eigen
 
 #endif // EIGEN_RETURNBYVALUE_H

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -180,15 +180,9 @@ inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
 template<typename Derived>
 inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
 {
-  typedef typename internal::conditional<NumTraits<Scalar>::IsInteger,
-                                        internal::scalar_quotient_op<Scalar>,
-                                        internal::scalar_product_op<Scalar> >::type BinOp;
   typedef typename Derived::PlainObject PlainObject;
-  SelfCwiseBinaryOp<BinOp, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+  SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
-  Scalar actual_other;
+  tmp = PlainObject::Constant(rows(),cols(), other);
-  if(NumTraits<Scalar>::IsInteger)  actual_other = other;
-  else                              actual_other = Scalar(1)/other;
-  tmp = PlainObject::Constant(rows(),cols(), actual_other);
   return derived();
 }
 

Eigen/src/Core/TriangularMatrix.h

@@ -278,21 +278,21 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
 
     /** Efficient triangular matrix times vector/matrix product */
     template<typename OtherDerived>
-    TriangularProduct<Mode,true,MatrixType,false,OtherDerived, OtherDerived::IsVectorAtCompileTime>
+    TriangularProduct<Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1>
     operator*(const MatrixBase<OtherDerived>& rhs) const
     {
       return TriangularProduct
-              <Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
+              <Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1>
               (m_matrix, rhs.derived());
     }
 
     /** Efficient vector/matrix times triangular matrix product */
     template<typename OtherDerived> friend
-    TriangularProduct<Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+    TriangularProduct<Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false>
     operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs)
     {
       return TriangularProduct
-              <Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+              <Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false>
               (lhs.derived(),rhs.m_matrix);
     }
 
@@ -380,19 +380,19 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
     EIGEN_STRONG_INLINE TriangularView& operator=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
     {
       setZero();
-      return assignProduct(other,1);
+      return assignProduct(other.derived(),1);
     }
     
     template<typename ProductDerived, typename Lhs, typename Rhs>
     EIGEN_STRONG_INLINE TriangularView& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
     {
-      return assignProduct(other,1);
+      return assignProduct(other.derived(),1);
     }
     
     template<typename ProductDerived, typename Lhs, typename Rhs>
     EIGEN_STRONG_INLINE TriangularView& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
     {
-      return assignProduct(other,-1);
+      return assignProduct(other.derived(),-1);
     }
     
     
@@ -400,25 +400,34 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
     EIGEN_STRONG_INLINE TriangularView& operator=(const ScaledProduct<ProductDerived>& other)
     {
       setZero();
-      return assignProduct(other,other.alpha());
+      return assignProduct(other.derived(),other.alpha());
     }
     
     template<typename ProductDerived>
     EIGEN_STRONG_INLINE TriangularView& operator+=(const ScaledProduct<ProductDerived>& other)
     {
-      return assignProduct(other,other.alpha());
+      return assignProduct(other.derived(),other.alpha());
     }
     
     template<typename ProductDerived>
     EIGEN_STRONG_INLINE TriangularView& operator-=(const ScaledProduct<ProductDerived>& other)
     {
-      return assignProduct(other,-other.alpha());
+      return assignProduct(other.derived(),-other.alpha());
     }
     
   protected:
     
     template<typename ProductDerived, typename Lhs, typename Rhs>
     EIGEN_STRONG_INLINE TriangularView& assignProduct(const ProductBase<ProductDerived, Lhs,Rhs>& prod, const Scalar& alpha);
+    
+    template<int Mode, bool LhsIsTriangular,
+         typename Lhs, bool LhsIsVector,
+         typename Rhs, bool RhsIsVector>
+    EIGEN_STRONG_INLINE TriangularView& assignProduct(const TriangularProduct<Mode, LhsIsTriangular, Lhs, LhsIsVector, Rhs, RhsIsVector>& prod, const Scalar& alpha)
+    {
+      lazyAssign(alpha*prod.eval());
+      return *this;
+    }
 
     MatrixTypeNested m_matrix;
 };

Eigen/src/Core/arch/NEON/Complex.h

@@ -110,7 +110,7 @@ template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<
 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
 
-template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { __pld((float *)addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { EIGEN_ARM_PREFETCH((float *)addr); }
 
 template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
 {

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

@@ -48,9 +48,18 @@ typedef uint32x4_t  Packet4ui;
   #define EIGEN_INIT_NEON_PACKET2(X, Y)       {X, Y}
   #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
 #endif
-    
+
-#ifndef __pld
+// arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
-#define __pld(x) asm volatile ( "   pld [%[addr]]\n" :: [addr] "r" (x) : "cc" );
+// which available on LLVM and GCC (at least)
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__)
+  #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#elif defined __pld
+  #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
+#elif !defined(__aarch64__)
+  #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( "   pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#else
+  // by default no explicit prefetching
+  #define EIGEN_ARM_PREFETCH(ADDR)
 #endif
 
 template<> struct packet_traits<float>  : default_packet_traits
@@ -209,8 +218,8 @@ template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& f
 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }
 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }
 
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { __pld(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { __pld(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { EIGEN_ARM_PREFETCH(addr); }
 
 // FIXME only store the 2 first elements ?
 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }
@@ -375,6 +384,7 @@ template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
   a_lo = vget_low_s32(a);
   a_hi = vget_high_s32(a);
   max = vpmax_s32(a_lo, a_hi);
+  max = vpmax_s32(max, max);
 
   return vget_lane_s32(max, 0);
 }

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

@@ -52,7 +52,7 @@ Packet4f plog<Packet4f>(const Packet4f& _x)
 
   Packet4i emm0;
 
-  Packet4f invalid_mask = _mm_cmplt_ps(x, _mm_setzero_ps());
+  Packet4f invalid_mask = _mm_cmpnge_ps(x, _mm_setzero_ps()); // not greater equal is true if x is NaN
   Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
 
   x = pmax(x, p4f_min_norm_pos);  /* cut off denormalized stuff */
@@ -126,7 +126,7 @@ Packet4f pexp<Packet4f>(const Packet4f& _x)
   _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
   _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
 
-  Packet4f tmp = _mm_setzero_ps(), fx;
+  Packet4f tmp, fx;
   Packet4i emm0;
 
   // clamp x
@@ -166,7 +166,7 @@ Packet4f pexp<Packet4f>(const Packet4f& _x)
   emm0 = _mm_cvttps_epi32(fx);
   emm0 = _mm_add_epi32(emm0, p4i_0x7f);
   emm0 = _mm_slli_epi32(emm0, 23);
-  return pmul(y, _mm_castsi128_ps(emm0));
+  return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x);
 }
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet2d pexp<Packet2d>(const Packet2d& _x)
@@ -195,7 +195,7 @@ Packet2d pexp<Packet2d>(const Packet2d& _x)
   _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
   static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
 
-  Packet2d tmp = _mm_setzero_pd(), fx;
+  Packet2d tmp, fx;
   Packet4i emm0;
 
   // clamp x
@@ -239,7 +239,7 @@ Packet2d pexp<Packet2d>(const Packet2d& _x)
   emm0 = _mm_add_epi32(emm0, p4i_1023_0);
   emm0 = _mm_slli_epi32(emm0, 20);
   emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
-  return pmul(x, _mm_castsi128_pd(emm0));
+  return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);
 }
 
 /* evaluation of 4 sines at onces, using SSE2 intrinsics.
@@ -279,7 +279,7 @@ Packet4f psin<Packet4f>(const Packet4f& _x)
   _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);
   _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
 
-  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
+  Packet4f xmm1, xmm2, xmm3, sign_bit, y;
 
   Packet4i emm0, emm2;
   sign_bit = x;
@@ -378,7 +378,7 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
   _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);
   _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
 
-  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
+  Packet4f xmm1, xmm2, xmm3, y;
   Packet4i emm0, emm2;
 
   x = pabs(x);

Eigen/src/Core/products/CoeffBasedProduct.h

@@ -90,6 +90,7 @@ struct traits<CoeffBasedProduct<LhsNested,RhsNested,NestingFlags> >
             | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0),
 
       CoeffReadCost = InnerSize == Dynamic ? Dynamic
+                    : InnerSize == 0 ? 0
                     : InnerSize * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
                       + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
 
@@ -133,7 +134,7 @@ class CoeffBasedProduct
     };
 
     typedef internal::product_coeff_impl<CanVectorizeInner ? InnerVectorizedTraversal : DefaultTraversal,
-                                   Unroll ? InnerSize-1 : Dynamic,
+                                   Unroll ? InnerSize : Dynamic,
                                    _LhsNested, _RhsNested, Scalar> ScalarCoeffImpl;
 
     typedef CoeffBasedProduct<LhsNested,RhsNested,NestByRefBit> LazyCoeffBasedProductType;
@@ -184,7 +185,7 @@ class CoeffBasedProduct
     {
       PacketScalar res;
       internal::product_packet_impl<Flags&RowMajorBit ? RowMajor : ColMajor,
-                              Unroll ? InnerSize-1 : Dynamic,
+                              Unroll ? InnerSize : Dynamic,
                               _LhsNested, _RhsNested, PacketScalar, LoadMode>
         ::run(row, col, m_lhs, m_rhs, res);
       return res;
@@ -242,12 +243,12 @@ struct product_coeff_impl<DefaultTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
   {
     product_coeff_impl<DefaultTraversal, UnrollingIndex-1, Lhs, Rhs, RetScalar>::run(row, col, lhs, rhs, res);
-    res += lhs.coeff(row, UnrollingIndex) * rhs.coeff(UnrollingIndex, col);
+    res += lhs.coeff(row, UnrollingIndex-1) * rhs.coeff(UnrollingIndex-1, col);
   }
 };
 
 template<typename Lhs, typename Rhs, typename RetScalar>
-struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
+struct product_coeff_impl<DefaultTraversal, 1, Lhs, Rhs, RetScalar>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
@@ -256,16 +257,23 @@ struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
   }
 };
 
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+  {
+    res = RetScalar(0);
+  }
+};
+
 template<typename Lhs, typename Rhs, typename RetScalar>
 struct product_coeff_impl<DefaultTraversal, Dynamic, Lhs, Rhs, RetScalar>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = (lhs.row(row).transpose().cwiseProduct( rhs.col(col) )).sum();
-    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
-      for(Index i = 1; i < lhs.cols(); ++i)
-        res += lhs.coeff(row, i) * rhs.coeff(i, col);
   }
 };
 
@@ -295,6 +303,16 @@ struct product_coeff_vectorized_unroller<0, Lhs, Rhs, Packet>
   }
 };
 
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<InnerVectorizedTraversal, 0, Lhs, Rhs, RetScalar>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+  {
+    res = 0;
+  }
+};
+
 template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
 struct product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
 {
@@ -304,8 +322,7 @@ struct product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, Re
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
   {
     Packet pres;
-    product_coeff_vectorized_unroller<UnrollingIndex+1-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
+    product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
-    product_coeff_impl<DefaultTraversal,UnrollingIndex,Lhs,Rhs,RetScalar>::run(row, col, lhs, rhs, res);
     res = predux(pres);
   }
 };
@@ -373,7 +390,7 @@ struct product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
   {
     product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
-    res =  pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex)), rhs.template packet<LoadMode>(UnrollingIndex, col), res);
+    res =  pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex-1)), rhs.template packet<LoadMode>(UnrollingIndex-1, col), res);
   }
 };
 
@@ -384,12 +401,12 @@ struct product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
   {
     product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
-    res =  pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex), pset1<Packet>(rhs.coeff(UnrollingIndex, col)), res);
+    res =  pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex-1), pset1<Packet>(rhs.coeff(UnrollingIndex-1, col)), res);
   }
 };
 
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+struct product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
@@ -399,7 +416,7 @@ struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
 };
 
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+struct product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
@@ -408,16 +425,35 @@ struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
   }
 };
 
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+  {
+    res = pset1<Packet>(0);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+  {
+    res = pset1<Packet>(0);
+  }
+};
+
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = pset1<Packet>(0);
-    res = pmul(pset1<Packet>(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
+    for(Index i = 0; i < lhs.cols(); ++i)
-      for(Index i = 1; i < lhs.cols(); ++i)
+      res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
-        res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
   }
 };
 
@@ -427,10 +463,9 @@ struct product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = pset1<Packet>(0);
-    res = pmul(lhs.template packet<LoadMode>(row, 0), pset1<Packet>(rhs.coeff(0, col)));
+    for(Index i = 0; i < lhs.cols(); ++i)
-      for(Index i = 1; i < lhs.cols(); ++i)
+      res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
-        res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
   }
 };
 

Eigen/src/Core/products/Parallelizer.h

@@ -125,19 +125,22 @@ void parallelize_gemm(const Functor& func, Index rows, Index cols, bool transpos
   if(transpose)
     std::swap(rows,cols);
 
-  Index blockCols = (cols / threads) & ~Index(0x3);
-  Index blockRows = (rows / threads) & ~Index(0x7);
-  
   GemmParallelInfo<Index>* info = new GemmParallelInfo<Index>[threads];
 
-  #pragma omp parallel for schedule(static,1) num_threads(threads)
+  #pragma omp parallel num_threads(threads)
-  for(Index i=0; i<threads; ++i)
   {
+    Index i = omp_get_thread_num();
+    // Note that the actual number of threads might be lower than the number of request ones.
+    Index actual_threads = omp_get_num_threads();
+    
+    Index blockCols = (cols / actual_threads) & ~Index(0x3);
+    Index blockRows = (rows / actual_threads) & ~Index(0x7);
+    
     Index r0 = i*blockRows;
-    Index actualBlockRows = (i+1==threads) ? rows-r0 : blockRows;
+    Index actualBlockRows = (i+1==actual_threads) ? rows-r0 : blockRows;
 
     Index c0 = i*blockCols;
-    Index actualBlockCols = (i+1==threads) ? cols-c0 : blockCols;
+    Index actualBlockCols = (i+1==actual_threads) ? cols-c0 : blockCols;
 
     info[i].rhs_start = c0;
     info[i].rhs_length = actualBlockCols;

Eigen/src/Core/products/TriangularMatrixMatrix_MKL.h

@@ -109,7 +109,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    if (rows != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
 \
      if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
@@ -223,7 +223,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    if (cols != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
 \
      if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \

Eigen/src/Core/products/TriangularSolverMatrix.h

@@ -302,9 +302,12 @@ EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conj
                 for (Index i=0; i<actual_mc; ++i)
                   r[i] -= a[i] * b;
               }
-              Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j));
+              if((Mode & UnitDiag)==0)
-              for (Index i=0; i<actual_mc; ++i)
+              {
-                r[i] *= b;
+                Scalar b = conj(rhs(j,j));
+                for (Index i=0; i<actual_mc; ++i)
+                  r[i] /= b;
+              }
             }
 
             // pack the just computed part of lhs to A

Eigen/src/Core/util/Constants.h

@@ -433,6 +433,19 @@ struct MatrixXpr {};
 /** The type used to identify an array expression */
 struct ArrayXpr {};
 
+namespace internal {
+  /** \internal
+  * Constants for comparison functors
+  */
+  enum ComparisonName {
+    cmp_EQ = 0,
+    cmp_LT = 1,
+    cmp_LE = 2,
+    cmp_UNORD = 3,
+    cmp_NEQ = 4
+  };
+}
+
 } // end namespace Eigen
 
 #endif // EIGEN_CONSTANTS_H

Eigen/src/Core/util/ForwardDeclarations.h

@@ -235,6 +235,9 @@ 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;

Eigen/src/Core/util/MKL_support.h

@@ -54,11 +54,60 @@
 #endif
 
 #if defined EIGEN_USE_MKL
+#   include <mkl.h> 
+/*Check IMKL version for compatibility: < 10.3 is not usable with Eigen*/
+#   ifndef INTEL_MKL_VERSION
+#       undef EIGEN_USE_MKL /* INTEL_MKL_VERSION is not even defined on older versions */
+#   elif INTEL_MKL_VERSION < 100305    /* the intel-mkl-103-release-notes say this was when the lapacke.h interface was added*/
+#       undef EIGEN_USE_MKL
+#   endif
+#   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
+#       undef   EIGEN_USE_LAPACKE
+#   endif
+#endif
 
-#include <mkl.h>
+#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 */
+/* MKL_BLAS, etc are not defined in 11.2 */
+#ifdef MKL_DOMAIN_ALL
+#define EIGEN_MKL_DOMAIN_ALL MKL_DOMAIN_ALL
+#else
+#define EIGEN_MKL_DOMAIN_ALL MKL_ALL
+#endif
+
+#ifdef MKL_DOMAIN_BLAS
+#define EIGEN_MKL_DOMAIN_BLAS MKL_DOMAIN_BLAS
+#else
+#define EIGEN_MKL_DOMAIN_BLAS MKL_BLAS
+#endif
+
+#ifdef MKL_DOMAIN_FFT
+#define EIGEN_MKL_DOMAIN_FFT MKL_DOMAIN_FFT
+#else
+#define EIGEN_MKL_DOMAIN_FFT MKL_FFT
+#endif
+
+#ifdef MKL_DOMAIN_VML
+#define EIGEN_MKL_DOMAIN_VML MKL_DOMAIN_VML
+#else
+#define EIGEN_MKL_DOMAIN_VML MKL_VML
+#endif
+
+#ifdef MKL_DOMAIN_PARDISO
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_DOMAIN_PARDISO
+#else
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO
+#endif
+
 namespace Eigen {
 
 typedef std::complex<double> dcomplex;

Eigen/src/Core/util/Macros.h

@@ -13,7 +13,7 @@
 
 #define EIGEN_WORLD_VERSION 3
 #define EIGEN_MAJOR_VERSION 2
-#define EIGEN_MINOR_VERSION 1
+#define EIGEN_MINOR_VERSION 7
 
 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
                                       (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
@@ -96,6 +96,27 @@
 #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
 #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
+
+// Do we support r-value references?
+#if (__has_feature(cxx_rvalue_references) || \
+     defined(__GXX_EXPERIMENTAL_CXX0X__) || \
+     (defined(_MSC_VER) && _MSC_VER >= 1600))
+  #define EIGEN_HAVE_RVALUE_REFERENCES
+#endif
+
+
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+#else
+#  define EIGEN_HAS_BUILTIN(x) 0
+#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:
@@ -247,7 +268,7 @@ namespace Eigen {
 
 #if !defined(EIGEN_ASM_COMMENT)
   #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
-    #define EIGEN_ASM_COMMENT(X)  asm("#" X)
+    #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
   #else
     #define EIGEN_ASM_COMMENT(X)
   #endif
@@ -271,6 +292,7 @@ namespace Eigen {
   #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
 #endif
 
+#define EIGEN_ALIGN8  EIGEN_ALIGN_TO_BOUNDARY(8)
 #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
 
 #if EIGEN_ALIGN_STATICALLY
@@ -289,7 +311,8 @@ namespace Eigen {
 #endif
 
 #ifndef EIGEN_STACK_ALLOCATION_LIMIT
-#define EIGEN_STACK_ALLOCATION_LIMIT 20000
+// 131072 == 128 KB
+#define EIGEN_STACK_ALLOCATION_LIMIT 131072
 #endif
 
 #ifndef EIGEN_DEFAULT_IO_FORMAT
@@ -305,7 +328,7 @@ namespace Eigen {
 // just an empty macro !
 #define EIGEN_EMPTY
 
-#if defined(_MSC_VER) && (!defined(__INTEL_COMPILER))
+#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)
@@ -324,8 +347,11 @@ namespace Eigen {
   }
 #endif
 
-#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+/** \internal
-  EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
 
 /**
 * Just a side note. Commenting within defines works only by documenting
@@ -397,6 +423,8 @@ 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))

Eigen/src/Core/util/Memory.h

@@ -63,7 +63,7 @@
 // Currently, let's include it only on unix systems:
 #if defined(__unix__) || defined(__unix)
   #include <unistd.h>
-  #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+  #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
@@ -272,12 +272,12 @@ inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
   // 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(_mm_free)
+  #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)
+#elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
   result = _aligned_realloc(ptr,new_size,16);
 #else
   result = handmade_aligned_realloc(ptr,new_size,old_size);
@@ -417,6 +417,8 @@ template<typename T, bool Align> inline T* conditional_aligned_realloc_new(T* pt
 
 template<typename T, bool Align> inline T* conditional_aligned_new_auto(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)
@@ -464,9 +466,8 @@ template<typename T, bool Align> inline void conditional_aligned_delete_auto(T *
 template<typename Scalar, typename Index>
 static inline Index first_aligned(const Scalar* array, Index size)
 {
-  enum { PacketSize = packet_traits<Scalar>::size,
+  static const Index PacketSize = packet_traits<Scalar>::size;
-         PacketAlignedMask = PacketSize-1
+  static const Index PacketAlignedMask = PacketSize-1;
-  };
 
   if(PacketSize==1)
   {
@@ -522,7 +523,7 @@ 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__)
+  #if (defined __linux__) || (defined __APPLE__) || (defined alloca)
     #define EIGEN_ALLOCA alloca
   #elif defined(_MSC_VER)
     #define EIGEN_ALLOCA _alloca
@@ -612,7 +613,6 @@ template<typename T> class aligned_stack_memory_handler
       void* operator new(size_t size, const std::nothrow_t&) throw() { \
         try { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
         catch (...) { return 0; } \
-        return 0; \
       }
   #else
     #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
@@ -777,9 +777,9 @@ namespace internal {
 
 #ifdef EIGEN_CPUID
 
-inline bool cpuid_is_vendor(int abcd[4], const char* vendor)
+inline bool cpuid_is_vendor(int abcd[4], const int vendor[3])
 {
-  return abcd[1]==(reinterpret_cast<const int*>(vendor))[0] && abcd[3]==(reinterpret_cast<const int*>(vendor))[1] && abcd[2]==(reinterpret_cast<const int*>(vendor))[2];
+  return abcd[1]==vendor[0] && abcd[3]==vendor[1] && abcd[2]==vendor[2];
 }
 
 inline void queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)
@@ -921,13 +921,16 @@ inline void queryCacheSizes(int& l1, int& l2, int& l3)
 {
   #ifdef EIGEN_CPUID
   int abcd[4];
+  const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};
+  const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};
+  const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574}; // "AMDisbetter!"
 
   // identify the CPU vendor
   EIGEN_CPUID(abcd,0x0,0);
   int max_std_funcs = abcd[1];
-  if(cpuid_is_vendor(abcd,"GenuineIntel"))
+  if(cpuid_is_vendor(abcd,GenuineIntel))
     queryCacheSizes_intel(l1,l2,l3,max_std_funcs);
-  else if(cpuid_is_vendor(abcd,"AuthenticAMD") || cpuid_is_vendor(abcd,"AMDisbetter!"))
+  else if(cpuid_is_vendor(abcd,AuthenticAMD) || cpuid_is_vendor(abcd,AMDisbetter_))
     queryCacheSizes_amd(l1,l2,l3);
   else
     // by default let's use Intel's API

Eigen/src/Core/util/StaticAssert.h

@@ -90,7 +90,9 @@
         YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED,
         THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE,
         THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH,
-        OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG
+        OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG,
+        IMPLICIT_CONVERSION_TO_SCALAR_IS_FOR_INNER_PRODUCT_ONLY,
+        STORAGE_LAYOUT_DOES_NOT_MATCH
       };
     };
 

Eigen/src/Core/util/XprHelper.h

@@ -341,7 +341,7 @@ template<typename T, int n=1, typename PlainObject = typename eval<T>::type> str
 };
 
 template<typename T>
-T* const_cast_ptr(const T* ptr)
+inline T* const_cast_ptr(const T* ptr)
 {
   return const_cast<T*>(ptr);
 }
@@ -366,17 +366,17 @@ struct dense_xpr_base<Derived, ArrayXpr>
 
 /** \internal Helper base class to add a scalar multiple operator
   * overloads for complex types */
-template<typename Derived,typename Scalar,typename OtherScalar,
+template<typename Derived, typename Scalar, typename OtherScalar, typename BaseType,
          bool EnableIt = !is_same<Scalar,OtherScalar>::value >
-struct special_scalar_op_base : public DenseCoeffsBase<Derived>
+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 Scalar,typename OtherScalar>
+template<typename Derived,typename Scalar,typename OtherScalar, typename BaseType>
-struct special_scalar_op_base<Derived,Scalar,OtherScalar,true>  : public DenseCoeffsBase<Derived>
+struct special_scalar_op_base<Derived,Scalar,OtherScalar,BaseType,true>  : public BaseType
 {
   const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
   operator*(const OtherScalar& scalar) const

Eigen/src/Eigen2Support/LeastSquares.h

@@ -147,7 +147,6 @@ void fitHyperplane(int numPoints,
 
   // compute the covariance matrix
   CovMatrixType covMat = CovMatrixType::Zero(size, size);
-  VectorType remean = VectorType::Zero(size);
   for(int i = 0; i < numPoints; ++i)
   {
     VectorType diff = (*(points[i]) - mean).conjugate();

Eigen/src/Eigenvalues/ComplexEigenSolver.h

@@ -234,6 +234,12 @@ template<typename _MatrixType> class ComplexEigenSolver
     }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     EigenvectorType m_eivec;
     EigenvalueType m_eivalues;
     ComplexSchur<MatrixType> m_schur;
@@ -251,6 +257,8 @@ template<typename MatrixType>
 ComplexEigenSolver<MatrixType>& 
 ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
 {
+  check_template_parameters();
+  
   // this code is inspired from Jampack
   eigen_assert(matrix.cols() == matrix.rows());
 

Eigen/src/Eigenvalues/EigenSolver.h

@@ -298,6 +298,13 @@ template<typename _MatrixType> class EigenSolver
     void doComputeEigenvectors();
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+    }
+    
     MatrixType m_eivec;
     EigenvalueType m_eivalues;
     bool m_isInitialized;
@@ -364,6 +371,8 @@ template<typename MatrixType>
 EigenSolver<MatrixType>& 
 EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
 {
+  check_template_parameters();
+  
   using std::sqrt;
   using std::abs;
   eigen_assert(matrix.cols() == matrix.rows());

Eigen/src/Eigenvalues/GeneralizedEigenSolver.h

@@ -263,6 +263,13 @@ template<typename _MatrixType> class GeneralizedEigenSolver
     }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+    }
+    
     MatrixType m_eivec;
     ComplexVectorType m_alphas;
     VectorType m_betas;
@@ -290,6 +297,8 @@ template<typename MatrixType>
 GeneralizedEigenSolver<MatrixType>&
 GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)
 {
+  check_template_parameters();
+  
   using std::sqrt;
   using std::abs;
   eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());

Eigen/src/Eigenvalues/RealQZ.h

@@ -240,10 +240,10 @@ namespace Eigen {
             m_S.coeffRef(i,j) = Scalar(0.0);
             m_S.rightCols(dim-j-1).applyOnTheLeft(i-1,i,G.adjoint());
             m_T.rightCols(dim-i+1).applyOnTheLeft(i-1,i,G.adjoint());
+            // update Q
+            if (m_computeQZ)
+              m_Q.applyOnTheRight(i-1,i,G);
           }
-          // update Q
-          if (m_computeQZ)
-            m_Q.applyOnTheRight(i-1,i,G);
           // kill T(i,i-1)
           if(m_T.coeff(i,i-1)!=Scalar(0))
           {
@@ -251,10 +251,10 @@ namespace Eigen {
             m_T.coeffRef(i,i-1) = Scalar(0.0);
             m_S.applyOnTheRight(i,i-1,G);
             m_T.topRows(i).applyOnTheRight(i,i-1,G);
+            // update Z
+            if (m_computeQZ)
+              m_Z.applyOnTheLeft(i,i-1,G.adjoint());
           }
-          // update Z
-          if (m_computeQZ)
-            m_Z.applyOnTheLeft(i,i-1,G.adjoint());
         }
       }
     }
@@ -313,7 +313,7 @@ namespace Eigen {
       using std::abs;
       using std::sqrt;
       const Index dim=m_S.cols();
-      if (abs(m_S.coeff(i+1,i)==Scalar(0)))
+      if (abs(m_S.coeff(i+1,i))==Scalar(0))
         return;
       Index z = findSmallDiagEntry(i,i+1);
       if (z==i-1)

Eigen/src/Eigenvalues/RealSchur.h

@@ -234,7 +234,7 @@ template<typename _MatrixType> class RealSchur
     typedef Matrix<Scalar,3,1> Vector3s;
 
     Scalar computeNormOfT();
-    Index findSmallSubdiagEntry(Index iu, const Scalar& norm);
+    Index findSmallSubdiagEntry(Index iu);
     void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift);
     void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);
     void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);
@@ -286,7 +286,7 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
   {
     while (iu >= 0)
     {
-      Index il = findSmallSubdiagEntry(iu, norm);
+      Index il = findSmallSubdiagEntry(iu);
 
       // Check for convergence
       if (il == iu) // One root found
@@ -343,16 +343,14 @@ inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()
 
 /** \internal Look for single small sub-diagonal element and returns its index */
 template<typename MatrixType>
-inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, const Scalar& norm)
+inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu)
 {
   using std::abs;
   Index res = iu;
   while (res > 0)
   {
     Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));
-    if (s == 0.0)
+    if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s)
-      s = norm;
-    if (abs(m_matT.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
       break;
     res--;
   }
@@ -457,9 +455,7 @@ inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const V
     const Scalar lhs = m_matT.coeff(im,im-1) * (abs(v.coeff(1)) + abs(v.coeff(2)));
     const Scalar rhs = v.coeff(0) * (abs(m_matT.coeff(im-1,im-1)) + abs(Tmm) + abs(m_matT.coeff(im+1,im+1)));
     if (abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)
-    {
       break;
-    }
   }
 }
 

Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h

@@ -80,6 +80,8 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     /** \brief Scalar type for matrices of type \p _MatrixType. */
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::Index Index;
+    
+    typedef Matrix<Scalar,Size,Size,ColMajor,MaxColsAtCompileTime,MaxColsAtCompileTime> EigenvectorsType;
 
     /** \brief Real scalar type for \p _MatrixType.
       *
@@ -225,7 +227,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
       *
       * \sa eigenvalues()
       */
-    const MatrixType& eigenvectors() const
+    const EigenvectorsType& eigenvectors() const
     {
       eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
       eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
@@ -351,7 +353,12 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     #endif // EIGEN2_SUPPORT
 
   protected:
-    MatrixType m_eivec;
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
+    EigenvectorsType m_eivec;
     RealVectorType m_eivalues;
     typename TridiagonalizationType::SubDiagonalType m_subdiag;
     ComputationInfo m_info;
@@ -376,7 +383,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
   * "implicit symmetric QR step with Wilkinson shift"
   */
 namespace internal {
-template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+template<typename RealScalar, typename Scalar, typename Index>
 static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n);
 }
 
@@ -384,6 +391,8 @@ template<typename MatrixType>
 SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
 ::compute(const MatrixType& matrix, int options)
 {
+  check_template_parameters();
+  
   using std::abs;
   eigen_assert(matrix.cols() == matrix.rows());
   eigen_assert((options&~(EigVecMask|GenEigMask))==0
@@ -406,7 +415,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
 
   // declare some aliases
   RealVectorType& diag = m_eivalues;
-  MatrixType& mat = m_eivec;
+  EigenvectorsType& mat = m_eivec;
 
   // map the matrix coefficients to [-1:1] to avoid over- and underflow.
   mat = matrix.template triangularView<Lower>();
@@ -442,7 +451,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
     while (start>0 && m_subdiag[start-1]!=0)
       start--;
 
-    internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
+    internal::tridiagonal_qr_step(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
   }
 
   if (iter <= m_maxIterations * n)
@@ -490,7 +499,13 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
   typedef typename SolverType::MatrixType MatrixType;
   typedef typename SolverType::RealVectorType VectorType;
   typedef typename SolverType::Scalar Scalar;
+  typedef typename MatrixType::Index Index;
+  typedef typename SolverType::EigenvectorsType EigenvectorsType;
   
+  /** \internal
+   * Computes the roots of the characteristic polynomial of \a m.
+   * For numerical stability m.trace() should be near zero and to avoid over- or underflow m should be normalized.
+   */
   static inline void computeRoots(const MatrixType& m, VectorType& roots)
   {
     using std::sqrt;
@@ -510,148 +525,123 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
     // Construct the parameters used in classifying the roots of the equation
     // and in solving the equation for the roots in closed form.
     Scalar c2_over_3 = c2*s_inv3;
-    Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3;
+    Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;
-    if (a_over_3 > Scalar(0))
+    if(a_over_3<Scalar(0))
       a_over_3 = Scalar(0);
 
     Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
 
-    Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3;
+    Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
-    if (q > Scalar(0))
+    if(q<Scalar(0))
       q = Scalar(0);
 
     // Compute the eigenvalues by solving for the roots of the polynomial.
-    Scalar rho = sqrt(-a_over_3);
+    Scalar rho = sqrt(a_over_3);
-    Scalar theta = atan2(sqrt(-q),half_b)*s_inv3;
+    Scalar theta = atan2(sqrt(q),half_b)*s_inv3;  // since sqrt(q) > 0, atan2 is in [0, pi] and theta is in [0, pi/3]
     Scalar cos_theta = cos(theta);
     Scalar sin_theta = sin(theta);
-    roots(0) = c2_over_3 + Scalar(2)*rho*cos_theta;
+    // roots are already sorted, since cos is monotonically decreasing on [0, pi]
-    roots(1) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
+    roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)
-    roots(2) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);
+    roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); // == 2*rho*cos(theta+ pi/3)
-
+    roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;
-    // Sort in increasing order.
-    if (roots(0) >= roots(1))
-      std::swap(roots(0),roots(1));
-    if (roots(1) >= roots(2))
-    {
-      std::swap(roots(1),roots(2));
-      if (roots(0) >= roots(1))
-        std::swap(roots(0),roots(1));
-    }
   }
-  
+
+  static inline bool extract_kernel(MatrixType& mat, Ref<VectorType> res, Ref<VectorType> representative)
+  {
+    using std::abs;
+    Index i0;
+    // Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):
+    mat.diagonal().cwiseAbs().maxCoeff(&i0);
+    // mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,
+    // so let's save it:
+    representative = mat.col(i0);
+    Scalar n0, n1;
+    VectorType c0, c1;
+    n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();
+    n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();
+    if(n0>n1) res = c0/std::sqrt(n0);
+    else      res = c1/std::sqrt(n1);
+
+    return true;
+  }
+
   static inline void run(SolverType& solver, const MatrixType& mat, int options)
   {
-    using std::sqrt;
     eigen_assert(mat.cols() == 3 && mat.cols() == mat.rows());
     eigen_assert((options&~(EigVecMask|GenEigMask))==0
             && (options&EigVecMask)!=EigVecMask
             && "invalid option parameter");
     bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
     
-    MatrixType& eivecs = solver.m_eivec;
+    EigenvectorsType& eivecs = solver.m_eivec;
     VectorType& eivals = solver.m_eivalues;
   
-    // map the matrix coefficients to [-1:1] to avoid over- and underflow.
+    // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
-    Scalar scale = mat.cwiseAbs().maxCoeff();
+    Scalar shift = mat.trace() / Scalar(3);
-    MatrixType scaledMat = mat / scale;
+    // TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later
+    MatrixType scaledMat = mat.template selfadjointView<Lower>();
+    scaledMat.diagonal().array() -= shift;
+    Scalar scale = scaledMat.cwiseAbs().maxCoeff();
+    if(scale > 0) scaledMat /= scale;   // TODO for scale==0 we could save the remaining operations
 
     // compute the eigenvalues
     computeRoots(scaledMat,eivals);
 
-    // compute the eigen vectors
+    // compute the eigenvectors
     if(computeEigenvectors)
     {
-      Scalar safeNorm2 = Eigen::NumTraits<Scalar>::epsilon();
-      safeNorm2 *= safeNorm2;
       if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
       {
+        // All three eigenvalues are numerically the same
         eivecs.setIdentity();
       }
       else
       {
-        scaledMat = scaledMat.template selfadjointView<Lower>();
         MatrixType tmp;
         tmp = scaledMat;
 
+        // Compute the eigenvector of the most distinct eigenvalue
         Scalar d0 = eivals(2) - eivals(1);
         Scalar d1 = eivals(1) - eivals(0);
-        int k =  d0 > d1 ? 2 : 0;
+        Index k(0), l(2);
-        d0 = d0 > d1 ? d1 : d0;
+        if(d0 > d1)
-
-        tmp.diagonal().array () -= eivals(k);
-        VectorType cross;
-        Scalar n;
-        n = (cross = tmp.row(0).cross(tmp.row(1))).squaredNorm();
-
-        if(n>safeNorm2)
-          eivecs.col(k) = cross / sqrt(n);
-        else
         {
-          n = (cross = tmp.row(0).cross(tmp.row(2))).squaredNorm();
+          std::swap(k,l);
-
+          d0 = d1;
-          if(n>safeNorm2)
-            eivecs.col(k) = cross / sqrt(n);
-          else
-          {
-            n = (cross = tmp.row(1).cross(tmp.row(2))).squaredNorm();
-
-            if(n>safeNorm2)
-              eivecs.col(k) = cross / sqrt(n);
-            else
-            {
-              // the input matrix and/or the eigenvaues probably contains some inf/NaN,
-              // => exit
-              // scale back to the original size.
-              eivals *= scale;
-
-              solver.m_info = NumericalIssue;
-              solver.m_isInitialized = true;
-              solver.m_eigenvectorsOk = computeEigenvectors;
-              return;
-            }
-          }
         }
 
-        tmp = scaledMat;
+        // Compute the eigenvector of index k
-        tmp.diagonal().array() -= eivals(1);
-
-        if(d0<=Eigen::NumTraits<Scalar>::epsilon())
-          eivecs.col(1) = eivecs.col(k).unitOrthogonal();
-        else
         {
-          n = (cross = eivecs.col(k).cross(tmp.row(0).normalized())).squaredNorm();
+          tmp.diagonal().array () -= eivals(k);
-          if(n>safeNorm2)
+          // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.
-            eivecs.col(1) = cross / sqrt(n);
+          extract_kernel(tmp, eivecs.col(k), eivecs.col(l));
-          else
-          {
-            n = (cross = eivecs.col(k).cross(tmp.row(1))).squaredNorm();
-            if(n>safeNorm2)
-              eivecs.col(1) = cross / sqrt(n);
-            else
-            {
-              n = (cross = eivecs.col(k).cross(tmp.row(2))).squaredNorm();
-              if(n>safeNorm2)
-                eivecs.col(1) = cross / sqrt(n);
-              else
-              {
-                // we should never reach this point,
-                // if so the last two eigenvalues are likely to ve very closed to each other
-                eivecs.col(1) = eivecs.col(k).unitOrthogonal();
-              }
-            }
-          }
-
-          // make sure that eivecs[1] is orthogonal to eivecs[2]
-          Scalar d = eivecs.col(1).dot(eivecs.col(k));
-          eivecs.col(1) = (eivecs.col(1) - d * eivecs.col(k)).normalized();
         }
 
-        eivecs.col(k==2 ? 0 : 2) = eivecs.col(k).cross(eivecs.col(1)).normalized();
+        // Compute eigenvector of index l
+        if(d0<=2*Eigen::NumTraits<Scalar>::epsilon()*d1)
+        {
+          // If d0 is too small, then the two other eigenvalues are numerically the same,
+          // and thus we only have to ortho-normalize the near orthogonal vector we saved above.
+          eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);
+          eivecs.col(l).normalize();
+        }
+        else
+        {
+          tmp = scaledMat;
+          tmp.diagonal().array () -= eivals(l);
+
+          VectorType dummy;
+          extract_kernel(tmp, eivecs.col(l), dummy);
+        }
+
+        // Compute last eigenvector from the other two
+        eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();
       }
     }
+
     // Rescale back to the original size.
     eivals *= scale;
+    eivals.array() += shift;
     
     solver.m_info = Success;
     solver.m_isInitialized = true;
@@ -665,11 +655,12 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
   typedef typename SolverType::MatrixType MatrixType;
   typedef typename SolverType::RealVectorType VectorType;
   typedef typename SolverType::Scalar Scalar;
+  typedef typename SolverType::EigenvectorsType EigenvectorsType;
   
   static inline void computeRoots(const MatrixType& m, VectorType& roots)
   {
     using std::sqrt;
-    const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*m(1,0)*m(1,0));
+    const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*numext::abs2(m(1,0)));
     const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));
     roots(0) = t1 - t0;
     roots(1) = t1 + t0;
@@ -678,13 +669,15 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
   static inline void run(SolverType& solver, const MatrixType& mat, int options)
   {
     using std::sqrt;
+    using std::abs;
+
     eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());
     eigen_assert((options&~(EigVecMask|GenEigMask))==0
             && (options&EigVecMask)!=EigVecMask
             && "invalid option parameter");
     bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
     
-    MatrixType& eivecs = solver.m_eivec;
+    EigenvectorsType& eivecs = solver.m_eivec;
     VectorType& eivals = solver.m_eivalues;
   
     // map the matrix coefficients to [-1:1] to avoid over- and underflow.
@@ -698,22 +691,29 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
     // compute the eigen vectors
     if(computeEigenvectors)
     {
-      scaledMat.diagonal().array () -= eivals(1);
+      if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())
-      Scalar a2 = numext::abs2(scaledMat(0,0));
-      Scalar c2 = numext::abs2(scaledMat(1,1));
-      Scalar b2 = numext::abs2(scaledMat(1,0));
-      if(a2>c2)
       {
-        eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+        eivecs.setIdentity();
-        eivecs.col(1) /= sqrt(a2+b2);
       }
       else
       {
-        eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+        scaledMat.diagonal().array () -= eivals(1);
-        eivecs.col(1) /= sqrt(c2+b2);
+        Scalar a2 = numext::abs2(scaledMat(0,0));
-      }
+        Scalar c2 = numext::abs2(scaledMat(1,1));
+        Scalar b2 = numext::abs2(scaledMat(1,0));
+        if(a2>c2)
+        {
+          eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+          eivecs.col(1) /= sqrt(a2+b2);
+        }
+        else
+        {
+          eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+          eivecs.col(1) /= sqrt(c2+b2);
+        }
 
-      eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+        eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+      }
     }
     
     // Rescale back to the original size.
@@ -736,7 +736,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
 }
 
 namespace internal {
-template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+template<typename RealScalar, typename Scalar, typename Index>
 static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)
 {
   using std::abs;
@@ -788,8 +788,7 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
     // apply the givens rotation to the unit matrix Q = Q * G
     if (matrixQ)
     {
-      // FIXME if StorageOrder == RowMajor this operation is not very efficient
+      Map<Matrix<Scalar,Dynamic,Dynamic,ColMajor> > q(matrixQ,n,n);
-      Map<Matrix<Scalar,Dynamic,Dynamic,StorageOrder> > q(matrixQ,n,n);
       q.applyOnTheRight(k,k+1,rot);
     }
   }

Eigen/src/Geometry/AlignedBox.h

@@ -19,10 +19,12 @@ namespace Eigen {
   *
   * \brief An axis aligned box
   *
-  * \param _Scalar the type of the scalar coefficients
+  * \tparam _Scalar the type of the scalar coefficients
-  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
   *
   * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+  * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
+  * \sa alignedboxtypedefs
   */
 template <typename _Scalar, int _AmbientDim>
 class AlignedBox
@@ -40,18 +42,21 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
   enum CornerType
   {
-    /** 1D names */
+    /** 1D names @{ */
     Min=0, Max=1,
+    /** @} */
 
-    /** Added names for 2D */
+    /** Identifier for 2D corner @{ */
     BottomLeft=0, BottomRight=1,
     TopLeft=2, TopRight=3,
+    /** @} */
 
-    /** Added names for 3D */
+    /** Identifier for 3D corner  @{ */
     BottomLeftFloor=0, BottomRightFloor=1,
     TopLeftFloor=2, TopRightFloor=3,
     BottomLeftCeil=4, BottomRightCeil=5,
     TopLeftCeil=6, TopRightCeil=7
+    /** @} */
   };
 
 
@@ -63,34 +68,33 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
   { setEmpty(); }
 
-  /** Constructs a box with extremities \a _min and \a _max. */
+  /** Constructs a box with extremities \a _min and \a _max.
+   * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
   template<typename OtherVectorType1, typename OtherVectorType2>
   inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
 
   /** Constructs a box containing a single point \a p. */
   template<typename Derived>
-  inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
+  inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
-  {
+  { }
-    typename internal::nested<Derived,2>::type p(a_p.derived());
-    m_min = p;
-    m_max = p;
-  }
 
   ~AlignedBox() {}
 
   /** \returns the dimension in which the box holds */
   inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
 
-  /** \deprecated use isEmpty */
+  /** \deprecated use isEmpty() */
   inline bool isNull() const { return isEmpty(); }
 
-  /** \deprecated use setEmpty */
+  /** \deprecated use setEmpty() */
   inline void setNull() { setEmpty(); }
 
-  /** \returns true if the box is empty. */
+  /** \returns true if the box is empty.
+   * \sa setEmpty */
   inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
 
-  /** Makes \c *this an empty box. */
+  /** Makes \c *this an empty box.
+   * \sa isEmpty */
   inline void setEmpty()
   {
     m_min.setConstant( ScalarTraits::highest() );
@@ -159,7 +163,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
    * a uniform distribution */
   inline VectorType sample() const
   {
-    VectorType r;
+    VectorType r(dim());
     for(Index d=0; d<dim(); ++d)
     {
       if(!ScalarTraits::IsInteger)
@@ -175,27 +179,34 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns true if the point \a p is inside the box \c *this. */
   template<typename Derived>
-  inline bool contains(const MatrixBase<Derived>& a_p) const
+  inline bool contains(const MatrixBase<Derived>& p) const
   {
-    typename internal::nested<Derived,2>::type p(a_p.derived());
+    typename internal::nested<Derived,2>::type p_n(p.derived());
-    return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
+    return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
   }
 
   /** \returns true if the box \a b is entirely inside the box \c *this. */
   inline bool contains(const AlignedBox& b) const
   { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
 
-  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
+  /** \returns true if the box \a b is intersecting the box \c *this.
+   * \sa intersection, clamp */
+  inline bool intersects(const AlignedBox& b) const
+  { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
+
+  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
+   * \sa extend(const AlignedBox&) */
   template<typename Derived>
-  inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
+  inline AlignedBox& extend(const MatrixBase<Derived>& p)
   {
-    typename internal::nested<Derived,2>::type p(a_p.derived());
+    typename internal::nested<Derived,2>::type p_n(p.derived());
-    m_min = m_min.cwiseMin(p);
+    m_min = m_min.cwiseMin(p_n);
-    m_max = m_max.cwiseMax(p);
+    m_max = m_max.cwiseMax(p_n);
     return *this;
   }
 
-  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
+  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
+   * \sa merged, extend(const MatrixBase&) */
   inline AlignedBox& extend(const AlignedBox& b)
   {
     m_min = m_min.cwiseMin(b.m_min);
@@ -203,7 +214,9 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     return *this;
   }
 
-  /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
+  /** Clamps \c *this by the box \a b and returns a reference to \c *this.
+   * \note If the boxes don't intersect, the resulting box is empty.
+   * \sa intersection(), intersects() */
   inline AlignedBox& clamp(const AlignedBox& b)
   {
     m_min = m_min.cwiseMax(b.m_min);
@@ -211,11 +224,15 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     return *this;
   }
 
-  /** Returns an AlignedBox that is the intersection of \a b and \c *this */
+  /** Returns an AlignedBox that is the intersection of \a b and \c *this
+   * \note If the boxes don't intersect, the resulting box is empty.
+   * \sa intersects(), clamp, contains()  */
   inline AlignedBox intersection(const AlignedBox& b) const
   {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
 
-  /** Returns an AlignedBox that is the union of \a b and \c *this */
+  /** Returns an AlignedBox that is the union of \a b and \c *this.
+   * \note Merging with an empty box may result in a box bigger than \c *this. 
+   * \sa extend(const AlignedBox&) */
   inline AlignedBox merged(const AlignedBox& b) const
   { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
 
@@ -231,20 +248,20 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns the squared distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
-    * \sa exteriorDistance()
+    * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
     */
   template<typename Derived>
-  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;
+  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
 
   /** \returns the squared distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
-    * \sa exteriorDistance()
+    * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
     */
   inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
 
   /** \returns the distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
-    * \sa squaredExteriorDistance()
+    * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
     */
   template<typename Derived>
   inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
@@ -252,7 +269,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns the distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
-    * \sa squaredExteriorDistance()
+    * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
     */
   inline NonInteger exteriorDistance(const AlignedBox& b) const
   { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }

Eigen/src/Geometry/AngleAxis.h

@@ -131,7 +131,7 @@ public:
     m_angle = Scalar(other.angle());
   }
 
-  static inline const AngleAxis Identity() { return AngleAxis(0, Vector3::UnitX()); }
+  static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }
 
   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
     * determined by \a prec.
@@ -165,8 +165,8 @@ AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived
   Scalar n2 = q.vec().squaredNorm();
   if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
   {
-    m_angle = 0;
+    m_angle = Scalar(0);
-    m_axis << 1, 0, 0;
+    m_axis << Scalar(1), Scalar(0), Scalar(0);
   }
   else
   {

Eigen/src/Geometry/Homogeneous.h

@@ -79,7 +79,7 @@ template<typename MatrixType,int _Direction> class Homogeneous
     {
       if(  (int(Direction)==Vertical   && row==m_matrix.rows())
         || (int(Direction)==Horizontal && col==m_matrix.cols()))
-        return 1;
+        return Scalar(1);
       return m_matrix.coeff(row, col);
     }
 

Eigen/src/Geometry/Hyperplane.h

@@ -100,7 +100,17 @@ public:
   {
     EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
     Hyperplane result(p0.size());
-    result.normal() = (p2 - p0).cross(p1 - p0).normalized();
+    VectorType v0(p2 - p0), v1(p1 - p0);
+    result.normal() = v0.cross(v1);
+    RealScalar norm = result.normal().norm();
+    if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
+    {
+      Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+      JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
+      result.normal() = svd.matrixV().col(2);
+    }
+    else
+      result.normal() /= norm;
     result.offset() = -p0.dot(result.normal());
     return result;
   }

Eigen/src/Geometry/Quaternion.h

@@ -102,11 +102,11 @@ public:
   /** \returns a quaternion representing an identity rotation
     * \sa MatrixBase::Identity()
     */
-  static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
+  static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
 
   /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
     */
-  inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
+  inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
 
   /** \returns the squared norm of the quaternion's coefficients
     * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
@@ -161,7 +161,7 @@ public:
   { return coeffs().isApprox(other.coeffs(), prec); }
 
 	/** return the result vector of \a v through the rotation*/
-  EIGEN_STRONG_INLINE Vector3 _transformVector(Vector3 v) const;
+  EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -203,6 +203,8 @@ public:
   * \li \c Quaternionf for \c float
   * \li \c Quaterniond for \c double
   *
+  * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
+  *
   * \sa  class AngleAxis, class Transform
   */
 
@@ -229,7 +231,7 @@ class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
 public:
   typedef _Scalar Scalar;
 
-  EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Quaternion)
+  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
   using Base::operator*=;
 
   typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
@@ -339,12 +341,12 @@ class Map<const Quaternion<_Scalar>, _Options >
   public:
     typedef _Scalar Scalar;
     typedef typename internal::traits<Map>::Coefficients Coefficients;
-    EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Map)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
     using Base::operator*=;
 
     /** Constructs a Mapped Quaternion object from the pointer \a coeffs
       *
-      * The pointer \a coeffs must reference the four coeffecients of Quaternion in the following order:
+      * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
       * \code *coeffs == {x, y, z, w} \endcode
       *
       * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
@@ -376,7 +378,7 @@ class Map<Quaternion<_Scalar>, _Options >
   public:
     typedef _Scalar Scalar;
     typedef typename internal::traits<Map>::Coefficients Coefficients;
-    EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Map)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
     using Base::operator*=;
 
     /** Constructs a Mapped Quaternion object from the pointer \a coeffs
@@ -459,12 +461,12 @@ EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const Quaterni
   */
 template <class Derived>
 EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
-QuaternionBase<Derived>::_transformVector(Vector3 v) const
+QuaternionBase<Derived>::_transformVector(const Vector3& v) const
 {
     // Note that this algorithm comes from the optimization by hand
     // of the conversion to a Matrix followed by a Matrix/Vector product.
     // It appears to be much faster than the common algorithm found
-    // in the litterature (30 versus 39 flops). It also requires two
+    // in the literature (30 versus 39 flops). It also requires two
     // Vector3 as temporaries.
     Vector3 uv = this->vec().cross(v);
     uv += uv;
@@ -584,7 +586,7 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri
   //    which yields a singular value problem
   if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
   {
-    c = max<Scalar>(c,-1);
+    c = (max)(c,Scalar(-1));
     Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
     JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
     Vector3 axis = svd.matrixV().col(2);
@@ -635,7 +637,7 @@ inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Der
 {
   // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
   Scalar n2 = this->squaredNorm();
-  if (n2 > 0)
+  if (n2 > Scalar(0))
     return Quaternion<Scalar>(conjugate().coeffs() / n2);
   else
   {
@@ -665,12 +667,10 @@ template <class OtherDerived>
 inline typename internal::traits<Derived>::Scalar
 QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
 {
-  using std::acos;
+  using std::atan2;
   using std::abs;
-  double d = abs(this->dot(other));
+  Quaternion<Scalar> d = (*this) * other.conjugate();
-  if (d>=1.0)
+  return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
-    return Scalar(0);
-  return static_cast<Scalar>(2 * acos(d));
 }
 
  
@@ -710,7 +710,7 @@ QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerive
     scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
     scale1 = sin( ( t * theta) ) / sinTheta;
   }
-  if(d<0) scale1 = -scale1;
+  if(d<Scalar(0)) scale1 = -scale1;
 
   return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
 }

Eigen/src/Geometry/Rotation2D.h

@@ -60,6 +60,9 @@ public:
 
   /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
   inline Rotation2D(const Scalar& a) : m_angle(a) {}
+  
+  /** Default constructor wihtout initialization. The represented rotation is undefined. */
+  Rotation2D() {}
 
   /** \returns the rotation angle */
   inline Scalar angle() const { return m_angle; }
@@ -81,10 +84,10 @@ public:
   /** Applies the rotation to a 2D vector */
   Vector2 operator* (const Vector2& vec) const
   { return toRotationMatrix() * vec; }
-
+  
   template<typename Derived>
   Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
-  Matrix2 toRotationMatrix(void) const;
+  Matrix2 toRotationMatrix() const;
 
   /** \returns the spherical interpolation between \c *this and \a other using
     * parameter \a t. It is in fact equivalent to a linear interpolation.

Eigen/src/Geometry/Transform.h

@@ -62,6 +62,8 @@ struct transform_construct_from_matrix;
 
 template<typename TransformType> struct transform_take_affine_part;
 
+template<int Mode> struct transform_make_affine;
+
 } // end namespace internal
 
 /** \geometry_module \ingroup Geometry_Module
@@ -194,9 +196,9 @@ public:
   /** type of the matrix used to represent the linear part of the transformation */
   typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
   /** type of read/write reference to the linear part of the transformation */
-  typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact)> LinearPart;
+  typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;
   /** type of read reference to the linear part of the transformation */
-  typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact)> ConstLinearPart;
+  typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;
   /** type of read/write reference to the affine part of the transformation */
   typedef typename internal::conditional<int(Mode)==int(AffineCompact),
                               MatrixType&,
@@ -230,8 +232,7 @@ public:
   inline Transform()
   {
     check_template_params();
-    if (int(Mode)==Affine)
+    internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
-      makeAffine();
   }
 
   inline Transform(const Transform& other)
@@ -591,11 +592,7 @@ public:
     */
   void makeAffine()
   {
-    if(int(Mode)!=int(AffineCompact))
+    internal::transform_make_affine<int(Mode)>::run(m_matrix);
-    {
-      matrix().template block<1,Dim>(Dim,0).setZero();
-      matrix().coeffRef(Dim,Dim) = Scalar(1);
-    }
   }
 
   /** \internal
@@ -1079,6 +1076,24 @@ Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBas
 
 namespace internal {
 
+template<int Mode>
+struct transform_make_affine
+{
+  template<typename MatrixType>
+  static void run(MatrixType &mat)
+  {
+    static const int Dim = MatrixType::ColsAtCompileTime-1;
+    mat.template block<1,Dim>(Dim,0).setZero();
+    mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
+  }
+};
+
+template<>
+struct transform_make_affine<AffineCompact>
+{
+  template<typename MatrixType> static void run(MatrixType &) { }
+};
+    
 // selector needed to avoid taking the inverse of a 3x4 matrix
 template<typename TransformType, int Mode=TransformType::Mode>
 struct projective_transform_inverse

Eigen/src/Geometry/Umeyama.h

@@ -113,7 +113,7 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
   const Index n = src.cols(); // number of measurements
 
   // required for demeaning ...
-  const RealScalar one_over_n = 1 / static_cast<RealScalar>(n);
+  const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);
 
   // computation of mean
   const VectorType src_mean = src.rowwise().sum() * one_over_n;
@@ -136,16 +136,16 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
 
   // Eq. (39)
   VectorType S = VectorType::Ones(m);
-  if (sigma.determinant()<0) S(m-1) = -1;
+  if (sigma.determinant()<Scalar(0)) S(m-1) = Scalar(-1);
 
   // Eq. (40) and (43)
   const VectorType& d = svd.singularValues();
   Index rank = 0; for (Index i=0; i<m; ++i) if (!internal::isMuchSmallerThan(d.coeff(i),d.coeff(0))) ++rank;
   if (rank == m-1) {
-    if ( svd.matrixU().determinant() * svd.matrixV().determinant() > 0 ) {
+    if ( svd.matrixU().determinant() * svd.matrixV().determinant() > Scalar(0) ) {
       Rt.block(0,0,m,m).noalias() = svd.matrixU()*svd.matrixV().transpose();
     } else {
-      const Scalar s = S(m-1); S(m-1) = -1;
+      const Scalar s = S(m-1); S(m-1) = Scalar(-1);
       Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
       S(m-1) = s;
     }
@@ -156,7 +156,7 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
   if (with_scaling)
   {
     // Eq. (42)
-    const Scalar c = 1/src_var * svd.singularValues().dot(S);
+    const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);
 
     // Eq. (41)
     Rt.col(m).head(m) = dst_mean;

Eigen/src/Householder/BlockHouseholder.h

@@ -48,7 +48,7 @@ void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vec
   typedef typename MatrixType::Index Index;
   enum { TFactorSize = MatrixType::ColsAtCompileTime };
   Index nbVecs = vectors.cols();
-  Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize> T(nbVecs,nbVecs);
+  Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, ColMajor> T(nbVecs,nbVecs);
   make_block_householder_triangular_factor(T, vectors, hCoeffs);
 
   const TriangularView<const VectorsType, UnitLower>& V(vectors);

Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h

@@ -65,10 +65,10 @@ class DiagonalPreconditioner
       {
         typename MatType::InnerIterator it(mat,j);
         while(it && it.index()!=j) ++it;
-        if(it && it.index()==j)
+        if(it && it.index()==j && it.value()!=Scalar(0))
           m_invdiag(j) = Scalar(1)/it.value();
         else
-          m_invdiag(j) = 0;
+          m_invdiag(j) = Scalar(1);
       }
       m_isInitialized = true;
       return *this;

Eigen/src/IterativeLinearSolvers/BiCGSTAB.h

@@ -39,7 +39,6 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
   int maxIters = iters;
 
   int n = mat.cols();
-  x = precond.solve(x);
   VectorType r  = rhs - mat * x;
   VectorType r0 = r;
   
@@ -61,6 +60,7 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
   VectorType s(n), t(n);
 
   RealScalar tol2 = tol*tol;
+  RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
   int i = 0;
   int restarts = 0;
 
@@ -69,7 +69,7 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
     Scalar rho_old = rho;
 
     rho = r0.dot(r);
-    if (internal::isMuchSmallerThan(rho,r0_sqnorm))
+    if (abs(rho) < eps2*r0_sqnorm)
     {
       // The new residual vector became too orthogonal to the arbitrarily choosen direction r0
       // Let's restart with a new r0:
@@ -142,7 +142,7 @@ struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
   * SparseMatrix<double> A(n,n);
   * // fill A and b
   * BiCGSTAB<SparseMatrix<double> > solver;
-  * solver(A);
+  * solver.compute(A);
   * x = solver.solve(b);
   * std::cout << "#iterations:     " << solver.iterations() << std::endl;
   * std::cout << "estimated error: " << solver.error()      << std::endl;
@@ -151,20 +151,7 @@ struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
   * \endcode
   * 
   * By default the iterations start with x=0 as an initial guess of the solution.
-  * One can control the start using the solveWithGuess() method. Here is a step by
+  * One can control the start using the solveWithGuess() method.
-  * step execution example starting with a random guess and printing the evolution
-  * of the estimated error:
-  * * \code
-  * x = VectorXd::Random(n);
-  * solver.setMaxIterations(1);
-  * int i = 0;
-  * do {
-  *   x = solver.solveWithGuess(b,x);
-  *   std::cout << i << " : " << solver.error() << std::endl;
-  *   ++i;
-  * } while (solver.info()!=Success && i<100);
-  * \endcode
-  * Note that such a step by step excution is slightly slower.
   * 
   * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
   */
@@ -199,7 +186,8 @@ public:
     * this class becomes invalid. Call compute() to update it with the new
     * matrix A, or modify a copy of A.
     */
-  BiCGSTAB(const MatrixType& A) : Base(A) {}
+  template<typename MatrixDerived>
+  explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
 
   ~BiCGSTAB() {}
   

Eigen/src/IterativeLinearSolvers/ConjugateGradient.h

@@ -112,9 +112,9 @@ struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
   * This class allows to solve for A.x = b sparse linear problems using a conjugate gradient algorithm.
   * The sparse matrix A must be selfadjoint. The vectors x and b can be either dense or sparse.
   *
-  * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.
+  * \tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.
-  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
+  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower,
-  *               or Upper. Default is Lower.
+  *               Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.
   * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
   *
   * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
@@ -137,20 +137,7 @@ struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
   * \endcode
   * 
   * By default the iterations start with x=0 as an initial guess of the solution.
-  * One can control the start using the solveWithGuess() method. Here is a step by
+  * One can control the start using the solveWithGuess() method.
-  * step execution example starting with a random guess and printing the evolution
-  * of the estimated error:
-  * * \code
-  * x = VectorXd::Random(n);
-  * cg.setMaxIterations(1);
-  * int i = 0;
-  * do {
-  *   x = cg.solveWithGuess(b,x);
-  *   std::cout << i << " : " << cg.error() << std::endl;
-  *   ++i;
-  * } while (cg.info()!=Success && i<100);
-  * \endcode
-  * Note that such a step by step excution is slightly slower.
   * 
   * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
   */
@@ -189,7 +176,8 @@ public:
     * this class becomes invalid. Call compute() to update it with the new
     * matrix A, or modify a copy of A.
     */
-  ConjugateGradient(const MatrixType& A) : Base(A) {}
+  template<typename MatrixDerived>
+  explicit ConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
 
   ~ConjugateGradient() {}
   
@@ -213,6 +201,10 @@ public:
   template<typename Rhs,typename Dest>
   void _solveWithGuess(const Rhs& b, Dest& x) const
   {
+    typedef typename internal::conditional<UpLo==(Lower|Upper),
+                                           const MatrixType&,
+                                           SparseSelfAdjointView<const MatrixType, UpLo>
+                                          >::type MatrixWrapperType;
     m_iterations = Base::maxIterations();
     m_error = Base::m_tolerance;
 
@@ -222,8 +214,7 @@ public:
       m_error = Base::m_tolerance;
 
       typename Dest::ColXpr xj(x,j);
-      internal::conjugate_gradient(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj,
+      internal::conjugate_gradient(MatrixWrapperType(*mp_matrix), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
-                                   Base::m_preconditioner, m_iterations, m_error);
     }
 
     m_isInitialized = true;
@@ -234,7 +225,7 @@ public:
   template<typename Rhs,typename Dest>
   void _solve(const Rhs& b, Dest& x) const
   {
-    x.setOnes();
+    x.setZero();
     _solveWithGuess(b,x);
   }
 

Eigen/src/IterativeLinearSolvers/IncompleteLUT.h

@@ -150,7 +150,6 @@ class IncompleteLUT : internal::noncopyable
     {
       analyzePattern(amat); 
       factorize(amat);
-      m_isInitialized = m_factorizationIsOk;
       return *this;
     }
 
@@ -160,7 +159,7 @@ class IncompleteLUT : internal::noncopyable
     template<typename Rhs, typename Dest>
     void _solve(const Rhs& b, Dest& x) const
     {
-      x = m_Pinv * b;  
+      x = m_Pinv * b;
       x = m_lu.template triangularView<UnitLower>().solve(x);
       x = m_lu.template triangularView<Upper>().solve(x);
       x = m_P * x; 
@@ -223,18 +222,29 @@ template<typename _MatrixType>
 void IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat)
 {
   // Compute the Fill-reducing permutation
+  // Since ILUT does not perform any numerical pivoting,
+  // it is highly preferable to keep the diagonal through symmetric permutations.
+#ifndef EIGEN_MPL2_ONLY
+  // To this end, let's symmetrize the pattern and perform AMD on it.
   SparseMatrix<Scalar,ColMajor, Index> mat1 = amat;
   SparseMatrix<Scalar,ColMajor, Index> mat2 = amat.transpose();
-  // Symmetrize the pattern
   // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice.
   //       on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered...
   SparseMatrix<Scalar,ColMajor, Index> AtA = mat2 + mat1;
-  AtA.prune(keep_diag());
+  AMDOrdering<Index> ordering;
-  internal::minimum_degree_ordering<Scalar, Index>(AtA, m_P);  // Then compute the AMD ordering...
+  ordering(AtA,m_P);
-
+  m_Pinv  = m_P.inverse(); // cache the inverse permutation
-  m_Pinv  = m_P.inverse(); // ... and the inverse permutation
+#else
+  // If AMD is not available, (MPL2-only), then let's use the slower COLAMD routine.
+  SparseMatrix<Scalar,ColMajor, Index> mat1 = amat;
+  COLAMDOrdering<Index> ordering;
+  ordering(mat1,m_Pinv);
+  m_P = m_Pinv.inverse();
+#endif
 
   m_analysisIsOk = true;
+  m_factorizationIsOk = false;
+  m_isInitialized = false;
 }
 
 template <typename Scalar>
@@ -442,6 +452,7 @@ void IncompleteLUT<Scalar>::factorize(const _MatrixType& amat)
   m_lu.makeCompressed();
 
   m_factorizationIsOk = true;
+  m_isInitialized = m_factorizationIsOk;
   m_info = Success;
 }
 

Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h

@@ -49,10 +49,11 @@ public:
     * this class becomes invalid. Call compute() to update it with the new
     * matrix A, or modify a copy of A.
     */
-  IterativeSolverBase(const MatrixType& A)
+  template<typename InputDerived>
+  IterativeSolverBase(const EigenBase<InputDerived>& A)
   {
     init();
-    compute(A);
+    compute(A.derived());
   }
 
   ~IterativeSolverBase() {}
@@ -62,9 +63,11 @@ public:
     * Currently, this function mostly call analyzePattern on the preconditioner. In the future
     * we might, for instance, implement column reodering for faster matrix vector products.
     */
-  Derived& analyzePattern(const MatrixType& A)
+  template<typename InputDerived>
+  Derived& analyzePattern(const EigenBase<InputDerived>& A)
   {
-    m_preconditioner.analyzePattern(A);
+    grabInput(A.derived());
+    m_preconditioner.analyzePattern(*mp_matrix);
     m_isInitialized = true;
     m_analysisIsOk = true;
     m_info = Success;
@@ -80,11 +83,12 @@ public:
     * this class becomes invalid. Call compute() to update it with the new
     * matrix A, or modify a copy of A.
     */
-  Derived& factorize(const MatrixType& A)
+  template<typename InputDerived>
+  Derived& factorize(const EigenBase<InputDerived>& A)
   {
+    grabInput(A.derived());
     eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); 
-    mp_matrix = &A;
+    m_preconditioner.factorize(*mp_matrix);
-    m_preconditioner.factorize(A);
     m_factorizationIsOk = true;
     m_info = Success;
     return derived();
@@ -100,10 +104,11 @@ public:
     * this class becomes invalid. Call compute() to update it with the new
     * matrix A, or modify a copy of A.
     */
-  Derived& compute(const MatrixType& A)
+  template<typename InputDerived>
+  Derived& compute(const EigenBase<InputDerived>& A)
   {
-    mp_matrix = &A;
+    grabInput(A.derived());
-    m_preconditioner.compute(A);
+    m_preconditioner.compute(*mp_matrix);
     m_isInitialized = true;
     m_analysisIsOk = true;
     m_factorizationIsOk = true;
@@ -212,6 +217,28 @@ public:
   }
 
 protected:
+
+  template<typename InputDerived>
+  void grabInput(const EigenBase<InputDerived>& A)
+  {
+    // we const cast to prevent the creation of a MatrixType temporary by the compiler.
+    grabInput_impl(A.const_cast_derived());
+  }
+
+  template<typename InputDerived>
+  void grabInput_impl(const EigenBase<InputDerived>& A)
+  {
+    m_copyMatrix = A;
+    mp_matrix = &m_copyMatrix;
+  }
+
+  void grabInput_impl(MatrixType& A)
+  {
+    if(MatrixType::RowsAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==Dynamic)
+      m_copyMatrix.resize(0,0);
+    mp_matrix = &A;
+  }
+
   void init()
   {
     m_isInitialized = false;
@@ -220,6 +247,7 @@ protected:
     m_maxIterations = -1;
     m_tolerance = NumTraits<Scalar>::epsilon();
   }
+  MatrixType m_copyMatrix;
   const MatrixType* mp_matrix;
   Preconditioner m_preconditioner;
 

Eigen/src/LU/FullPivLU.h

@@ -20,10 +20,11 @@ namespace Eigen {
   *
   * \param MatrixType the type of the matrix of which we are computing the LU decomposition
   *
-  * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A
+  * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is
-  * is decomposed as A = PLUQ where L is unit-lower-triangular, U is upper-triangular, and P and Q
+  * decomposed as \f$ A = P^{-1} L U Q^{-1} \f$ where L is unit-lower-triangular, U is
-  * are permutation matrices. This is a rank-revealing LU decomposition. The eigenvalues (diagonal
+  * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU
-  * coefficients) of U are sorted in such a way that any zeros are at the end.
+  * decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any
+  * zeros are at the end.
   *
   * This decomposition provides the generic approach to solving systems of linear equations, computing
   * the rank, invertibility, inverse, kernel, and determinant.
@@ -373,6 +374,12 @@ template<typename _MatrixType> class FullPivLU
     inline Index cols() const { return m_lu.cols(); }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_lu;
     PermutationPType m_p;
     PermutationQType m_q;
@@ -417,6 +424,8 @@ FullPivLU<MatrixType>::FullPivLU(const MatrixType& matrix)
 template<typename MatrixType>
 FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
 {
+  check_template_parameters();
+  
   // the permutations are stored as int indices, so just to be sure:
   eigen_assert(matrix.rows()<=NumTraits<int>::highest() && matrix.cols()<=NumTraits<int>::highest());
   
@@ -511,8 +520,8 @@ typename internal::traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant
 }
 
 /** \returns the matrix represented by the decomposition,
- * i.e., it returns the product: P^{-1} L U Q^{-1}.
+ * i.e., it returns the product: \f$ P^{-1} L U Q^{-1} \f$.
- * This function is provided for debug purpose. */
+ * This function is provided for debug purposes. */
 template<typename MatrixType>
 MatrixType FullPivLU<MatrixType>::reconstructedMatrix() const
 {

Eigen/src/LU/PartialPivLU.h

@@ -171,6 +171,12 @@ template<typename _MatrixType> class PartialPivLU
     inline Index cols() const { return m_lu.cols(); }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_lu;
     PermutationType m_p;
     TranspositionType m_rowsTranspositions;
@@ -386,6 +392,8 @@ void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, t
 template<typename MatrixType>
 PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const MatrixType& matrix)
 {
+  check_template_parameters();
+  
   // the row permutation is stored as int indices, so just to be sure:
   eigen_assert(matrix.rows()<NumTraits<int>::highest());
   

Eigen/src/OrderingMethods/Amd.h

@@ -137,22 +137,27 @@ void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,Index>& C, Permutation
     degree[i] = len[i];                 // degree of node i
   }
   mark = internal::cs_wclear<Index>(0, 0, w, n);         /* clear w */
-  elen[n] = -2;                         /* n is a dead element */
-  Cp[n] = -1;                           /* n is a root of assembly tree */
-  w[n] = 0;                             /* n is a dead element */
   
   /* --- Initialize degree lists ------------------------------------------ */
   for(i = 0; i < n; i++)
   {
+    bool has_diag = false;
+    for(p = Cp[i]; p<Cp[i+1]; ++p)
+      if(Ci[p]==i)
+      {
+        has_diag = true;
+        break;
+      }
+   
     d = degree[i];
-    if(d == 0)                         /* node i is empty */
+    if(d == 1 && has_diag)           /* node i is empty */
     {
       elen[i] = -2;                 /* element i is dead */
       nel++;
       Cp[i] = -1;                   /* i is a root of assembly tree */
       w[i] = 0;
     }
-    else if(d > dense)                 /* node i is dense */
+    else if(d > dense || !has_diag)  /* node i is dense or has no structural diagonal element */
     {
       nv[i] = 0;                    /* absorb i into element n */
       elen[i] = -1;                 /* node i is dead */
@@ -168,6 +173,10 @@ void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,Index>& C, Permutation
     }
   }
   
+  elen[n] = -2;                         /* n is a dead element */
+  Cp[n] = -1;                           /* n is a root of assembly tree */
+  w[n] = 0;                             /* n is a dead element */
+  
   while (nel < n)                         /* while (selecting pivots) do */
   {
     /* --- Select node of minimum approximate degree -------------------- */

Eigen/src/OrderingMethods/Ordering.h

@@ -109,7 +109,7 @@ class NaturalOrdering
   * \class COLAMDOrdering
   *
   * Functor computing the \em column \em approximate \em minimum \em degree ordering 
-  * The matrix should be in column-major format
+  * The matrix should be in column-major and \b compressed format (see SparseMatrix::makeCompressed()).
   */
 template<typename Index>
 class COLAMDOrdering
@@ -118,10 +118,14 @@ class COLAMDOrdering
     typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType; 
     typedef Matrix<Index, Dynamic, 1> IndexVector;
     
-    /** Compute the permutation vector form a sparse matrix */
+    /** Compute the permutation vector \a perm form the sparse matrix \a mat
+      * \warning The input sparse matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+      */
     template <typename MatrixType>
     void operator() (const MatrixType& mat, PermutationType& perm)
     {
+      eigen_assert(mat.isCompressed() && "COLAMDOrdering requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to COLAMDOrdering");
+      
       Index m = mat.rows();
       Index n = mat.cols();
       Index nnz = mat.nonZeros();
@@ -132,12 +136,12 @@ class COLAMDOrdering
       Index stats [COLAMD_STATS];
       internal::colamd_set_defaults(knobs);
       
-      Index info;
       IndexVector p(n+1), A(Alen); 
       for(Index i=0; i <= n; i++)   p(i) = mat.outerIndexPtr()[i];
       for(Index i=0; i < nnz; i++)  A(i) = mat.innerIndexPtr()[i];
       // Call Colamd routine to compute the ordering 
-      info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats); 
+      Index info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats); 
+      EIGEN_UNUSED_VARIABLE(info);
       eigen_assert( info && "COLAMD failed " );
       
       perm.resize(n);

Eigen/src/PardisoSupport/PardisoSupport.h

@@ -219,7 +219,7 @@ class PardisoImpl
     void pardisoInit(int type)
     {
       m_type = type;
-      bool symmetric = abs(m_type) < 10;
+      bool symmetric = std::abs(m_type) < 10;
       m_iparm[0] = 1;   // No solver default
       m_iparm[1] = 3;   // use Metis for the ordering
       m_iparm[2] = 1;   // Numbers of processors, value of OMP_NUM_THREADS

Eigen/src/QR/ColPivHouseholderQR.h

@@ -76,7 +76,8 @@ template<typename _MatrixType> class ColPivHouseholderQR
         m_colsTranspositions(),
         m_temp(),
         m_colSqNorms(),
-        m_isInitialized(false) {}
+        m_isInitialized(false),
+        m_usePrescribedThreshold(false) {}
 
     /** \brief Default Constructor with memory preallocation
       *
@@ -383,6 +384,12 @@ template<typename _MatrixType> class ColPivHouseholderQR
     }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_qr;
     HCoeffsType m_hCoeffs;
     PermutationType m_colsPermutation;
@@ -421,6 +428,8 @@ typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::logAbsDetermina
 template<typename MatrixType>
 ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
 {
+  check_template_parameters();
+  
   using std::abs;
   Index rows = matrix.rows();
   Index cols = matrix.cols();
@@ -462,20 +471,10 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
     // we store that back into our table: it can't hurt to correct our table.
     m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;
 
-    // if the current biggest column is smaller than epsilon times the initial biggest column,
+    // Track the number of meaningful pivots but do not stop the decomposition to make
-    // terminate to avoid generating nan/inf values.
+    // sure that the initial matrix is properly reproduced. See bug 941.
-    // Note that here, if we test instead for "biggest == 0", we get a failure every 1000 (or so)
+    if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
-    // repetitions of the unit test, with the result of solve() filled with large values of the order
-    // of 1/(size*epsilon).
-    if(biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
-    {
       m_nonzero_pivots = k;
-      m_hCoeffs.tail(size-k).setZero();
-      m_qr.bottomRightCorner(rows-k,cols-k)
-          .template triangularView<StrictlyLower>()
-          .setZero();
-      break;
-    }
 
     // apply the transposition to the columns
     m_colsTranspositions.coeffRef(k) = biggest_col_index;
@@ -504,7 +503,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
   }
 
   m_colsPermutation.setIdentity(PermIndexType(cols));
-  for(PermIndexType k = 0; k < m_nonzero_pivots; ++k)
+  for(PermIndexType k = 0; k < size/*m_nonzero_pivots*/; ++k)
     m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));
 
   m_det_pq = (number_of_transpositions%2) ? -1 : 1;
@@ -554,13 +553,15 @@ struct solve_retval<ColPivHouseholderQR<_MatrixType>, Rhs>
 
 } // end namespace internal
 
-/** \returns the matrix Q as a sequence of householder transformations */
+/** \returns the matrix Q as a sequence of householder transformations.
+  * You can extract the meaningful part only by using:
+  * \code qr.householderQ().setLength(qr.nonzeroPivots()) \endcode*/
 template<typename MatrixType>
 typename ColPivHouseholderQR<MatrixType>::HouseholderSequenceType ColPivHouseholderQR<MatrixType>
   ::householderQ() const
 {
   eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate()).setLength(m_nonzero_pivots);
+  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
 }
 
 /** \return the column-pivoting Householder QR decomposition of \c *this.

Eigen/src/QR/FullPivHouseholderQR.h

@@ -368,6 +368,12 @@ template<typename _MatrixType> class FullPivHouseholderQR
     RealScalar maxPivot() const { return m_maxpivot; }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_qr;
     HCoeffsType m_hCoeffs;
     IntDiagSizeVectorType m_rows_transpositions;
@@ -407,6 +413,8 @@ typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDetermin
 template<typename MatrixType>
 FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
 {
+  check_template_parameters();
+  
   using std::abs;
   Index rows = matrix.rows();
   Index cols = matrix.cols();

Eigen/src/QR/HouseholderQR.h

@@ -189,6 +189,12 @@ template<typename _MatrixType> class HouseholderQR
     const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
 
   protected:
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_qr;
     HCoeffsType m_hCoeffs;
     RowVectorType m_temp;
@@ -251,56 +257,62 @@ void householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, typename
 }
 
 /** \internal */
-template<typename MatrixQR, typename HCoeffs>
+template<typename MatrixQR, typename HCoeffs,
-void householder_qr_inplace_blocked(MatrixQR& mat, HCoeffs& hCoeffs,
+  typename MatrixQRScalar = typename MatrixQR::Scalar,
-                                       typename MatrixQR::Index maxBlockSize=32,
+  bool InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 && HCoeffs::InnerStrideAtCompileTime == 1)>
-                                       typename MatrixQR::Scalar* tempData = 0)
+struct householder_qr_inplace_blocked
 {
-  typedef typename MatrixQR::Index Index;
+  // This is specialized for MKL-supported Scalar types in HouseholderQR_MKL.h
-  typedef typename MatrixQR::Scalar Scalar;
+  static void run(MatrixQR& mat, HCoeffs& hCoeffs,
-  typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;
+      typename MatrixQR::Index maxBlockSize=32,
-
+      typename MatrixQR::Scalar* tempData = 0)
-  Index rows = mat.rows();
-  Index cols = mat.cols();
-  Index size = (std::min)(rows, cols);
-
-  typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;
-  TempType tempVector;
-  if(tempData==0)
   {
-    tempVector.resize(cols);
+    typedef typename MatrixQR::Index Index;
-    tempData = tempVector.data();
+    typedef typename MatrixQR::Scalar Scalar;
-  }
+    typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;
 
-  Index blockSize = (std::min)(maxBlockSize,size);
+    Index rows = mat.rows();
+    Index cols = mat.cols();
+    Index size = (std::min)(rows, cols);
 
-  Index k = 0;
+    typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;
-  for (k = 0; k < size; k += blockSize)
+    TempType tempVector;
-  {
+    if(tempData==0)
-    Index bs = (std::min)(size-k,blockSize);  // actual size of the block
-    Index tcols = cols - k - bs;            // trailing columns
-    Index brows = rows-k;                   // rows of the block
-
-    // partition the matrix:
-    //        A00 | A01 | A02
-    // mat  = A10 | A11 | A12
-    //        A20 | A21 | A22
-    // and performs the qr dec of [A11^T A12^T]^T
-    // and update [A21^T A22^T]^T using level 3 operations.
-    // Finally, the algorithm continue on A22
-
-    BlockType A11_21 = mat.block(k,k,brows,bs);
-    Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);
-
-    householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);
-
-    if(tcols)
     {
-      BlockType A21_22 = mat.block(k,k+bs,brows,tcols);
+      tempVector.resize(cols);
-      apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint());
+      tempData = tempVector.data();
+    }
+
+    Index blockSize = (std::min)(maxBlockSize,size);
+
+    Index k = 0;
+    for (k = 0; k < size; k += blockSize)
+    {
+      Index bs = (std::min)(size-k,blockSize);  // actual size of the block
+      Index tcols = cols - k - bs;            // trailing columns
+      Index brows = rows-k;                   // rows of the block
+
+      // partition the matrix:
+      //        A00 | A01 | A02
+      // mat  = A10 | A11 | A12
+      //        A20 | A21 | A22
+      // and performs the qr dec of [A11^T A12^T]^T
+      // and update [A21^T A22^T]^T using level 3 operations.
+      // Finally, the algorithm continue on A22
+
+      BlockType A11_21 = mat.block(k,k,brows,bs);
+      Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);
+
+      householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);
+
+      if(tcols)
+      {
+        BlockType A21_22 = mat.block(k,k+bs,brows,tcols);
+        apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint());
+      }
     }
   }
-}
+};
 
 template<typename _MatrixType, typename Rhs>
 struct solve_retval<HouseholderQR<_MatrixType>, Rhs>
@@ -343,6 +355,8 @@ struct solve_retval<HouseholderQR<_MatrixType>, Rhs>
 template<typename MatrixType>
 HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType& matrix)
 {
+  check_template_parameters();
+  
   Index rows = matrix.rows();
   Index cols = matrix.cols();
   Index size = (std::min)(rows,cols);
@@ -352,7 +366,7 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType&
 
   m_temp.resize(cols);
 
-  internal::householder_qr_inplace_blocked(m_qr, m_hCoeffs, 48, m_temp.data());
+  internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data());
 
   m_isInitialized = true;
   return *this;

Eigen/src/QR/HouseholderQR_MKL.h

@@ -34,28 +34,30 @@
 #ifndef EIGEN_QR_MKL_H
 #define EIGEN_QR_MKL_H
 
-#include "Eigen/src/Core/util/MKL_support.h"
+#include "../Core/util/MKL_support.h"
 
 namespace Eigen { 
 
-namespace internal {
+  namespace internal {
 
-/** \internal Specialization for the data types supported by MKL */
+    /** \internal Specialization for the data types supported by MKL */
 
 #define EIGEN_MKL_QR_NOPIV(EIGTYPE, MKLTYPE, MKLPREFIX) \
 template<typename MatrixQR, typename HCoeffs> \
-void householder_qr_inplace_blocked(MatrixQR& mat, HCoeffs& hCoeffs, \
+struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \
-                                       typename MatrixQR::Index maxBlockSize=32, \
-                                       EIGTYPE* tempData = 0) \
 { \
-  lapack_int m = mat.rows(); \
+  static void run(MatrixQR& mat, HCoeffs& hCoeffs, \
-  lapack_int n = mat.cols(); \
+      typename MatrixQR::Index = 32, \
-  lapack_int lda = mat.outerStride(); \
+      typename MatrixQR::Scalar* = 0) \
-  lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
+  { \
-  LAPACKE_##MKLPREFIX##geqrf( matrix_order, m, n, (MKLTYPE*)mat.data(), lda, (MKLTYPE*)hCoeffs.data()); \
+    lapack_int m = (lapack_int) mat.rows(); \
-  hCoeffs.adjointInPlace(); \
+    lapack_int n = (lapack_int) mat.cols(); \
-\
+    lapack_int lda = (lapack_int) mat.outerStride(); \
-}
+    lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
+    LAPACKE_##MKLPREFIX##geqrf( matrix_order, m, n, (MKLTYPE*)mat.data(), lda, (MKLTYPE*)hCoeffs.data()); \
+    hCoeffs.adjointInPlace(); \
+  } \
+};
 
 EIGEN_MKL_QR_NOPIV(double, double, d)
 EIGEN_MKL_QR_NOPIV(float, float, s)

Eigen/src/SPQRSupport/SuiteSparseQRSupport.h

@@ -47,7 +47,7 @@ namespace Eigen {
  * You can then apply it to a vector.
  * 
  * R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix.
- * NOTE : The Index type of R is always UF_long. You can get it with SPQR::Index
+ * NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index
  * 
  * \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>
  * NOTE 
@@ -59,24 +59,18 @@ class SPQR
   public:
     typedef typename _MatrixType::Scalar Scalar;
     typedef typename _MatrixType::RealScalar RealScalar;
-    typedef UF_long Index ; 
+    typedef SuiteSparse_long Index ;
     typedef SparseMatrix<Scalar, ColMajor, Index> MatrixType;
     typedef PermutationMatrix<Dynamic, Dynamic> PermutationType;
   public:
     SPQR() 
-      : m_isInitialized(false),
+      : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
-      m_ordering(SPQR_ORDERING_DEFAULT),
-      m_allow_tol(SPQR_DEFAULT_TOL),
-      m_tolerance (NumTraits<Scalar>::epsilon())
     { 
       cholmod_l_start(&m_cc);
     }
     
-    SPQR(const _MatrixType& matrix) 
+    SPQR(const _MatrixType& matrix)
-    : m_isInitialized(false),
+    : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
-      m_ordering(SPQR_ORDERING_DEFAULT),
-      m_allow_tol(SPQR_DEFAULT_TOL),
-      m_tolerance (NumTraits<Scalar>::epsilon())
     {
       cholmod_l_start(&m_cc);
       compute(matrix);
@@ -101,10 +95,26 @@ class SPQR
       if(m_isInitialized) SPQR_free();
 
       MatrixType mat(matrix);
+      
+      /* Compute the default threshold as in MatLab, see:
+       * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+       * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 
+       */
+      RealScalar pivotThreshold = m_tolerance;
+      if(m_useDefaultThreshold) 
+      {
+        using std::max;
+        RealScalar max2Norm = 0.0;
+        for (int j = 0; j < mat.cols(); j++) max2Norm = (max)(max2Norm, mat.col(j).norm());
+        if(max2Norm==RealScalar(0))
+          max2Norm = RealScalar(1);
+        pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
+      }
+      
       cholmod_sparse A; 
       A = viewAsCholmod(mat);
       Index col = matrix.cols();
-      m_rank = SuiteSparseQR<Scalar>(m_ordering, m_tolerance, col, &A, 
+      m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A, 
                              &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);
 
       if (!m_cR)
@@ -120,7 +130,7 @@ class SPQR
     /** 
      * Get the number of rows of the input matrix and the Q matrix
      */
-    inline Index rows() const {return m_H->nrow; }
+    inline Index rows() const {return m_cR->nrow; }
     
     /** 
      * Get the number of columns of the input matrix. 
@@ -145,16 +155,25 @@ class SPQR
     {
       eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
       eigen_assert(b.cols()==1 && "This method is for vectors only");
-      
+
       //Compute Q^T * b
-      typename Dest::PlainObject y;
+      typename Dest::PlainObject y, y2;
       y = matrixQ().transpose() * b;
-        // Solves with the triangular matrix R
+      
+      // Solves with the triangular matrix R
       Index rk = this->rank();
-      y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y.topRows(rk));
+      y2 = y;
-      y.bottomRows(cols()-rk).setZero();
+      y.resize((std::max)(cols(),Index(y.rows())),y.cols());
+      y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));
+
       // Apply the column permutation 
-      dest.topRows(cols()) = colsPermutation() * y.topRows(cols());
+      // colsPermutation() performs a copy of the permutation,
+      // so let's apply it manually:
+      for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
+      for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
+      
+//       y.bottomRows(y.rows()-rk).setZero();
+//       dest = colsPermutation() * y.topRows(cols());
       
       m_info = Success;
     }
@@ -197,7 +216,11 @@ class SPQR
     /// Set the fill-reducing ordering method to be used
     void setSPQROrdering(int ord) { m_ordering = ord;}
     /// Set the tolerance tol to treat columns with 2-norm < =tol as zero
-    void setPivotThreshold(const RealScalar& tol) { m_tolerance = tol; }
+    void setPivotThreshold(const RealScalar& tol)
+    {
+      m_useDefaultThreshold = false;
+      m_tolerance = tol;
+    }
     
     /** \returns a pointer to the SPQR workspace */
     cholmod_common *cholmodCommon() const { return &m_cc; }
@@ -230,6 +253,7 @@ class SPQR
     mutable cholmod_dense *m_HTau; // The Householder coefficients
     mutable Index m_rank; // The rank of the matrix
     mutable cholmod_common m_cc; // Workspace and parameters
+    bool m_useDefaultThreshold;     // Use default threshold
     template<typename ,typename > friend struct SPQR_QProduct;
 };
 

Eigen/src/SVD/JacobiSVD.h

@@ -375,17 +375,19 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
     Scalar z;
     JacobiRotation<Scalar> rot;
     RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
+    
     if(n==0)
     {
       z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
       work_matrix.row(p) *= z;
       if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
       if(work_matrix.coeff(q,q)!=Scalar(0))
+      {
         z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
-      else
+        work_matrix.row(q) *= z;
-        z = Scalar(0);
+        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
-      work_matrix.row(q) *= z;
+      }
-      if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+      // otherwise the second row is already zero, so we have nothing to do.
     }
     else
     {
@@ -415,6 +417,7 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
                             JacobiRotation<RealScalar> *j_right)
 {
   using std::sqrt;
+  using std::abs;
   Matrix<RealScalar,2,2> m;
   m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
        numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
@@ -428,9 +431,11 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   }
   else
   {
-    RealScalar u = d / t;
+    RealScalar t2d2 = numext::hypot(t,d);
-    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.c() = abs(t)/t2d2;
-    rot1.s() = rot1.c() * u;
+    rot1.s() = d/t2d2;
+    if(t<RealScalar(0))
+      rot1.s() = -rot1.s();
   }
   m.applyOnTheLeft(0,1,rot1);
   j_right->makeJacobi(m,0,1);
@@ -531,8 +536,9 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
     JacobiSVD()
       : m_isInitialized(false),
         m_isAllocated(false),
+        m_usePrescribedThreshold(false),
         m_computationOptions(0),
-        m_rows(-1), m_cols(-1)
+        m_rows(-1), m_cols(-1), m_diagSize(0)
     {}
 
 
@@ -545,6 +551,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
     JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
       : m_isInitialized(false),
         m_isAllocated(false),
+        m_usePrescribedThreshold(false),
         m_computationOptions(0),
         m_rows(-1), m_cols(-1)
     {
@@ -564,6 +571,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
     JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
       : m_isInitialized(false),
         m_isAllocated(false),
+        m_usePrescribedThreshold(false),
         m_computationOptions(0),
         m_rows(-1), m_cols(-1)
     {
@@ -665,23 +673,92 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
       return m_nonzeroSingularValues;
     }
+    
+    /** \returns the rank of the matrix of which \c *this is the SVD.
+      *
+      * \note This method has to determine which singular values should be considered nonzero.
+      *       For that, it uses the threshold value that you can control by calling
+      *       setThreshold(const RealScalar&).
+      */
+    inline Index rank() const
+    {
+      using std::abs;
+      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+      if(m_singularValues.size()==0) return 0;
+      RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
+      Index i = m_nonzeroSingularValues-1;
+      while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
+      return i+1;
+    }
+    
+    /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
+      * which need to determine when singular values are to be considered nonzero.
+      * This is not used for the SVD decomposition itself.
+      *
+      * When it needs to get the threshold value, Eigen calls threshold().
+      * The default is \c NumTraits<Scalar>::epsilon()
+      *
+      * \param threshold The new value to use as the threshold.
+      *
+      * A singular value will be considered nonzero if its value is strictly greater than
+      *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
+      *
+      * If you want to come back to the default behavior, call setThreshold(Default_t)
+      */
+    JacobiSVD& setThreshold(const RealScalar& threshold)
+    {
+      m_usePrescribedThreshold = true;
+      m_prescribedThreshold = threshold;
+      return *this;
+    }
+
+    /** Allows to come back to the default behavior, letting Eigen use its default formula for
+      * determining the threshold.
+      *
+      * You should pass the special object Eigen::Default as parameter here.
+      * \code svd.setThreshold(Eigen::Default); \endcode
+      *
+      * See the documentation of setThreshold(const RealScalar&).
+      */
+    JacobiSVD& setThreshold(Default_t)
+    {
+      m_usePrescribedThreshold = false;
+      return *this;
+    }
+
+    /** Returns the threshold that will be used by certain methods such as rank().
+      *
+      * See the documentation of setThreshold(const RealScalar&).
+      */
+    RealScalar threshold() const
+    {
+      eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+      return m_usePrescribedThreshold ? m_prescribedThreshold
+                                      : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
+    }
 
     inline Index rows() const { return m_rows; }
     inline Index cols() const { return m_cols; }
 
   private:
     void allocate(Index rows, Index cols, unsigned int computationOptions);
+    
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
 
   protected:
     MatrixUType m_matrixU;
     MatrixVType m_matrixV;
     SingularValuesType m_singularValues;
     WorkMatrixType m_workMatrix;
-    bool m_isInitialized, m_isAllocated;
+    bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
     bool m_computeFullU, m_computeThinU;
     bool m_computeFullV, m_computeThinV;
     unsigned int m_computationOptions;
     Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
+    RealScalar m_prescribedThreshold;
 
     template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
     friend struct internal::svd_precondition_2x2_block_to_be_real;
@@ -690,6 +767,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
 
     internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
     internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
+    MatrixType m_scaledMatrix;
 };
 
 template<typename MatrixType, int QRPreconditioner>
@@ -736,14 +814,17 @@ void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, u
                             : 0);
   m_workMatrix.resize(m_diagSize, m_diagSize);
   
-  if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this);
+  if(m_cols>m_rows)   m_qr_precond_morecols.allocate(*this);
-  if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this);
+  if(m_rows>m_cols)   m_qr_precond_morerows.allocate(*this);
+  if(m_cols!=m_cols)  m_scaledMatrix.resize(rows,cols);
 }
 
 template<typename MatrixType, int QRPreconditioner>
 JacobiSVD<MatrixType, QRPreconditioner>&
 JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
 {
+  check_template_parameters();
+  
   using std::abs;
   allocate(matrix.rows(), matrix.cols(), computationOptions);
 
@@ -754,11 +835,21 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
   // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
   const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
 
+  // Scaling factor to reduce over/under-flows
+  RealScalar scale = matrix.cwiseAbs().maxCoeff();
+  if(scale==RealScalar(0)) scale = RealScalar(1);
+  
   /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
 
-  if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix))
+  if(m_rows!=m_cols)
   {
-    m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize);
+    m_scaledMatrix = matrix / scale;
+    m_qr_precond_morecols.run(*this, m_scaledMatrix);
+    m_qr_precond_morerows.run(*this, m_scaledMatrix);
+  }
+  else
+  {
+    m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;
     if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows);
     if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize);
     if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols);
@@ -784,7 +875,8 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
         using std::max;
         RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
                                                                        abs(m_workMatrix.coeff(q,q))));
-        if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
+        // We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
+        if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
         {
           finished = false;
 
@@ -833,6 +925,8 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
       if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
     }
   }
+  
+  m_singularValues *= scale;
 
   m_isInitialized = true;
   return *this;
@@ -854,11 +948,11 @@ struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
     // So A^{-1} = V S^{-1} U^*
 
     Matrix<Scalar, Dynamic, Rhs::ColsAtCompileTime, 0, _MatrixType::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime> tmp;
-    Index nonzeroSingVals = dec().nonzeroSingularValues();
+    Index rank = dec().rank();
     
-    tmp.noalias() = dec().matrixU().leftCols(nonzeroSingVals).adjoint() * rhs();
+    tmp.noalias() = dec().matrixU().leftCols(rank).adjoint() * rhs();
-    tmp = dec().singularValues().head(nonzeroSingVals).asDiagonal().inverse() * tmp;
+    tmp = dec().singularValues().head(rank).asDiagonal().inverse() * tmp;
-    dst = dec().matrixV().leftCols(nonzeroSingVals) * tmp;
+    dst = dec().matrixV().leftCols(rank) * tmp;
   }
 };
 } // end namespace internal

Eigen/src/SparseCholesky/SimplicialCholesky.h

@@ -37,6 +37,7 @@ class SimplicialCholeskyBase : internal::noncopyable
 {
   public:
     typedef typename internal::traits<Derived>::MatrixType MatrixType;
+    typedef typename internal::traits<Derived>::OrderingType OrderingType;
     enum { UpLo = internal::traits<Derived>::UpLo };
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
@@ -240,15 +241,16 @@ class SimplicialCholeskyBase : internal::noncopyable
     RealScalar m_shiftScale;
 };
 
-template<typename _MatrixType, int _UpLo = Lower> class SimplicialLLT;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLLT;
-template<typename _MatrixType, int _UpLo = Lower> class SimplicialLDLT;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLDLT;
-template<typename _MatrixType, int _UpLo = Lower> class SimplicialCholesky;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialCholesky;
 
 namespace internal {
 
-template<typename _MatrixType, int _UpLo> struct traits<SimplicialLLT<_MatrixType,_UpLo> >
+template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
 {
   typedef _MatrixType MatrixType;
+  typedef _Ordering OrderingType;
   enum { UpLo = _UpLo };
   typedef typename MatrixType::Scalar                         Scalar;
   typedef typename MatrixType::Index                          Index;
@@ -259,9 +261,10 @@ template<typename _MatrixType, int _UpLo> struct traits<SimplicialLLT<_MatrixTyp
   static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
 };
 
-template<typename _MatrixType,int _UpLo> struct traits<SimplicialLDLT<_MatrixType,_UpLo> >
+template<typename _MatrixType,int _UpLo, typename _Ordering> struct traits<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
 {
   typedef _MatrixType MatrixType;
+  typedef _Ordering OrderingType;
   enum { UpLo = _UpLo };
   typedef typename MatrixType::Scalar                             Scalar;
   typedef typename MatrixType::Index                              Index;
@@ -272,9 +275,10 @@ template<typename _MatrixType,int _UpLo> struct traits<SimplicialLDLT<_MatrixTyp
   static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
 };
 
-template<typename _MatrixType, int _UpLo> struct traits<SimplicialCholesky<_MatrixType,_UpLo> >
+template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
 {
   typedef _MatrixType MatrixType;
+  typedef _Ordering OrderingType;
   enum { UpLo = _UpLo };
 };
 
@@ -294,11 +298,12 @@ template<typename _MatrixType, int _UpLo> struct traits<SimplicialCholesky<_Matr
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
   *               or Upper. Default is Lower.
+  * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
   *
-  * \sa class SimplicialLDLT
+  * \sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering
   */
-template<typename _MatrixType, int _UpLo>
+template<typename _MatrixType, int _UpLo, typename _Ordering>
-    class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo> >
+    class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
 {
 public:
     typedef _MatrixType MatrixType;
@@ -382,11 +387,12 @@ public:
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
   *               or Upper. Default is Lower.
+  * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
   *
-  * \sa class SimplicialLLT
+  * \sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering
   */
-template<typename _MatrixType, int _UpLo>
+template<typename _MatrixType, int _UpLo, typename _Ordering>
-    class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo> >
+    class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
 {
 public:
     typedef _MatrixType MatrixType;
@@ -467,8 +473,8 @@ public:
   *
   * \sa class SimplicialLDLT, class SimplicialLLT
   */
-template<typename _MatrixType, int _UpLo>
+template<typename _MatrixType, int _UpLo, typename _Ordering>
-    class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo> >
+    class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
 {
 public:
     typedef _MatrixType MatrixType;
@@ -612,15 +618,13 @@ void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, CholMatrixTy
 {
   eigen_assert(a.rows()==a.cols());
   const Index size = a.rows();
-  // TODO allows to configure the permutation
   // Note that amd compute the inverse permutation
   {
     CholMatrixType C;
     C = a.template selfadjointView<UpLo>();
-    // remove diagonal entries:
+    
-    // seems not to be needed
+    OrderingType ordering;
-    // C.prune(keep_diag());
+    ordering(C,m_Pinv);
-    internal::minimum_degree_ordering(C, m_Pinv);
   }
 
   if(m_Pinv.size()>0)

Eigen/src/SparseCore/AmbiVector.h

@@ -69,7 +69,7 @@ class AmbiVector
       delete[] m_buffer;
       if (size<1000)
       {
-        Index allocSize = (size * sizeof(ListEl))/sizeof(Scalar);
+        Index allocSize = (size * sizeof(ListEl) + sizeof(Scalar) - 1)/sizeof(Scalar);
         m_allocatedElements = (allocSize*sizeof(Scalar))/sizeof(ListEl);
         m_buffer = new Scalar[allocSize];
       }
@@ -88,7 +88,7 @@ class AmbiVector
       Index copyElements = m_allocatedElements;
       m_allocatedElements = (std::min)(Index(m_allocatedElements*1.5),m_size);
       Index allocSize = m_allocatedElements * sizeof(ListEl);
-      allocSize = allocSize/sizeof(Scalar) + (allocSize%sizeof(Scalar)>0?1:0);
+      allocSize = (allocSize + sizeof(Scalar) - 1)/sizeof(Scalar);
       Scalar* newBuffer = new Scalar[allocSize];
       memcpy(newBuffer,  m_buffer,  copyElements * sizeof(ListEl));
       delete[] m_buffer;

Eigen/src/SparseCore/CompressedStorage.h

@@ -51,8 +51,8 @@ class CompressedStorage
     CompressedStorage& operator=(const CompressedStorage& other)
     {
       resize(other.size());
-      memcpy(m_values, other.m_values, m_size * sizeof(Scalar));
+      internal::smart_copy(other.m_values,  other.m_values  + m_size, m_values);
-      memcpy(m_indices, other.m_indices, m_size * sizeof(Index));
+      internal::smart_copy(other.m_indices, other.m_indices + m_size, m_indices);
       return *this;
     }
 
@@ -83,10 +83,10 @@ class CompressedStorage
         reallocate(m_size);
     }
 
-    void resize(size_t size, float reserveSizeFactor = 0)
+    void resize(size_t size, double reserveSizeFactor = 0)
     {
       if (m_allocatedSize<size)
-        reallocate(size + size_t(reserveSizeFactor*size));
+        reallocate(size + size_t(reserveSizeFactor*double(size)));
       m_size = size;
     }
 

Eigen/src/SparseCore/SparseBlock.h

@@ -57,6 +57,16 @@ public:
     inline BlockImpl(const XprType& xpr, int startRow, int startCol, int blockRows, int blockCols)
       : m_matrix(xpr), m_outerStart(IsRowMajor ? startRow : startCol), m_outerSize(IsRowMajor ? blockRows : blockCols)
     {}
+    
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row + IsRowMajor ? m_outerStart : 0, col +IsRowMajor ? 0 :  m_outerStart);
+    }
+    
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index :  m_outerStart);
+    }
 
     EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
     EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
@@ -68,6 +78,8 @@ public:
     const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
 
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+  private:
+    Index nonZeros() const;
 };
 
 
@@ -82,6 +94,7 @@ class BlockImpl<SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true
     typedef SparseMatrix<_Scalar, _Options, _Index> SparseMatrixType;
     typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _MatrixTypeNested;
     typedef Block<SparseMatrixType, BlockRows, BlockCols, true> BlockType;
+    typedef Block<const SparseMatrixType, BlockRows, BlockCols, true> ConstBlockType;
 public:
     enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
     EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
@@ -223,6 +236,118 @@ public:
       else
         return Map<const Matrix<Index,OuterSize,1> >(m_matrix.innerNonZeroPtr()+m_outerStart, m_outerSize.value()).sum();
     }
+    
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));
+    }
+    
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));
+    }
+    
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index :  m_outerStart);
+    }
+
+    const Scalar& lastCoeff() const
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(BlockImpl);
+      eigen_assert(nonZeros()>0);
+      if(m_matrix.isCompressed())
+        return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart+1]-1];
+      else
+        return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart]+m_matrix.innerNonZeroPtr()[m_outerStart]-1];
+    }
+
+    EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+    EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+  protected:
+
+    typename SparseMatrixType::Nested m_matrix;
+    Index m_outerStart;
+    const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+};
+
+
+template<typename _Scalar, int _Options, typename _Index, int BlockRows, int BlockCols>
+class BlockImpl<const SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true,Sparse>
+  : public SparseMatrixBase<Block<const SparseMatrix<_Scalar, _Options, _Index>,BlockRows,BlockCols,true> >
+{
+    typedef SparseMatrix<_Scalar, _Options, _Index> SparseMatrixType;
+    typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _MatrixTypeNested;
+    typedef Block<const SparseMatrixType, BlockRows, BlockCols, true> BlockType;
+public:
+    enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+    EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+protected:
+    enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+public:
+    
+    class InnerIterator: public SparseMatrixType::InnerIterator
+    {
+      public:
+        inline InnerIterator(const BlockType& xpr, Index outer)
+          : SparseMatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+        {}
+        inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+        inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+      protected:
+        Index m_outer;
+    };
+    class ReverseInnerIterator: public SparseMatrixType::ReverseInnerIterator
+    {
+      public:
+        inline ReverseInnerIterator(const BlockType& xpr, Index outer)
+          : SparseMatrixType::ReverseInnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
+        {}
+        inline Index row() const { return IsRowMajor ? m_outer : this->index(); }
+        inline Index col() const { return IsRowMajor ? this->index() : m_outer; }
+      protected:
+        Index m_outer;
+    };
+
+    inline BlockImpl(const SparseMatrixType& xpr, int i)
+      : m_matrix(xpr), m_outerStart(i), m_outerSize(OuterSize)
+    {}
+
+    inline BlockImpl(const SparseMatrixType& xpr, int startRow, int startCol, int blockRows, int blockCols)
+      : m_matrix(xpr), m_outerStart(IsRowMajor ? startRow : startCol), m_outerSize(IsRowMajor ? blockRows : blockCols)
+    {}
+
+    inline const Scalar* valuePtr() const
+    { return m_matrix.valuePtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+    inline const Index* innerIndexPtr() const
+    { return m_matrix.innerIndexPtr() + m_matrix.outerIndexPtr()[m_outerStart]; }
+
+    inline const Index* outerIndexPtr() const
+    { return m_matrix.outerIndexPtr() + m_outerStart; }
+
+    Index nonZeros() const
+    {
+      if(m_matrix.isCompressed())
+        return  std::size_t(m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()])
+              - std::size_t(m_matrix.outerIndexPtr()[m_outerStart]);
+      else if(m_outerSize.value()==0)
+        return 0;
+      else
+        return Map<const Matrix<Index,OuterSize,1> >(m_matrix.innerNonZeroPtr()+m_outerStart, m_outerSize.value()).sum();
+    }
+    
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));
+    }
+    
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index :  m_outerStart);
+    }
 
     const Scalar& lastCoeff() const
     {
@@ -265,7 +390,8 @@ const typename SparseMatrixBase<Derived>::ConstInnerVectorReturnType SparseMatri
   * is col-major (resp. row-major).
   */
 template<typename Derived>
-Block<Derived,Dynamic,Dynamic,true> SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize)
+typename SparseMatrixBase<Derived>::InnerVectorsReturnType
+SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize)
 {
   return Block<Derived,Dynamic,Dynamic,true>(derived(),
                                              IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
@@ -277,7 +403,8 @@ Block<Derived,Dynamic,Dynamic,true> SparseMatrixBase<Derived>::innerVectors(Inde
   * is col-major (resp. row-major). Read-only.
   */
 template<typename Derived>
-const Block<const Derived,Dynamic,Dynamic,true> SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize) const
+const typename SparseMatrixBase<Derived>::ConstInnerVectorsReturnType
+SparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize) const
 {
   return Block<const Derived,Dynamic,Dynamic,true>(derived(),
                                                   IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
@@ -304,8 +431,8 @@ public:
       : m_matrix(xpr),
         m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
         m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
-        m_blockRows(xpr.rows()),
+        m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
-        m_blockCols(xpr.cols())
+        m_blockCols(BlockCols==1 ? 1 : xpr.cols())
     {}
 
     /** Dynamic-size constructor
@@ -407,3 +534,4 @@ public:
 } // end namespace Eigen
 
 #endif // EIGEN_SPARSE_BLOCK_H
+

Eigen/src/SparseCore/SparseCwiseBinaryOp.h

@@ -73,7 +73,8 @@ class CwiseBinaryOpImpl<BinaryOp,Lhs,Rhs,Sparse>::InnerIterator
     typedef internal::sparse_cwise_binary_op_inner_iterator_selector<
       BinaryOp,Lhs,Rhs, InnerIterator> Base;
 
-    EIGEN_STRONG_INLINE InnerIterator(const CwiseBinaryOpImpl& binOp, Index outer)
+    // NOTE: we have to prefix Index by "typename Lhs::" to avoid an ICE with VC11
+    EIGEN_STRONG_INLINE InnerIterator(const CwiseBinaryOpImpl& binOp, typename Lhs::Index outer)
       : Base(binOp.derived(),outer)
     {}
 };
@@ -313,10 +314,10 @@ SparseMatrixBase<Derived>::operator+=(const SparseMatrixBase<OtherDerived>& othe
 
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_STRONG_INLINE const EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE
+EIGEN_STRONG_INLINE const typename SparseMatrixBase<Derived>::template CwiseProductDenseReturnType<OtherDerived>::Type
 SparseMatrixBase<Derived>::cwiseProduct(const MatrixBase<OtherDerived> &other) const
 {
-  return EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE(derived(), other.derived());
+  return typename CwiseProductDenseReturnType<OtherDerived>::Type(derived(), other.derived());
 }
 
 } // end namespace Eigen

Eigen/src/SparseCore/SparseDenseProduct.h

@@ -19,7 +19,10 @@ template<typename Lhs, typename Rhs, int InnerSize> struct SparseDenseProductRet
 
 template<typename Lhs, typename Rhs> struct SparseDenseProductReturnType<Lhs,Rhs,1>
 {
-  typedef SparseDenseOuterProduct<Lhs,Rhs,false> Type;
+  typedef typename internal::conditional<
+    Lhs::IsRowMajor,
+    SparseDenseOuterProduct<Rhs,Lhs,true>,
+    SparseDenseOuterProduct<Lhs,Rhs,false> >::type Type;
 };
 
 template<typename Lhs, typename Rhs, int InnerSize> struct DenseSparseProductReturnType
@@ -29,7 +32,10 @@ template<typename Lhs, typename Rhs, int InnerSize> struct DenseSparseProductRet
 
 template<typename Lhs, typename Rhs> struct DenseSparseProductReturnType<Lhs,Rhs,1>
 {
-  typedef SparseDenseOuterProduct<Rhs,Lhs,true> Type;
+  typedef typename internal::conditional<
+    Rhs::IsRowMajor,
+    SparseDenseOuterProduct<Rhs,Lhs,true>,
+    SparseDenseOuterProduct<Lhs,Rhs,false> >::type Type;
 };
 
 namespace internal {
@@ -114,17 +120,30 @@ class SparseDenseOuterProduct<Lhs,Rhs,Transpose>::InnerIterator : public _LhsNes
     typedef typename SparseDenseOuterProduct::Index Index;
   public:
     EIGEN_STRONG_INLINE InnerIterator(const SparseDenseOuterProduct& prod, Index outer)
-      : Base(prod.lhs(), 0), m_outer(outer), m_factor(prod.rhs().coeff(outer))
+      : Base(prod.lhs(), 0), m_outer(outer), m_factor(get(prod.rhs(), outer, typename internal::traits<Rhs>::StorageKind() ))
-    {
+    { }
-    }
 
     inline Index outer() const { return m_outer; }
-    inline Index row() const { return Transpose ? Base::row() : m_outer; }
+    inline Index row() const { return Transpose ? m_outer : Base::index(); }
-    inline Index col() const { return Transpose ? m_outer : Base::row(); }
+    inline Index col() const { return Transpose ? Base::index() : m_outer; }
 
     inline Scalar value() const { return Base::value() * m_factor; }
 
   protected:
+    static Scalar get(const _RhsNested &rhs, Index outer, Dense = Dense())
+    {
+      return rhs.coeff(outer);
+    }
+    
+    static Scalar get(const _RhsNested &rhs, Index outer, Sparse = Sparse())
+    {
+      typename Traits::_RhsNested::InnerIterator it(rhs, outer);
+      if (it && it.index()==0)
+        return it.value();
+      
+      return Scalar(0);
+    }
+    
     Index m_outer;
     Scalar m_factor;
 };
@@ -161,7 +180,7 @@ struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, R
         typename Res::Scalar tmp(0);
         for(LhsInnerIterator it(lhs,j); it ;++it)
           tmp += it.value() * rhs.coeff(it.index(),c);
-        res.coeffRef(j,c) = alpha * tmp;
+        res.coeffRef(j,c) += alpha * tmp;
       }
     }
   }
@@ -287,15 +306,6 @@ class DenseTimeSparseProduct
     DenseTimeSparseProduct& operator=(const DenseTimeSparseProduct&);
 };
 
-// sparse * dense
-template<typename Derived>
-template<typename OtherDerived>
-inline const typename SparseDenseProductReturnType<Derived,OtherDerived>::Type
-SparseMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
-{
-  return typename SparseDenseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
-}
-
 } // end namespace Eigen
 
 #endif // EIGEN_SPARSEDENSEPRODUCT_H

Eigen/src/SparseCore/SparseMatrix.h

@@ -691,7 +691,8 @@ class SparseMatrix
       m_data.swap(other.m_data);
     }
 
-    /** Sets *this to the identity matrix */
+    /** Sets *this to the identity matrix.
+      * This function also turns the matrix into compressed mode, and drop any reserved memory. */
     inline void setIdentity()
     {
       eigen_assert(rows() == cols() && "ONLY FOR SQUARED MATRICES");
@@ -699,6 +700,8 @@ class SparseMatrix
       Eigen::Map<Matrix<Index, Dynamic, 1> >(&this->m_data.index(0), rows()).setLinSpaced(0, rows()-1);
       Eigen::Map<Matrix<Scalar, Dynamic, 1> >(&this->m_data.value(0), rows()).setOnes();
       Eigen::Map<Matrix<Index, Dynamic, 1> >(this->m_outerIndex, rows()+1).setLinSpaced(0, rows());
+      std::free(m_innerNonZeros);
+      m_innerNonZeros = 0;
     }
     inline SparseMatrix& operator=(const SparseMatrix& other)
     {
@@ -940,7 +943,7 @@ void set_from_triplets(const InputIterator& begin, const InputIterator& end, Spa
   enum { IsRowMajor = SparseMatrixType::IsRowMajor };
   typedef typename SparseMatrixType::Scalar Scalar;
   typedef typename SparseMatrixType::Index Index;
-  SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor> trMat(mat.rows(),mat.cols());
+  SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor,Index> trMat(mat.rows(),mat.cols());
 
   if(begin!=end)
   {
@@ -1178,7 +1181,7 @@ EIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_Index>::Scalar& Sparse
   size_t p = m_outerIndex[outer+1];
   ++m_outerIndex[outer+1];
 
-  float reallocRatio = 1;
+  double reallocRatio = 1;
   if (m_data.allocatedSize()<=m_data.size())
   {
     // if there is no preallocated memory, let's reserve a minimum of 32 elements
@@ -1190,13 +1193,13 @@ EIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_Index>::Scalar& Sparse
     {
       // we need to reallocate the data, to reduce multiple reallocations
       // we use a smart resize algorithm based on the current filling ratio
-      // in addition, we use float to avoid integers overflows
+      // in addition, we use double to avoid integers overflows
-      float nnzEstimate = float(m_outerIndex[outer])*float(m_outerSize)/float(outer+1);
+      double nnzEstimate = double(m_outerIndex[outer])*double(m_outerSize)/double(outer+1);
-      reallocRatio = (nnzEstimate-float(m_data.size()))/float(m_data.size());
+      reallocRatio = (nnzEstimate-double(m_data.size()))/double(m_data.size());
       // furthermore we bound the realloc ratio to:
       //   1) reduce multiple minor realloc when the matrix is almost filled
       //   2) avoid to allocate too much memory when the matrix is almost empty
-      reallocRatio = (std::min)((std::max)(reallocRatio,1.5f),8.f);
+      reallocRatio = (std::min)((std::max)(reallocRatio,1.5),8.);
     }
   }
   m_data.resize(m_data.size()+1,reallocRatio);

Eigen/src/SparseCore/SparseMatrixBase.h

@@ -23,7 +23,14 @@ namespace Eigen {
   * This class can be extended with the help of the plugin mechanism described on the page
   * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_SPARSEMATRIXBASE_PLUGIN.
   */
-template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
+template<typename Derived> class SparseMatrixBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  : public internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+                                            typename NumTraits<typename internal::traits<Derived>::Scalar>::Real,
+                                            EigenBase<Derived> >
+#else
+  : public EigenBase<Derived>
+#endif // not EIGEN_PARSED_BY_DOXYGEN
 {
   public:
 
@@ -36,7 +43,6 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
                      >::type PacketReturnType;
 
     typedef SparseMatrixBase StorageBaseType;
-    typedef EigenBase<Derived> Base;
     
     template<typename OtherDerived>
     Derived& operator=(const EigenBase<OtherDerived> &other)
@@ -132,6 +138,9 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
     inline Derived& derived() { return *static_cast<Derived*>(this); }
     inline Derived& const_cast_derived() const
     { return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }
+
+    typedef internal::special_scalar_op_base<Derived, Scalar, RealScalar, EigenBase<Derived> > Base;
+    using Base::operator*;
 #endif // not EIGEN_PARSED_BY_DOXYGEN
 
 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::SparseMatrixBase
@@ -317,20 +326,18 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
     Derived& operator*=(const Scalar& other);
     Derived& operator/=(const Scalar& other);
 
-    #define EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE \
+    template<typename OtherDerived> struct CwiseProductDenseReturnType {
-      CwiseBinaryOp< \
+      typedef CwiseBinaryOp<internal::scalar_product_op<typename internal::scalar_product_traits<
-        internal::scalar_product_op< \
+                                                          typename internal::traits<Derived>::Scalar,
-          typename internal::scalar_product_traits< \
+                                                          typename internal::traits<OtherDerived>::Scalar
-            typename internal::traits<Derived>::Scalar, \
+                                                        >::ReturnType>,
-            typename internal::traits<OtherDerived>::Scalar \
+                            const Derived,
-          >::ReturnType \
+                            const OtherDerived
-        >, \
+                          > Type;
-        const Derived, \
+    };
-        const OtherDerived \
-      >
 
     template<typename OtherDerived>
-    EIGEN_STRONG_INLINE const EIGEN_SPARSE_CWISE_PRODUCT_RETURN_TYPE
+    EIGEN_STRONG_INLINE const typename CwiseProductDenseReturnType<OtherDerived>::Type
     cwiseProduct(const MatrixBase<OtherDerived> &other) const;
 
     // sparse * sparse
@@ -358,7 +365,8 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
     /** sparse * dense (returns a dense object unless it is an outer product) */
     template<typename OtherDerived>
     const typename SparseDenseProductReturnType<Derived,OtherDerived>::Type
-    operator*(const MatrixBase<OtherDerived> &other) const;
+    operator*(const MatrixBase<OtherDerived> &other) const
+    { return typename SparseDenseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived()); }
     
      /** \returns an expression of P H P^-1 where H is the matrix represented by \c *this */
     SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const
@@ -403,8 +411,10 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
     const ConstInnerVectorReturnType innerVector(Index outer) const;
 
     // set of inner-vectors
-    Block<Derived,Dynamic,Dynamic,true> innerVectors(Index outerStart, Index outerSize);
+    typedef Block<Derived,Dynamic,Dynamic,true> InnerVectorsReturnType;
-    const Block<const Derived,Dynamic,Dynamic,true> innerVectors(Index outerStart, Index outerSize) const;
+    typedef Block<const Derived,Dynamic,Dynamic,true> ConstInnerVectorsReturnType;
+    InnerVectorsReturnType innerVectors(Index outerStart, Index outerSize);
+    const ConstInnerVectorsReturnType innerVectors(Index outerStart, Index outerSize) const;
 
     /** \internal use operator= */
     template<typename DenseDerived>

Eigen/src/SparseCore/SparsePermutation.h

@@ -61,7 +61,7 @@ struct permut_sparsematrix_product_retval
         for(Index j=0; j<m_matrix.outerSize(); ++j)
         {
           Index jp = m_permutation.indices().coeff(j);
-          sizes[((Side==OnTheLeft) ^ Transposed) ? jp : j] = m_matrix.innerVector(((Side==OnTheRight) ^ Transposed) ? jp : j).size();
+          sizes[((Side==OnTheLeft) ^ Transposed) ? jp : j] = m_matrix.innerVector(((Side==OnTheRight) ^ Transposed) ? jp : j).nonZeros();
         }
         tmp.reserve(sizes);
         for(Index j=0; j<m_matrix.outerSize(); ++j)

Eigen/src/SparseCore/SparseTranspose.h

@@ -26,7 +26,7 @@ template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>
     inline Index nonZeros() const { return derived().nestedExpression().nonZeros(); }
 };
 
-// NOTE: VC10 trigger an ICE if don't put typename TransposeImpl<MatrixType,Sparse>:: in front of Index,
+// NOTE: VC10 and VC11 trigger an ICE if don't put typename TransposeImpl<MatrixType,Sparse>:: in front of Index,
 // a typedef typename TransposeImpl<MatrixType,Sparse>::Index Index;
 // does not fix the issue.
 // An alternative is to define the nested class in the parent class itself.
@@ -40,8 +40,8 @@ template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>::InnerItera
     EIGEN_STRONG_INLINE InnerIterator(const TransposeImpl& trans, typename TransposeImpl<MatrixType,Sparse>::Index outer)
       : Base(trans.derived().nestedExpression(), outer)
     {}
-    Index row() const { return Base::col(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
-    Index col() const { return Base::row(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index col() const { return Base::row(); }
 };
 
 template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>::ReverseInnerIterator
@@ -54,8 +54,8 @@ template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>::ReverseInn
     EIGEN_STRONG_INLINE ReverseInnerIterator(const TransposeImpl& xpr, typename TransposeImpl<MatrixType,Sparse>::Index outer)
       : Base(xpr.derived().nestedExpression(), outer)
     {}
-    Index row() const { return Base::col(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
-    Index col() const { return Base::row(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index col() const { return Base::row(); }
 };
 
 } // end namespace Eigen

Eigen/src/SparseCore/SparseUtil.h

@@ -67,7 +67,6 @@ const int InnerRandomAccessPattern  = 0x2 | CoherentAccessPattern;
 const int OuterRandomAccessPattern  = 0x4 | CoherentAccessPattern;
 const int RandomAccessPattern       = 0x8 | OuterRandomAccessPattern | InnerRandomAccessPattern;
 
-template<typename Derived> class SparseMatrixBase;
 template<typename _Scalar, int _Flags = 0, typename _Index = int>  class SparseMatrix;
 template<typename _Scalar, int _Flags = 0, typename _Index = int>  class DynamicSparseMatrix;
 template<typename _Scalar, int _Flags = 0, typename _Index = int>  class SparseVector;
@@ -84,8 +83,10 @@ template<typename Lhs, typename Rhs>        class DenseTimeSparseProduct;
 template<typename Lhs, typename Rhs, bool Transpose> class SparseDenseOuterProduct;
 
 template<typename Lhs, typename Rhs> struct SparseSparseProductReturnType;
-template<typename Lhs, typename Rhs, int InnerSize = internal::traits<Lhs>::ColsAtCompileTime> struct DenseSparseProductReturnType;
+template<typename Lhs, typename Rhs,
-template<typename Lhs, typename Rhs, int InnerSize = internal::traits<Lhs>::ColsAtCompileTime> struct SparseDenseProductReturnType;
+         int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct DenseSparseProductReturnType;         
+template<typename Lhs, typename Rhs,
+         int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct SparseDenseProductReturnType;
 template<typename MatrixType,int UpLo> class SparseSymmetricPermutationProduct;
 
 namespace internal {

Eigen/src/SparseCore/SparseVector.h

@@ -158,6 +158,7 @@ class SparseVector
       
       Index inner = IsColVector ? row : col;
       Index outer = IsColVector ? col : row;
+      EIGEN_ONLY_USED_FOR_DEBUG(outer);
       eigen_assert(outer==0);
       return insert(inner);
     }

Eigen/src/SparseCore/TriangularSolver.h

@@ -69,7 +69,7 @@ struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>
       for(int i=lhs.rows()-1 ; i>=0 ; --i)
       {
         Scalar tmp = other.coeff(i,col);
-        Scalar l_ii = 0;
+        Scalar l_ii(0);
         typename Lhs::InnerIterator it(lhs, i);
         while(it && it.index()<i)
           ++it;

Eigen/src/SparseLU/SparseLU.h

@@ -260,16 +260,16 @@ class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typ
       eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
       // Initialize with the determinant of the row matrix
       Scalar det = Scalar(1.);
-      //Note that the diagonal blocks of U are stored in supernodes,
+      // Note that the diagonal blocks of U are stored in supernodes,
       // which are available in the  L part :)
       for (Index j = 0; j < this->cols(); ++j)
       {
         for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
         {
-          if(it.row() < j) continue;
+          if(it.index() == j)
-          if(it.row() == j)
           {
-            det *= (std::abs)(it.value());
+            using std::abs;
+            det *= abs(it.value());
             break;
           }
         }
@@ -296,7 +296,8 @@ class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typ
            if(it.row() < j) continue;
            if(it.row() == j)
            {
-             det += (std::log)((std::abs)(it.value()));
+             using std::log; using std::abs;
+             det += log(abs(it.value()));
              break;
            }
          }
@@ -304,21 +305,64 @@ class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typ
        return det;
      }
 
-     /** \returns A number representing the sign of the determinant
+    /** \returns A number representing the sign of the determinant
-       *
+      *
-       * \sa absDeterminant(), logAbsDeterminant()
+      * \sa absDeterminant(), logAbsDeterminant()
-       */
+      */
-     Scalar signDeterminant()
+    Scalar signDeterminant()
-     {
+    {
-       eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+      eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
-       return Scalar(m_detPermR);
+      // Initialize with the determinant of the row matrix
-     }
+      Index det = 1;
+      // Note that the diagonal blocks of U are stored in supernodes,
+      // which are available in the  L part :)
+      for (Index j = 0; j < this->cols(); ++j)
+      {
+        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+        {
+          if(it.index() == j)
+          {
+            if(it.value()<0)
+              det = -det;
+            else if(it.value()==0)
+              return 0;
+            break;
+          }
+        }
+      }
+      return det * m_detPermR * m_detPermC;
+    }
+    
+    /** \returns The determinant of the matrix.
+      *
+      * \sa absDeterminant(), logAbsDeterminant()
+      */
+    Scalar determinant()
+    {
+      eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+      // Initialize with the determinant of the row matrix
+      Scalar det = Scalar(1.);
+      // Note that the diagonal blocks of U are stored in supernodes,
+      // which are available in the  L part :)
+      for (Index j = 0; j < this->cols(); ++j)
+      {
+        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+        {
+          if(it.index() == j)
+          {
+            det *= it.value();
+            break;
+          }
+        }
+      }
+      return det * Scalar(m_detPermR * m_detPermC);
+    }
 
   protected:
     // Functions 
     void initperfvalues()
     {
-      m_perfv.panel_size = 1;
+      m_perfv.panel_size = 16;
       m_perfv.relax = 1; 
       m_perfv.maxsuper = 128; 
       m_perfv.rowblk = 16; 
@@ -346,8 +390,8 @@ class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typ
     // values for performance 
     internal::perfvalues<Index> m_perfv; 
     RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
-    Index m_nnzL, m_nnzU; // Nonzeros in L and U factors 
+    Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
-    Index m_detPermR; // Determinant of the coefficient matrix
+    Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
   private:
     // Disable copy constructor 
     SparseLU (const SparseLU& );
@@ -623,7 +667,8 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
       }
       
       // Update the determinant of the row permutation matrix
-      if (pivrow != jj) m_detPermR *= -1;
+      // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
+      if (pivrow != jj) m_detPermR = -m_detPermR;
 
       // Prune columns (0:jj-1) using column jj
       Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu); 
@@ -638,10 +683,13 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
     jcol += panel_size;  // Move to the next panel
   } // end for -- end elimination 
   
+  m_detPermR = m_perm_r.determinant();
+  m_detPermC = m_perm_c.determinant();
+  
   // Count the number of nonzeros in factors 
   Base::countnz(n, m_nnzL, m_nnzU, m_glu); 
   // Apply permutation  to the L subscripts 
-  Base::fixupL(n, m_perm_r.indices(), m_glu); 
+  Base::fixupL(n, m_perm_r.indices(), m_glu);
   
   // Create supernode matrix L 
   m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup); 
@@ -701,8 +749,8 @@ struct SparseLUMatrixUReturnType : internal::no_assignment_operator
       }
       else
       {
-        Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+        Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
-        Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+        Map< Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
         U = A.template triangularView<Upper>().solve(U);
       }
 

Eigen/src/SparseLU/SparseLUImpl.h

@@ -21,6 +21,8 @@ class SparseLUImpl
 {
   public:
     typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+    typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> ScalarMatrix;
+    typedef Map<ScalarMatrix, 0,  OuterStride<> > MappedMatrixBlock;
     typedef Matrix<Index,Dynamic,1> IndexVector; 
     typedef typename ScalarVector::RealScalar RealScalar; 
     typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;

Eigen/src/SparseLU/SparseLU_Memory.h

@@ -153,8 +153,8 @@ Index SparseLUImpl<Scalar,Index>::memInit(Index m, Index n, Index annz, Index lw
 {
   Index& num_expansions = glu.num_expansions; //No memory expansions so far
   num_expansions = 0;
-  glu.nzumax = glu.nzlumax = (std::min)(fillratio * annz / n, m) * n; // estimated number of nonzeros in U 
+  glu.nzumax = glu.nzlumax = (std::min)(fillratio * (annz+1) / n, m) * n; // estimated number of nonzeros in U 
-  glu.nzlmax = (std::max)(Index(4), fillratio) * annz / 4; // estimated  nnz in L factor
+  glu.nzlmax = (std::max)(Index(4), fillratio) * (annz+1) / 4; // estimated  nnz in L factor
   // Return the estimated size to the user if necessary
   Index tempSpace;
   tempSpace = (2*panel_size + 4 + LUNoMarker) * m * sizeof(Index) + (panel_size + 1) * m * sizeof(Scalar);

Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h

@@ -189,8 +189,8 @@ class MappedSuperNodalMatrix<Scalar,Index>::InnerIterator
         m_idval(mat.colIndexPtr()[outer]),
         m_startidval(m_idval),
         m_endidval(mat.colIndexPtr()[outer+1]),
-        m_idrow(mat.rowIndexPtr()[outer]),
+        m_idrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]]),
-        m_endidrow(mat.rowIndexPtr()[outer+1])
+        m_endidrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]+1])
     {}
     inline InnerIterator& operator++()
     { 
@@ -236,7 +236,7 @@ void MappedSuperNodalMatrix<Scalar,Index>::solveInPlace( MatrixBase<Dest>&X) con
     Index n = X.rows(); 
     Index nrhs = X.cols(); 
     const Scalar * Lval = valuePtr();                 // Nonzero values 
-    Matrix<Scalar,Dynamic,Dynamic> work(n, nrhs);     // working vector
+    Matrix<Scalar,Dynamic,Dynamic, ColMajor> work(n, nrhs);     // working vector
     work.setZero();
     for (Index k = 0; k <= nsuper(); k ++)
     {
@@ -267,12 +267,12 @@ void MappedSuperNodalMatrix<Scalar,Index>::solveInPlace( MatrixBase<Dest>&X) con
         Index lda = colIndexPtr()[fsupc+1] - luptr;
         
         // Triangular solve 
-        Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) ); 
+        Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );
-        Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) ); 
+        Map< Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) ); 
         U = A.template triangularView<UnitLower>().solve(U); 
         
         // Matrix-vector product 
-        new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) ); 
+        new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
         work.block(0, 0, nrow, nrhs) = A * U; 
         
         //Begin Scatter 

Eigen/src/SparseLU/SparseLU_column_bmod.h

@@ -162,11 +162,11 @@ Index SparseLUImpl<Scalar,Index>::column_bmod(const Index jcol, const Index nseg
     // points to the beginning of jcol in snode L\U(jsupno) 
     ufirst = glu.xlusup(jcol) + d_fsupc; 
     Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
-    Map<Matrix<Scalar,Dynamic,Dynamic>, 0,  OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) ); 
+    MappedMatrixBlock A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
     VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc); 
     u = A.template triangularView<UnitLower>().solve(u); 
     
-    new (&A) Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) ); 
+    new (&A) MappedMatrixBlock ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
     VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow); 
     l.noalias() -= A * u;
     

Eigen/src/SparseLU/SparseLU_kernel_bmod.h

@@ -56,7 +56,7 @@ EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const int segsi
   // Dense triangular solve -- start effective triangle
   luptr += lda * no_zeros + no_zeros; 
   // Form Eigen matrix and vector 
-  Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );
+  Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );
   Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);
   
   u = A.template triangularView<UnitLower>().solve(u); 
@@ -65,7 +65,7 @@ EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const int segsi
   luptr += segsize;
   const Index PacketSize = internal::packet_traits<Scalar>::size;
   Index ldl = internal::first_multiple(nrow, PacketSize);
-  Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
+  Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
   Index aligned_offset = internal::first_aligned(tempv.data()+segsize, PacketSize);
   Index aligned_with_B_offset = (PacketSize-internal::first_aligned(B.data(), PacketSize))%PacketSize;
   Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );