bump to 3.2.6

(grafted from 75a60d3ac0
)

CMakeLists.txt

@@ -204,7 +204,7 @@ if(NOT MSVC)
 
   option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
   if(EIGEN_TEST_NEON)
-    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon -mcpu=cortex-a"8)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon -mcpu=cortex-a8")
     message(STATUS "Enabling NEON in tests/examples")
   endif()
 

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/Eigen2Support

@@ -14,12 +14,25 @@
 #error Eigen2 support must be enabled by defining EIGEN2_SUPPORT before including any Eigen header
 #endif
 
+#ifndef EIGEN_NO_EIGEN2_DEPRECATED_WARNING
+
+#if defined(__GNUC__) || defined(__INTEL_COMPILER) || defined(__clang__)
+#warning "Eigen2 support is deprecated in Eigen 3.2.x and it will be removed in Eigen 3.3. (Define EIGEN_NO_EIGEN2_DEPRECATED_WARNING to disable this warning)"
+#else
+#pragma message ("Eigen2 support is deprecated in Eigen 3.2.x and it will be removed in Eigen 3.3. (Define EIGEN_NO_EIGEN2_DEPRECATED_WARNING to disable this warning)")
+#endif
+
+#endif // EIGEN_NO_EIGEN2_DEPRECATED_WARNING
+
 #include "src/Core/util/DisableStupidWarnings.h"
 
 /** \ingroup Support_modules
   * \defgroup Eigen2Support_Module Eigen2 support module
-  * This module provides a couple of deprecated functions improving the compatibility with Eigen2.
   *
+  * \warning Eigen2 support is deprecated in Eigen 3.2.x and it will be removed in Eigen 3.3.
+  *
+  * This module provides a couple of deprecated functions improving the compatibility with Eigen2.
+  * 
   * To use it, define EIGEN2_SUPPORT before including any Eigen header
   * \code
   * #define EIGEN2_SUPPORT

Eigen/src/Cholesky/LDLT.h

@@ -16,7 +16,10 @@
 namespace Eigen { 
 
 namespace internal {
-template<typename MatrixType, int UpLo> struct LDLT_Traits;
+  template<typename MatrixType, int UpLo> struct LDLT_Traits;
+
+  // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
+  enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
 }
 
 /** \ingroup Cholesky_Module
@@ -69,7 +72,12 @@ template<typename _MatrixType, int _UpLo> class LDLT
       * The default constructor is useful in cases in which the user intends to
       * perform decompositions via LDLT::compute(const MatrixType&).
       */
-    LDLT() : m_matrix(), m_transpositions(), m_isInitialized(false) {}
+    LDLT() 
+      : m_matrix(), 
+        m_transpositions(), 
+        m_sign(internal::ZeroSign),
+        m_isInitialized(false) 
+    {}
 
     /** \brief Default Constructor with memory preallocation
       *
@@ -81,6 +89,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
       : m_matrix(size, size),
         m_transpositions(size),
         m_temporary(size),
+        m_sign(internal::ZeroSign),
         m_isInitialized(false)
     {}
 
@@ -93,6 +102,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
       : m_matrix(matrix.rows(), matrix.cols()),
         m_transpositions(matrix.rows()),
         m_temporary(matrix.rows()),
+        m_sign(internal::ZeroSign),
         m_isInitialized(false)
     {
       compute(matrix);
@@ -139,7 +149,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
     inline bool isPositive() const
     {
       eigen_assert(m_isInitialized && "LDLT is not initialized.");
-      return m_sign == 1;
+      return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
     }
     
     #ifdef EIGEN2_SUPPORT
@@ -153,7 +163,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
     inline bool isNegative(void) const
     {
       eigen_assert(m_isInitialized && "LDLT is not initialized.");
-      return m_sign == -1;
+      return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
     }
 
     /** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
@@ -225,6 +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.
@@ -235,7 +250,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
     MatrixType m_matrix;
     TranspositionType m_transpositions;
     TmpMatrixType m_temporary;
-    int m_sign;
+    internal::SignMatrix m_sign;
     bool m_isInitialized;
 };
 
@@ -246,7 +261,7 @@ template<int UpLo> struct ldlt_inplace;
 template<> struct ldlt_inplace<Lower>
 {
   template<typename MatrixType, typename TranspositionType, typename Workspace>
-  static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, int* sign=0)
+  static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
   {
     using std::abs;
     typedef typename MatrixType::Scalar Scalar;
@@ -258,36 +273,19 @@ template<> struct ldlt_inplace<Lower>
     if (size <= 1)
     {
       transpositions.setIdentity();
-      if(sign)
-        *sign = numext::real(mat.coeff(0,0))>0 ? 1:-1;
+      if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef;
+      else if (numext::real(mat.coeff(0,0)) < 0) sign = NegativeSemiDef;
+      else sign = ZeroSign;
       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;
-        if(sign) *sign = 0;
-        break;
-      }
-
       transpositions.coeffRef(k) = index_of_biggest_in_corner;
       if(k != index_of_biggest_in_corner)
       {
@@ -318,22 +316,27 @@ 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);
       
-      if(sign)
-      {
-        // LDLT is not guaranteed to work for indefinite matrices, but let's try to get the sign right
-        int newSign = numext::real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
-        if(k == 0)
-          *sign = newSign;
-        else if(*sign != newSign)
-          *sign = 0;
+      // 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) {
+        if (realAkk > 0) sign = Indefinite;
+      } else if (sign == ZeroSign) {
+        if (realAkk > 0) sign = PositiveSemiDef;
+        else if (realAkk < 0) sign = NegativeSemiDef;
       }
     }
 
@@ -399,7 +402,7 @@ template<> struct ldlt_inplace<Lower>
 template<> struct ldlt_inplace<Upper>
 {
   template<typename MatrixType, typename TranspositionType, typename Workspace>
-  static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, int* sign=0)
+  static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
   {
     Transpose<MatrixType> matt(mat);
     return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
@@ -436,6 +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();
 
@@ -444,8 +449,9 @@ 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);
+  internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign);
 
   m_isInitialized = true;
   return *this;
@@ -458,7 +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)
@@ -473,7 +479,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Deri
     for (Index i = 0; i < size; i++)
       m_transpositions.coeffRef(i) = i;
     m_temporary.resize(size);
-    m_sign = sigma>=0 ? 1 : -1;
+    m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
     m_isInitialized = true;
   }
 
@@ -504,16 +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();
-    RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
-				 RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
+    const typename Diagonal<const MatrixType>::RealReturnType vectorD(dec().vectorD());
+    // In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon
+    // 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)
@@ -566,7 +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.
@@ -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

@@ -58,10 +58,12 @@ cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
   res.p       = mat.outerIndexPtr();
   res.i       = mat.innerIndexPtr();
   res.x       = mat.valuePtr();
+  res.z       = 0;
   res.sorted  = 1;
   if(mat.isCompressed())
   {
     res.packed  = 1;
+    res.nz = 0;
   }
   else
   {
@@ -170,6 +172,7 @@ class CholmodBase : internal::noncopyable
     CholmodBase()
       : m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
     {
+      m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
       cholmod_start(&m_cholmod);
     }
 
@@ -241,7 +244,7 @@ class CholmodBase : internal::noncopyable
       return internal::sparse_solve_retval<CholmodBase, Rhs>(*this, b.derived());
     }
     
-    /** Performs a symbolic decomposition on the sparcity of \a matrix.
+    /** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
       *
       * This function is particularly useful when solving for several problems having the same structure.
       * 
@@ -265,7 +268,7 @@ class CholmodBase : internal::noncopyable
     
     /** Performs a numeric decomposition of \a matrix
       *
-      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+      * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
       *
       * \sa analyzePattern()
       */
@@ -302,7 +305,7 @@ class CholmodBase : internal::noncopyable
       {
         this->m_info = NumericalIssue;
       }
-      // TODO optimize this copy by swapping when possible (be carreful with alignment, etc.)
+      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
       dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
       cholmod_free_dense(&x_cd, &m_cholmod);
     }
@@ -323,7 +326,7 @@ class CholmodBase : internal::noncopyable
       {
         this->m_info = NumericalIssue;
       }
-      // TODO optimize this copy by swapping when possible (be carreful with alignment, etc.)
+      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
       dest = viewAsEigen<DestScalar,DestOptions,DestIndex>(*x_cs);
       cholmod_free_sparse(&x_cs, &m_cholmod);
     }
@@ -365,8 +368,8 @@ class CholmodBase : internal::noncopyable
   *
   * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
   * using the Cholmod library.
-  * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Thefore, it has little practical interest.
-  * The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
+  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
   * X and B can be either dense or sparse.
   *
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
@@ -412,8 +415,8 @@ class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimpl
   *
   * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
   * using the Cholmod library.
-  * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Thefore, it has little practical interest.
-  * The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
+  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
   * X and B can be either dense or sparse.
   *
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
@@ -458,7 +461,7 @@ class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimp
   * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
   * using the Cholmod library.
   * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
-  * The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
+  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
   * X and B can be either dense or sparse.
   *
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
@@ -501,7 +504,7 @@ class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSuper
   * \brief A general Cholesky factorization and solver based on Cholmod
   *
   * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
-  * using the Cholmod library. The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
+  * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
   * X and B can be either dense or sparse.
   *
   * This variant permits to change the underlying Cholesky method at runtime.

Eigen/src/Core/Array.h

@@ -210,7 +210,7 @@ class Array
       : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
     {
       Base::_check_template_params();
-      Base::resize(other.rows(), other.cols());
+      Base::_resize_to_match(other);
       *this = other;
     }
 

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
-                       : internal::first_aligned(&dst.coeffRef(0,0), innerSize);
+    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, 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
-               : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+    IsDense = is_same<StorageKind,Dense>::value,
+    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/BooleanRedux.h

@@ -29,9 +29,9 @@ struct all_unroller
 };
 
 template<typename Derived>
-struct all_unroller<Derived, 1>
+struct all_unroller<Derived, 0>
 {
-  static inline bool run(const Derived &mat) { return mat.coeff(0, 0); }
+  static inline bool run(const Derived &/*mat*/) { return true; }
 };
 
 template<typename Derived>
@@ -55,9 +55,9 @@ struct any_unroller
 };
 
 template<typename Derived>
-struct any_unroller<Derived, 1>
+struct any_unroller<Derived, 0>
 {
-  static inline bool run(const Derived &mat) { return mat.coeff(0, 0); }
+  static inline bool run(const Derived & /*mat*/) { return false; }
 };
 
 template<typename Derived>
@@ -131,7 +131,7 @@ inline typename DenseBase<Derived>::Index DenseBase<Derived>::count() const
 
 /** \returns true is \c *this contains at least one Not A Number (NaN).
   *
-  * \sa isFinite()
+  * \sa allFinite()
   */
 template<typename Derived>
 inline bool DenseBase<Derived>::hasNaN() const
@@ -144,7 +144,7 @@ inline bool DenseBase<Derived>::hasNaN() const
   * \sa hasNaN()
   */
 template<typename Derived>
-inline bool DenseBase<Derived>::isFinite() const
+inline bool DenseBase<Derived>::allFinite() const
 {
   return !((derived()-derived()).hasNaN());
 }

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/DenseBase.h

@@ -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
-    /** Copies \a other into *this without evaluating other. \returns a reference to *this. */
+    /** \internal 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);
 
@@ -348,7 +346,7 @@ template<typename Derived> class DenseBase
     bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
     
     inline bool hasNaN() const;
-    inline bool isFinite() const;
+    inline bool allFinite() const;
 
     inline Derived& operator*=(const Scalar& other);
     inline Derived& operator/=(const Scalar& other);
@@ -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;
-    const Replicate<Derived,Dynamic,Dynamic> replicate(Index rowFacor,Index colFactor) const;
+    inline const Replicate<Derived,RowFactor,ColFactor> replicate() 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>();
   }
 };
 

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

@@ -34,7 +34,7 @@ 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
   };
 };

Eigen/src/Core/EigenBase.h

@@ -126,36 +126,6 @@ Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
   return derived();
 }
 
-/** replaces \c *this by \c *this * \a other.
-  *
-  * \returns a reference to \c *this
-  */
-template<typename Derived>
-template<typename OtherDerived>
-inline Derived&
-MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
-{
-  other.derived().applyThisOnTheRight(derived());
-  return derived();
-}
-
-/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
-  */
-template<typename Derived>
-template<typename OtherDerived>
-inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
-{
-  other.derived().applyThisOnTheRight(derived());
-}
-
-/** replaces \c *this by \c *this * \a other. */
-template<typename Derived>
-template<typename OtherDerived>
-inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
-{
-  other.derived().applyThisOnTheLeft(derived());
-}
-
 } // end namespace Eigen
 
 #endif // EIGEN_EIGENBASE_H

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/IO.h

@@ -185,21 +185,22 @@ std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat&
     explicit_precision = fmt.precision;
   }
 
+  std::streamsize old_precision = 0;
+  if(explicit_precision) old_precision = s.precision(explicit_precision);
+
   bool align_cols = !(fmt.flags & DontAlignCols);
   if(align_cols)
   {
     // compute the largest width
-    for(Index j = 1; j < m.cols(); ++j)
+    for(Index j = 0; j < m.cols(); ++j)
       for(Index i = 0; i < m.rows(); ++i)
       {
         std::stringstream sstr;
-        if(explicit_precision) sstr.precision(explicit_precision);
+        sstr.copyfmt(s);
         sstr << m.coeff(i,j);
         width = std::max<Index>(width, Index(sstr.str().length()));
       }
   }
-  std::streamsize old_precision = 0;
-  if(explicit_precision) old_precision = s.precision(explicit_precision);
   s << fmt.matPrefix;
   for(Index i = 0; i < m.rows(); ++i)
   {

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

@@ -304,7 +304,7 @@ class Matrix
       : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
     {
       Base::_check_template_params();
-      Base::resize(other.rows(), other.cols());
+      Base::_resize_to_match(other);
       // FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
       //              go for pure _set() implementations, right?
       *this = other;

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.
-    // On the other hand they confuse MSVC8...
-    #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
+    DiagonalDynamicIndexReturnType diagonal(Index index);
+    ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
 
     #ifdef EIGEN2_SUPPORT
     template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
@@ -510,6 +504,51 @@ template<typename Derived> class MatrixBase
     {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
 };
 
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** replaces \c *this by \c *this * \a other.
+  *
+  * \returns a reference to \c *this
+  *
+  * Example: \include MatrixBase_applyOnTheRight.cpp
+  * Output: \verbinclude MatrixBase_applyOnTheRight.out
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived&
+MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
+{
+  other.derived().applyThisOnTheRight(derived());
+  return derived();
+}
+
+/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
+  *
+  * Example: \include MatrixBase_applyOnTheRight.cpp
+  * Output: \verbinclude MatrixBase_applyOnTheRight.out
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
+{
+  other.derived().applyThisOnTheRight(derived());
+}
+
+/** replaces \c *this by \a other * \c *this.
+  *
+  * Example: \include MatrixBase_applyOnTheLeft.cpp
+  * Output: \verbinclude MatrixBase_applyOnTheLeft.out
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
+{
+  other.derived().applyThisOnTheLeft(derived());
+}
+
 } // end namespace Eigen
 
 #endif // EIGEN_MATRIXBASE_H

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:
 
@@ -553,8 +582,12 @@ struct permut_matrix_product_retval
     template<typename Dest> inline void evalTo(Dest& dst) const
     {
       const Index n = Side==OnTheLeft ? rows() : cols();
-
-      if(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))
+      // 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
+          && 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

@@ -47,7 +47,10 @@ template<> struct check_rows_cols_for_overflow<Dynamic> {
   }
 };
 
-template <typename Derived, typename OtherDerived = Derived, bool IsVector = bool(Derived::IsVectorAtCompileTime)> struct conservative_resize_like_impl;
+template <typename Derived,
+          typename OtherDerived = Derived,
+          bool IsVector = bool(Derived::IsVectorAtCompileTime) && bool(OtherDerived::IsVectorAtCompileTime)>
+struct conservative_resize_like_impl;
 
 template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;
 
@@ -434,6 +437,22 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
     }
 #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)
     {
@@ -570,6 +589,8 @@ 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
@@ -668,8 +689,10 @@ private:
     enum { ThisConstantIsPrivateInPlainObjectBase };
 };
 
+namespace internal {
+
 template <typename Derived, typename OtherDerived, bool IsVector>
-struct internal::conservative_resize_like_impl
+struct conservative_resize_like_impl
 {
   typedef typename Derived::Index Index;
   static void run(DenseBase<Derived>& _this, Index rows, Index cols)
@@ -729,11 +752,14 @@ struct internal::conservative_resize_like_impl
   }
 };
 
-namespace internal {
-
+// Here, the specialization for vectors inherits from the general matrix case
+// to allow calling .conservativeResize(rows,cols) on vectors.
 template <typename Derived, typename OtherDerived>
 struct conservative_resize_like_impl<Derived,OtherDerived,true>
+  : conservative_resize_like_impl<Derived,OtherDerived,false>
 {
+  using conservative_resize_like_impl<Derived,OtherDerived,false>::run;
+  
   typedef typename Derived::Index Index;
   static void run(DenseBase<Derived>& _this, Index size)
   {

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/Ref.h

@@ -94,24 +94,26 @@ struct traits<Ref<_PlainObjectType, _Options, _StrideType> >
   typedef _PlainObjectType PlainObjectType;
   typedef _StrideType StrideType;
   enum {
-    Options = _Options
+    Options = _Options,
+    Flags = traits<Map<_PlainObjectType, _Options, _StrideType> >::Flags | NestByRefBit
   };
 
   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;
   };
-
+  
 };
 
 template<typename Derived>
@@ -171,8 +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;
@@ -182,7 +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;
@@ -194,17 +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,
-               int = Derived::ThisConstantIsPrivateInPlainObjectBase)
+               typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
     #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());
     }
 
@@ -223,13 +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/StableNorm.h

@@ -17,16 +17,29 @@ namespace internal {
 template<typename ExpressionType, typename Scalar>
 inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
 {
-  Scalar max = bl.cwiseAbs().maxCoeff();
-  if (max>scale)
+  using std::max;
+  Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
+  
+  if (maxCoeff>scale)
   {
-    ssq = ssq * numext::abs2(scale/max);
-    scale = max;
-    invScale = Scalar(1)/scale;
+    ssq = ssq * numext::abs2(scale/maxCoeff);
+    Scalar tmp = Scalar(1)/maxCoeff;
+    if(tmp > NumTraits<Scalar>::highest())
+    {
+      invScale = NumTraits<Scalar>::highest();
+      scale = Scalar(1)/invScale;
+    }
+    else
+    {
+      scale = maxCoeff;
+      invScale = tmp;
+    }
   }
-  // TODO if the max is much much smaller than the current scale,
+  
+  // TODO if the maxCoeff is much much smaller than the current scale,
   // then we can neglect this sub vector
-  ssq += (bl*invScale).squaredNorm();
+  if(scale>Scalar(0)) // if scale==0, then bl is 0 
+    ssq += (bl*invScale).squaredNorm();
 }
 
 template<typename Derived>

Eigen/src/Core/Transpose.h

@@ -284,7 +284,8 @@ struct inplace_transpose_selector<MatrixType,false> { // non square matrix
   * Notice however that this method is only useful if you want to replace a matrix by its own transpose.
   * If you just need the transpose of a matrix, use transpose().
   *
-  * \note if the matrix is not square, then \c *this must be a resizable matrix.
+  * \note if the matrix is not square, then \c *this must be a resizable matrix. 
+  * This excludes (non-square) fixed-size matrices, block-expressions and maps.
   *
   * \sa transpose(), adjoint(), adjointInPlace() */
 template<typename Derived>
@@ -315,6 +316,7 @@ inline void DenseBase<Derived>::transposeInPlace()
   * If you just need the adjoint of a matrix, use adjoint().
   *
   * \note if the matrix is not square, then \c *this must be a resizable matrix.
+  * This excludes (non-square) fixed-size matrices, block-expressions and maps.
   *
   * \sa transpose(), adjoint(), transposeInPlace() */
 template<typename 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/VectorwiseOp.h

@@ -50,7 +50,7 @@ struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
     MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
     Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
     Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
-    TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime
+    TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime :  MatrixType::ColsAtCompileTime
   };
   #if EIGEN_GNUC_AT_LEAST(3,4)
   typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
@@ -58,7 +58,8 @@ struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
   typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
   #endif
   enum {
-    CoeffReadCost = TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
+    CoeffReadCost = TraversalSize==Dynamic ? Dynamic
+                  : TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
   };
 };
 }

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
-#define __pld(x) asm volatile ( "   pld [%[addr]]\n" :: [addr] "r" (x) : "cc" );
+
+// arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
+// 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<int>(const int*     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) { 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 */
@@ -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)
@@ -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.
@@ -442,8 +442,11 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
   return _mm_xor_ps(y, sign_bit);
 }
 
+#if EIGEN_FAST_MATH
+
 // This is based on Quake3's fast inverse square root.
 // For detail see here: http://www.beyond3d.com/content/articles/8/
+// It lacks 1 (or 2 bits in some rare cases) of precision, and does not handle negative, +inf, or denormalized numbers correctly.
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet4f psqrt<Packet4f>(const Packet4f& _x)
 {
@@ -457,6 +460,14 @@ Packet4f psqrt<Packet4f>(const Packet4f& _x)
   return pmul(_x,x);
 }
 
+#else
+
+template<> EIGEN_STRONG_INLINE Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
+
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
+
 } // end namespace internal
 
 } // end namespace Eigen

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

@@ -83,7 +83,8 @@ template<> struct packet_traits<double> : default_packet_traits
     size=2,
 
     HasDiv  = 1,
-    HasExp  = 1
+    HasExp  = 1,
+    HasSqrt = 1
   };
 };
 template<> struct packet_traits<int>    : default_packet_traits
@@ -507,8 +508,8 @@ template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
   // for GCC (eg., it does not like using std::min after the pstore !!)
   EIGEN_ALIGN16 int aux[4];
   pstore(aux, a);
-  register int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
-  register int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
+  int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
+  int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
   return aux0<aux2 ? aux0 : aux2;
 }
 
@@ -528,8 +529,8 @@ template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
   // for GCC (eg., it does not like using std::min after the pstore !!)
   EIGEN_ALIGN16 int aux[4];
   pstore(aux, a);
-  register int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
-  register int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
+  int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
+  int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
   return aux0>aux2 ? aux0 : aux2;
 }
 

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.coeff(row, 0) * rhs.coeff(0, col);
-      for(Index i = 1; i < lhs.cols(); ++i)
-        res += lhs.coeff(row, i) * rhs.coeff(i, col);
+    res = (lhs.row(row).transpose().cwiseProduct( rhs.col(col) )).sum();
   }
 };
 
@@ -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_impl<DefaultTraversal,UnrollingIndex,Lhs,Rhs,RetScalar>::run(row, col, lhs, rhs, res);
+    product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
     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 = pmul(pset1<Packet>(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
-      for(Index i = 1; i < lhs.cols(); ++i)
-        res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
+    res = pset1<Packet>(0);
+    for(Index i = 0; i < lhs.cols(); ++i)
+      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 = pmul(lhs.template packet<LoadMode>(row, 0), pset1<Packet>(rhs.coeff(0, col)));
-      for(Index i = 1; i < lhs.cols(); ++i)
-        res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
+    res = pset1<Packet>(0);
+    for(Index i = 0; i < lhs.cols(); ++i)
+      res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
   }
 };
 

Eigen/src/Core/products/GeneralBlockPanelKernel.h

@@ -1128,6 +1128,8 @@ EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, Pack1, Pack2, StorageOrder,
   enum { PacketSize = packet_traits<Scalar>::size };
 
   EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
+  EIGEN_UNUSED_VARIABLE(stride)
+  EIGEN_UNUSED_VARIABLE(offset)
   eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
   eigen_assert( (StorageOrder==RowMajor) || ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) );
   conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
@@ -1215,6 +1217,8 @@ EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, ColMajor, Conjugate, Pan
   ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
 {
   EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
+  EIGEN_UNUSED_VARIABLE(stride)
+  EIGEN_UNUSED_VARIABLE(offset)
   eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
   conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
   Index packet_cols = (cols/nr) * nr;
@@ -1266,6 +1270,8 @@ EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, nr, RowMajor, Conjugate, Pan
   ::operator()(Scalar* blockB, const Scalar* rhs, Index rhsStride, Index depth, Index cols, Index stride, Index offset)
 {
   EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
+  EIGEN_UNUSED_VARIABLE(stride)
+  EIGEN_UNUSED_VARIABLE(offset)
   eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
   conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
   Index packet_cols = (cols/nr) * nr;

Eigen/src/Core/products/GeneralMatrixVector.h

@@ -52,11 +52,7 @@ EIGEN_DONT_INLINE static void run(
   Index rows, Index cols,
   const LhsScalar* lhs, Index lhsStride,
   const RhsScalar* rhs, Index rhsIncr,
-  ResScalar* res, Index
-  #ifdef EIGEN_INTERNAL_DEBUGGING
-    resIncr
-  #endif
-  , RhsScalar alpha);
+  ResScalar* res, Index resIncr, RhsScalar alpha);
 };
 
 template<typename Index, typename LhsScalar, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs, int Version>
@@ -64,12 +60,9 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,Co
   Index rows, Index cols,
   const LhsScalar* lhs, Index lhsStride,
   const RhsScalar* rhs, Index rhsIncr,
-  ResScalar* res, Index
-  #ifdef EIGEN_INTERNAL_DEBUGGING
-    resIncr
-  #endif
-  , RhsScalar alpha)
+  ResScalar* res, Index resIncr, RhsScalar alpha)
 {
+  EIGEN_UNUSED_VARIABLE(resIncr)
   eigen_internal_assert(resIncr==1);
   #ifdef _EIGEN_ACCUMULATE_PACKETS
   #error _EIGEN_ACCUMULATE_PACKETS has already been defined
@@ -265,7 +258,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,Co
         // process aligned result's coeffs
         if ((size_t(lhs0+alignedStart)%sizeof(LhsPacket))==0)
           for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
-            pstore(&res[i], pcj.pmadd(ploadu<LhsPacket>(&lhs0[i]), ptmp0, pload<ResPacket>(&res[i])));
+            pstore(&res[i], pcj.pmadd(pload<LhsPacket>(&lhs0[i]), ptmp0, pload<ResPacket>(&res[i])));
         else
           for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
             pstore(&res[i], pcj.pmadd(ploadu<LhsPacket>(&lhs0[i]), ptmp0, pload<ResPacket>(&res[i])));

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)
-  for(Index i=0; i<threads; ++i)
+  #pragma omp parallel num_threads(threads)
   {
+    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/SelfadjointMatrixVector.h

@@ -79,8 +79,8 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
   for (Index j=FirstTriangular ? bound : 0;
        j<(FirstTriangular ? size : bound);j+=2)
   {
-    register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
-    register const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
+    const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+    const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
 
     Scalar t0 = cjAlpha * rhs[j];
     Packet ptmp0 = pset1<Packet>(t0);
@@ -147,7 +147,7 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
   }
   for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
   {
-    register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+    const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
 
     Scalar t1 = cjAlpha * rhs[j];
     Scalar t2(0);

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/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/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

@@ -12,8 +12,8 @@
 #define EIGEN_MACROS_H
 
 #define EIGEN_WORLD_VERSION 3
-#define EIGEN_MAJOR_VERSION 1
-#define EIGEN_MINOR_VERSION 92
+#define EIGEN_MAJOR_VERSION 2
+#define EIGEN_MINOR_VERSION 6
 
 #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 +96,13 @@
 #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
 #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:
@@ -238,11 +245,16 @@
 #endif
 
 // Suppresses 'unused variable' warnings.
-#define EIGEN_UNUSED_VARIABLE(var) (void)var;
+namespace Eigen {
+  namespace internal {
+    template<typename T> void ignore_unused_variable(const T&) {}
+  }
+}
+#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
 
 #if !defined(EIGEN_ASM_COMMENT)
   #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
-    #define EIGEN_ASM_COMMENT(X)  asm("#" X)
+    #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
   #else
     #define EIGEN_ASM_COMMENT(X)
   #endif
@@ -266,6 +278,7 @@
   #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
@@ -284,7 +297,8 @@
 #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
@@ -300,7 +314,7 @@
 // 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)
@@ -319,8 +333,11 @@
   }
 #endif
 
-#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
-  EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+/** \internal
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
 
 /**
 * Just a side note. Commenting within defines works only by documenting

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,
-         PacketAlignedMask = PacketSize-1
-  };
+  static const Index PacketSize = packet_traits<Scalar>::size;
+  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
@@ -578,7 +579,7 @@ template<typename T> class aligned_stack_memory_handler
   */
 #ifdef EIGEN_ALLOCA
 
-  #ifdef __arm__
+  #if defined(__arm__) || defined(_WIN32)
     #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((reinterpret_cast<size_t>(EIGEN_ALLOCA(SIZE+16)) & ~(size_t(15))) + 16)
   #else
     #define EIGEN_ALIGNED_ALLOCA EIGEN_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) \
@@ -634,7 +634,9 @@ template<typename T> class aligned_stack_memory_handler
       /* memory allocated we can safely let the default implementation handle */ \
       /* this particular case. */ \
       static void *operator new(size_t size, void *ptr) { return ::operator new(size,ptr); } \
+      static void *operator new[](size_t size, void* ptr) { return ::operator new[](size,ptr); } \
       void operator delete(void * memory, void *ptr) throw() { return ::operator delete(memory,ptr); } \
+      void operator delete[](void * memory, void *ptr) throw() { return ::operator delete[](memory,ptr); } \
       /* nothrow-new (returns zero instead of std::bad_alloc) */ \
       EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
       void operator delete(void *ptr, const std::nothrow_t&) throw() { \
@@ -729,15 +731,6 @@ public:
         ::new( p ) T( value );
     }
 
-    // Support for c++11
-#if (__cplusplus >= 201103L)
-    template<typename... Args>
-    void  construct(pointer p, Args&&... args)
-    {
-      ::new(p) T(std::forward<Args>(args)...);
-    }
-#endif
-
     void destroy( pointer p )
     {
         p->~T();
@@ -784,9 +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)
@@ -928,13 +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);
 }

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/Eigen2Support/SVD.h

@@ -512,8 +512,7 @@ template<typename MatrixType>
 template<typename OtherDerived, typename ResultType>
 bool SVD<MatrixType>::solve(const MatrixBase<OtherDerived> &b, ResultType* result) const
 {
-  const int rows = m_matU.rows();
-  ei_assert(b.rows() == rows);
+  ei_assert(b.rows() == m_matU.rows());
 
   Scalar maxVal = m_sigma.cwise().abs().maxCoeff();
   for (int j=0; j<b.cols(); ++j)

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)
-      s = norm;
-    if (abs(m_matT.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
+    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;
-    if (a_over_3 > Scalar(0))
+    Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;
+    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;
-    if (q > Scalar(0))
+    Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
+    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 theta = atan2(sqrt(-q),half_b)*s_inv3;
+    Scalar rho = sqrt(a_over_3);
+    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(1) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
-    roots(2) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_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));
-    }
+    // roots are already sorted, since cos is monotonically decreasing on [0, pi]
+    roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)
+    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;
   }
-  
+
+  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.
-    Scalar scale = mat.cwiseAbs().maxCoeff();
-    MatrixType scaledMat = mat / scale;
+    // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
+    Scalar shift = mat.trace() / Scalar(3);
+    // 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;
-        d0 = d0 > d1 ? d1 : d0;
-
-        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
+        Index k(0), l(2);
+        if(d0 > d1)
         {
-          n = (cross = tmp.row(0).cross(tmp.row(2))).squaredNorm();
-
-          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;
-            }
-          }
+          std::swap(k,l);
+          d0 = d1;
         }
 
-        tmp = scaledMat;
-        tmp.diagonal().array() -= eivals(1);
-
-        if(d0<=Eigen::NumTraits<Scalar>::epsilon())
-          eivecs.col(1) = eivecs.col(k).unitOrthogonal();
-        else
+        // Compute the eigenvector of index k
         {
-          n = (cross = eivecs.col(k).cross(tmp.row(0).normalized())).squaredNorm();
-          if(n>safeNorm2)
-            eivecs.col(1) = cross / sqrt(n);
-          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();
+          tmp.diagonal().array () -= eivals(k);
+          // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.
+          extract_kernel(tmp, eivecs.col(k), eivecs.col(l));
         }
 
-        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);
-      Scalar a2 = numext::abs2(scaledMat(0,0));
-      Scalar c2 = numext::abs2(scaledMat(1,1));
-      Scalar b2 = numext::abs2(scaledMat(1,0));
-      if(a2>c2)
+      if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())
       {
-        eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
-        eivecs.col(1) /= sqrt(a2+b2);
+        eivecs.setIdentity();
       }
       else
       {
-        eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
-        eivecs.col(1) /= sqrt(c2+b2);
-      }
+        scaledMat.diagonal().array () -= eivals(1);
+        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,StorageOrder> > q(matrixQ,n,n);
+      Map<Matrix<Scalar,Dynamic,Dynamic,ColMajor> > 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
-  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  * \tparam _Scalar the type of the scalar coefficients
+  * \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)
-  {
-    typename internal::nested<Derived,2>::type p(a_p.derived());
-    m_min = p;
-    m_max = p;
-  }
+  inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
+  { }
 
   ~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());
-    return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
+    typename internal::nested<Derived,2>::type p_n(p.derived());
+    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());
-    m_min = m_min.cwiseMin(p);
-    m_max = m_max.cwiseMax(p);
+    typename internal::nested<Derived,2>::type p_n(p.derived());
+    m_min = m_min.cwiseMin(p_n);
+    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/EulerAngles.h

@@ -28,7 +28,7 @@ namespace Eigen {
   *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
   * This corresponds to the right-multiply conventions (with right hand side frames).
   * 
-  * The returned angles are in the ranges [0:pi]x[0:pi]x[-pi:pi].
+  * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
   * 
   * \sa class AngleAxis
   */

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()
@@ -150,10 +150,6 @@ public:
   /** \returns the conjugated quaternion */
   Quaternion<Scalar> conjugate() const;
 
-  /** \returns an interpolation for a constant motion between \a other and \c *this
-    * \a t in [0;1]
-    * see http://en.wikipedia.org/wiki/Slerp
-    */
   template<class OtherDerived> Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
 
   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
@@ -165,7 +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
     *
@@ -194,11 +190,11 @@ public:
   * \brief The quaternion class used to represent 3D orientations and rotations
   *
   * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  * \tparam _Options controls the memory alignement of the coeffecients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
+  * \tparam _Options controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
   *
   * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
   * orientations and rotations of objects in three dimensions. Compared to other representations
-  * like Euler angles or 3x3 matrices, quatertions offer the following advantages:
+  * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
   * \li \b compact storage (4 scalars)
   * \li \b efficient to compose (28 flops),
   * \li \b stable spherical interpolation
@@ -207,6 +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
   */
 
@@ -233,7 +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;
@@ -343,12 +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. */
@@ -380,12 +378,12 @@ 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
       *
-      * 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. */
@@ -399,16 +397,16 @@ class Map<Quaternion<_Scalar>, _Options >
 };
 
 /** \ingroup Geometry_Module
-  * Map an unaligned array of single precision scalar as a quaternion */
+  * Map an unaligned array of single precision scalars as a quaternion */
 typedef Map<Quaternion<float>, 0>         QuaternionMapf;
 /** \ingroup Geometry_Module
-  * Map an unaligned array of double precision scalar as a quaternion */
+  * Map an unaligned array of double precision scalars as a quaternion */
 typedef Map<Quaternion<double>, 0>        QuaternionMapd;
 /** \ingroup Geometry_Module
-  * Map a 16-bits aligned array of double precision scalars as a quaternion */
+  * Map a 16-byte aligned array of single precision scalars as a quaternion */
 typedef Map<Quaternion<float>, Aligned>   QuaternionMapAlignedf;
 /** \ingroup Geometry_Module
-  * Map a 16-bits aligned array of double precision scalars as a quaternion */
+  * Map a 16-byte aligned array of double precision scalars as a quaternion */
 typedef Map<Quaternion<double>, Aligned>  QuaternionMapAlignedd;
 
 /***************************************************************************
@@ -463,12 +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;
@@ -579,7 +577,7 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri
   Scalar c = v1.dot(v0);
 
   // if dot == -1, vectors are nearly opposites
-  // => accuraletly compute the rotation axis by computing the
+  // => accurately compute the rotation axis by computing the
   //    intersection of the two planes. This is done by solving:
   //       x^T v0 = 0
   //       x^T v1 = 0
@@ -588,7 +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);
@@ -639,7 +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
   {
@@ -669,16 +667,19 @@ 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));
-  if (d>=1.0)
-    return Scalar(0);
-  return static_cast<Scalar>(2 * acos(d));
+  Quaternion<Scalar> d = (*this) * other.conjugate();
+  return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
 }
 
+ 
+    
 /** \returns the spherical linear interpolation between the two quaternions
-  * \c *this and \a other at the parameter \a t
+  * \c *this and \a other at the parameter \a t in [0;1].
+  * 
+  * This represents an interpolation for a constant motion between \c *this and \a other,
+  * see also http://en.wikipedia.org/wiki/Slerp.
   */
 template <class Derived>
 template <class OtherDerived>
@@ -709,7 +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)
-      makeAffine();
+    internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
   }
 
   inline Transform(const Transform& other)
@@ -530,9 +531,9 @@ public:
 
   inline Transform& operator=(const UniformScaling<Scalar>& t);
   inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
-  inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Isometry)> operator*(const UniformScaling<Scalar>& s) const
+  inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode))> operator*(const UniformScaling<Scalar>& s) const
   {
-    Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Isometry),Options> res = *this;
+    Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode)),Options> res = *this;
     res.scale(s.factor());
     return res;
   }
@@ -591,11 +592,7 @@ public:
     */
   void makeAffine()
   {
-    if(int(Mode)!=int(AffineCompact))
-    {
-      matrix().template block<1,Dim>(Dim,0).setZero();
-      matrix().coeffRef(Dim,Dim) = Scalar(1);
-    }
+    internal::transform_make_affine<int(Mode)>::run(m_matrix);
   }
 
   /** \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
-  * 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.
+  * One can control the start using the solveWithGuess() method.
   * 
   * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
   */

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 _UpLo the triangular part that will be used for the computations. It can be Lower
-  *               or Upper. Default is Lower.
+  * \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,
+  *               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
-  * 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.
+  * One can control the start using the solveWithGuess() method.
   * 
   * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
   */
@@ -213,6 +200,10 @@ 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 +213,7 @@ public:
       m_error = Base::m_tolerance;
 
       typename Dest::ColXpr xj(x,j);
-      internal::conjugate_gradient(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj,
-                                   Base::m_preconditioner, m_iterations, m_error);
+      internal::conjugate_gradient(MatrixWrapperType(*mp_matrix), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
     }
 
     m_isInitialized = true;
@@ -234,7 +224,7 @@ 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;
     }
 
@@ -235,6 +234,8 @@ void IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat)
   m_Pinv  = m_P.inverse(); // ... and the inverse permutation
 
   m_analysisIsOk = true;
+  m_factorizationIsOk = false;
+  m_isInitialized = false;
 }
 
 template <typename Scalar>
@@ -442,6 +443,7 @@ void IncompleteLUT<Scalar>::factorize(const _MatrixType& amat)
   m_lu.makeCompressed();
 
   m_factorizationIsOk = true;
+  m_isInitialized = m_factorizationIsOk;
   m_info = Success;
 }
 

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
-  * is decomposed as A = PLUQ where L is unit-lower-triangular, U is upper-triangular, and P and Q
-  * are permutation matrices. This is a rank-revealing LU decomposition. The eigenvalues (diagonal
-  * coefficients) of U are sorted in such a way that any zeros are at the end.
+  * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is
+  * decomposed as \f$ A = P^{-1} L U Q^{-1} \f$ where L is unit-lower-triangular, U is
+  * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU
+  * 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}.
- * This function is provided for debug purpose. */
+ * i.e., it returns the product: \f$ P^{-1} L U Q^{-1} \f$.
+ * 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
       *
@@ -349,7 +350,7 @@ template<typename _MatrixType> class ColPivHouseholderQR
       return m_usePrescribedThreshold ? m_prescribedThreshold
       // this formula comes from experimenting (see "LU precision tuning" thread on the list)
       // and turns out to be identical to Higham's formula used already in LDLt.
-                                      : NumTraits<Scalar>::epsilon() * m_qr.diagonalSize();
+                                      : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
     }
 
     /** \returns the number of nonzero pivots in the QR decomposition.
@@ -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,
-    // terminate to avoid generating nan/inf values.
-    // Note that here, if we test instead for "biggest == 0", we get a failure every 1000 (or so)
-    // 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))
-    {
+    // Track the number of meaningful pivots but do not stop the decomposition to make
+    // sure that the initial matrix is properly reproduced. See bug 941.
+    if(m_nonzero_pivots==size && 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

@@ -63,9 +63,10 @@ template<typename _MatrixType> class FullPivHouseholderQR
     typedef typename MatrixType::Index Index;
     typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;
     typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
-    typedef Matrix<Index, 1, ColsAtCompileTime, RowMajor, 1, MaxColsAtCompileTime> IntRowVectorType;
+    typedef Matrix<Index, 1,
+                   EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1,
+                   EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> IntDiagSizeVectorType;
     typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
-    typedef typename internal::plain_col_type<MatrixType, Index>::type IntColVectorType;
     typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
     typedef typename internal::plain_col_type<MatrixType>::type ColVectorType;
 
@@ -93,10 +94,10 @@ template<typename _MatrixType> class FullPivHouseholderQR
     FullPivHouseholderQR(Index rows, Index cols)
       : m_qr(rows, cols),
         m_hCoeffs((std::min)(rows,cols)),
-        m_rows_transpositions(rows),
-        m_cols_transpositions(cols),
+        m_rows_transpositions((std::min)(rows,cols)),
+        m_cols_transpositions((std::min)(rows,cols)),
         m_cols_permutation(cols),
-        m_temp((std::min)(rows,cols)),
+        m_temp(cols),
         m_isInitialized(false),
         m_usePrescribedThreshold(false) {}
 
@@ -115,10 +116,10 @@ template<typename _MatrixType> class FullPivHouseholderQR
     FullPivHouseholderQR(const MatrixType& matrix)
       : m_qr(matrix.rows(), matrix.cols()),
         m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
-        m_rows_transpositions(matrix.rows()),
-        m_cols_transpositions(matrix.cols()),
+        m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),
+        m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
         m_cols_permutation(matrix.cols()),
-        m_temp((std::min)(matrix.rows(), matrix.cols())),
+        m_temp(matrix.cols()),
         m_isInitialized(false),
         m_usePrescribedThreshold(false)
     {
@@ -126,11 +127,12 @@ template<typename _MatrixType> class FullPivHouseholderQR
     }
 
     /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
-      * *this is the QR decomposition, if any exists.
+      * \c *this is the QR decomposition.
       *
       * \param b the right-hand-side of the equation to solve.
       *
-      * \returns a solution.
+      * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,
+      * and an arbitrary solution otherwise.
       *
       * \note The case where b is a matrix is not yet implemented. Also, this
       *       code is space inefficient.
@@ -172,7 +174,7 @@ template<typename _MatrixType> class FullPivHouseholderQR
     }
 
     /** \returns a const reference to the vector of indices representing the rows transpositions */
-    const IntColVectorType& rowsTranspositions() const
+    const IntDiagSizeVectorType& rowsTranspositions() const
     {
       eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
       return m_rows_transpositions;
@@ -344,7 +346,7 @@ template<typename _MatrixType> class FullPivHouseholderQR
       return m_usePrescribedThreshold ? m_prescribedThreshold
       // this formula comes from experimenting (see "LU precision tuning" thread on the list)
       // and turns out to be identical to Higham's formula used already in LDLt.
-                                      : NumTraits<Scalar>::epsilon() * m_qr.diagonalSize();
+                                      : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
     }
 
     /** \returns the number of nonzero pivots in the QR decomposition.
@@ -366,10 +368,16 @@ 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;
-    IntColVectorType m_rows_transpositions;
-    IntRowVectorType m_cols_transpositions;
+    IntDiagSizeVectorType m_rows_transpositions;
+    IntDiagSizeVectorType m_cols_transpositions;
     PermutationType m_cols_permutation;
     RowVectorType m_temp;
     bool m_isInitialized, m_usePrescribedThreshold;
@@ -405,6 +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();
@@ -415,10 +425,10 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
 
   m_temp.resize(cols);
 
-  m_precision = NumTraits<Scalar>::epsilon() * size;
+  m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);
 
-  m_rows_transpositions.resize(matrix.rows());
-  m_cols_transpositions.resize(matrix.cols());
+  m_rows_transpositions.resize(size);
+  m_cols_transpositions.resize(size);
   Index number_of_transpositions = 0;
 
   RealScalar biggest(0);
@@ -516,17 +526,6 @@ struct solve_retval<FullPivHouseholderQR<_MatrixType>, Rhs>
                                   dec().hCoeffs().coeff(k), &temp.coeffRef(0));
     }
 
-    if(!dec().isSurjective())
-    {
-      // is c is in the image of R ?
-      RealScalar biggest_in_upper_part_of_c = c.topRows(   dec().rank()     ).cwiseAbs().maxCoeff();
-      RealScalar biggest_in_lower_part_of_c = c.bottomRows(rows-dec().rank()).cwiseAbs().maxCoeff();
-      // FIXME brain dead
-      const RealScalar m_precision = NumTraits<Scalar>::epsilon() * (std::min)(rows,cols);
-      // this internal:: prefix is needed by at least gcc 3.4 and ICC
-      if(!internal::isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision))
-        return;
-    }
     dec().matrixQR()
        .topLeftCorner(dec().rank(), dec().rank())
        .template triangularView<Upper>()
@@ -548,14 +547,14 @@ template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType
 {
 public:
   typedef typename MatrixType::Index Index;
-  typedef typename internal::plain_col_type<MatrixType, Index>::type IntColVectorType;
+  typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType;
   typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
   typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,
                  MatrixType::MaxRowsAtCompileTime> WorkVectorType;
 
   FullPivHouseholderQRMatrixQReturnType(const MatrixType&       qr,
                                         const HCoeffsType&      hCoeffs,
-                                        const IntColVectorType& rowsTranspositions)
+                                        const IntDiagSizeVectorType& rowsTranspositions)
     : m_qr(qr),
       m_hCoeffs(hCoeffs),
       m_rowsTranspositions(rowsTranspositions)
@@ -595,7 +594,7 @@ public:
 protected:
   typename MatrixType::Nested m_qr;
   typename HCoeffsType::Nested m_hCoeffs;
-  typename IntColVectorType::Nested m_rowsTranspositions;
+  typename IntDiagSizeVectorType::Nested m_rowsTranspositions;
 };
 
 } // end namespace internal

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>
-void householder_qr_inplace_blocked(MatrixQR& mat, HCoeffs& hCoeffs,
-                                       typename MatrixQR::Index maxBlockSize=32,
-                                       typename MatrixQR::Scalar* tempData = 0)
+template<typename MatrixQR, typename HCoeffs,
+  typename MatrixQRScalar = typename MatrixQR::Scalar,
+  bool InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 && HCoeffs::InnerStrideAtCompileTime == 1)>
+struct householder_qr_inplace_blocked
 {
-  typedef typename MatrixQR::Index Index;
-  typedef typename MatrixQR::Scalar Scalar;
-  typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;
-
-  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)
+  // This is specialized for MKL-supported Scalar types in HouseholderQR_MKL.h
+  static void run(MatrixQR& mat, HCoeffs& hCoeffs,
+      typename MatrixQR::Index maxBlockSize=32,
+      typename MatrixQR::Scalar* tempData = 0)
   {
-    tempVector.resize(cols);
-    tempData = tempVector.data();
-  }
+    typedef typename MatrixQR::Index Index;
+    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;
-  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)
+    typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;
+    TempType tempVector;
+    if(tempData==0)
     {
-      BlockType A21_22 = mat.block(k,k+bs,brows,tcols);
-      apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint());
+      tempVector.resize(cols);
+      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, \
-                                       typename MatrixQR::Index maxBlockSize=32, \
-                                       EIGTYPE* tempData = 0) \
+struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \
 { \
-  lapack_int m = mat.rows(); \
-  lapack_int n = mat.cols(); \
-  lapack_int lda = 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(); \
-\
-}
+  static void run(MatrixQR& mat, HCoeffs& hCoeffs, \
+      typename MatrixQR::Index = 32, \
+      typename MatrixQR::Scalar* = 0) \
+  { \
+    lapack_int m = (lapack_int) mat.rows(); \
+    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

@@ -64,17 +64,13 @@ class SPQR
     typedef PermutationMatrix<Dynamic, Dynamic> PermutationType;
   public:
     SPQR() 
-    : m_ordering(SPQR_ORDERING_DEFAULT),
-      m_allow_tol(SPQR_DEFAULT_TOL),
-      m_tolerance (NumTraits<Scalar>::epsilon())
+      : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
     { 
       cholmod_l_start(&m_cc);
     }
     
-    SPQR(const _MatrixType& matrix) 
-    : m_ordering(SPQR_ORDERING_DEFAULT),
-      m_allow_tol(SPQR_DEFAULT_TOL),
-      m_tolerance (NumTraits<Scalar>::epsilon())
+    SPQR(const _MatrixType& matrix)
+    : m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
     {
       cholmod_l_start(&m_cc);
       compute(matrix);
@@ -82,21 +78,43 @@ class SPQR
     
     ~SPQR()
     {
-      // Calls SuiteSparseQR_free()
+      SPQR_free();
+      cholmod_l_finish(&m_cc);
+    }
+    void SPQR_free()
+    {
       cholmod_l_free_sparse(&m_H, &m_cc);
       cholmod_l_free_sparse(&m_cR, &m_cc);
       cholmod_l_free_dense(&m_HTau, &m_cc);
       std::free(m_E);
       std::free(m_HPinv);
-      cholmod_l_finish(&m_cc);
     }
+
     void compute(const _MatrixType& matrix)
     {
+      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)
@@ -112,7 +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. 
@@ -137,16 +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
-      Dest 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));
-      y.bottomRows(cols()-rk).setZero();
+      y2 = y;
+      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;
     }
@@ -189,7 +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; }
@@ -222,6 +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

@@ -375,14 +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);
-      z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
-      work_matrix.row(q) *= z;
-      if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+      if(work_matrix.coeff(q,q)!=Scalar(0))
+      {
+        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+        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
     {
@@ -412,6 +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));
@@ -425,9 +431,11 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   }
   else
   {
-    RealScalar u = d / t;
-    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
-    rot1.s() = rot1.c() * u;
+    RealScalar t2d2 = numext::hypot(t,d);
+    rot1.c() = abs(t)/t2d2;
+    rot1.s() = d/t2d2;
+    if(t<RealScalar(0))
+      rot1.s() = -rot1.s();
   }
   m.applyOnTheLeft(0,1,rot1);
   j_right->makeJacobi(m,0,1);
@@ -528,8 +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)
     {}
 
 
@@ -542,6 +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)
     {
@@ -561,6 +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)
     {
@@ -662,23 +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;
@@ -687,6 +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>
@@ -733,14 +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_rows>m_cols) m_qr_precond_morerows.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_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);
 
@@ -751,11 +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);
@@ -781,7 +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;
 
@@ -830,6 +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;
@@ -851,11 +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 = dec().singularValues().head(nonzeroSingVals).asDiagonal().inverse() * tmp;
-    dst = dec().matrixV().leftCols(nonzeroSingVals) * tmp;
+    tmp.noalias() = dec().matrixU().leftCols(rank).adjoint() * rhs();
+    tmp = dec().singularValues().head(rank).asDiagonal().inverse() * 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> class SimplicialLDLT;
-template<typename _MatrixType, int _UpLo = Lower> class SimplicialCholesky;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLLT;
+template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLDLT;
+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>
-    class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo> >
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+    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>
-    class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo> >
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+    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>
-    class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo> >
+template<typename _MatrixType, int _UpLo, typename _Ordering>
+    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
-    // C.prune(keep_diag());
-    internal::minimum_degree_ordering(C, m_Pinv);
+    
+    OrderingType ordering;
+    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));
-      memcpy(m_indices, other.m_indices, m_size * sizeof(Index));
+      internal::smart_copy(other.m_values,  other.m_values  + m_size, m_values);
+      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/ConservativeSparseSparseProduct.h

@@ -66,9 +66,9 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
     }
 
     // unordered insertion
-    for(int k=0; k<nnz; ++k)
+    for(Index k=0; k<nnz; ++k)
     {
-      int i = indices[k];
+      Index i = indices[k];
       res.insertBackByOuterInnerUnordered(j,i) = values[i];
       mask[i] = false;
     }
@@ -76,8 +76,8 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
 #if 0
     // alternative ordered insertion code:
 
-    int t200 = rows/(log2(200)*1.39);
-    int t = (rows*100)/139;
+    Index t200 = rows/(log2(200)*1.39);
+    Index t = (rows*100)/139;
 
     // FIXME reserve nnz non zeros
     // FIXME implement fast sort algorithms for very small nnz
@@ -90,9 +90,9 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
     if(true)
     {
       if(nnz>1) std::sort(indices.data(),indices.data()+nnz);
-      for(int k=0; k<nnz; ++k)
+      for(Index k=0; k<nnz; ++k)
       {
-        int i = indices[k];
+        Index i = indices[k];
         res.insertBackByOuterInner(j,i) = values[i];
         mask[i] = false;
       }
@@ -100,7 +100,7 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
     else
     {
       // dense path
-      for(int i=0; i<rows; ++i)
+      for(Index i=0; i<rows; ++i)
       {
         if(mask[i])
         {
@@ -134,8 +134,8 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,C
 
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,RowMajor> RowMajorMatrix;
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
     ColMajorMatrix resCol(lhs.rows(),rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);
     // sort the non zeros:
@@ -149,7 +149,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,C
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-     typedef SparseMatrix<typename ResultType::Scalar,RowMajor> RowMajorMatrix;
+     typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
      RowMajorMatrix rhsRow = rhs;
      RowMajorMatrix resRow(lhs.rows(), rhs.cols());
      internal::conservative_sparse_sparse_product_impl<RowMajorMatrix,Lhs,RowMajorMatrix>(rhsRow, lhs, resRow);
@@ -162,7 +162,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,R
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,RowMajor> RowMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
     RowMajorMatrix lhsRow = lhs;
     RowMajorMatrix resRow(lhs.rows(), rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Rhs,RowMajorMatrix,RowMajorMatrix>(rhs, lhsRow, resRow);
@@ -175,7 +175,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,R
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,RowMajor> RowMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
     RowMajorMatrix resRow(lhs.rows(), rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);
     res = resRow;
@@ -190,7 +190,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,C
 
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
     ColMajorMatrix resCol(lhs.rows(), rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);
     res = resCol;
@@ -202,7 +202,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,C
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
     ColMajorMatrix lhsCol = lhs;
     ColMajorMatrix resCol(lhs.rows(), rhs.cols());
     internal::conservative_sparse_sparse_product_impl<ColMajorMatrix,Rhs,ColMajorMatrix>(lhsCol, rhs, resCol);
@@ -215,7 +215,7 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,R
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
     ColMajorMatrix rhsCol = rhs;
     ColMajorMatrix resCol(lhs.rows(), rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Lhs,ColMajorMatrix,ColMajorMatrix>(lhs, rhsCol, resCol);
@@ -228,8 +228,8 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,R
 {
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,RowMajor> RowMajorMatrix;
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
     RowMajorMatrix resRow(lhs.rows(),rhs.cols());
     internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);
     // sort the non zeros:

Eigen/src/SparseCore/MappedSparseMatrix.h

@@ -50,6 +50,8 @@ class MappedSparseMatrix
     inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
     inline Index innerSize() const { return m_innerSize; }
     inline Index outerSize() const { return m_outerSize; }
+    
+    bool isCompressed() const { return true; }
 
     //----------------------------------------
     // direct access interface

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(); }
@@ -66,6 +76,10 @@ public:
     typename XprType::Nested m_matrix;
     Index m_outerStart;
     const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+  private:
+    Index nonZeros() const;
 };
 
 
@@ -80,6 +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)
@@ -221,6 +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
     {
@@ -263,7 +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,
@@ -275,7 +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,
@@ -302,8 +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_blockCols(xpr.cols())
+        m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+        m_blockCols(BlockCols==1 ? 1 : xpr.cols())
     {}
 
     /** Dynamic-size constructor
@@ -391,6 +520,8 @@ public:
   protected:
     friend class InnerIterator;
     friend class ReverseInnerIterator;
+    
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
 
     typename XprType::Nested m_matrix;
     const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
@@ -403,3 +534,4 @@ public:
 } // end namespace Eigen
 
 #endif // EIGEN_SPARSE_BLOCK_H
+

Eigen/src/SparseCore/SparseColEtree.h

@@ -63,6 +63,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   typedef typename MatrixType::Index Index;
   Index nc = mat.cols(); // Number of columns 
   Index m = mat.rows();
+  Index diagSize = (std::min)(nc,m);
   IndexVector root(nc); // root of subtree of etree 
   root.setZero();
   IndexVector pp(nc); // disjoint sets 
@@ -72,7 +73,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   Index row,col; 
   firstRowElt.resize(m);
   firstRowElt.setConstant(nc);
-  firstRowElt.segment(0, nc).setLinSpaced(nc, 0, nc-1);
+  firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);
   bool found_diag;
   for (col = 0; col < nc; col++)
   {
@@ -91,7 +92,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   Index rset, cset, rroot; 
   for (col = 0; col < nc; col++) 
   {
-    found_diag = false;
+    found_diag = col>=m;
     pp(col) = col; 
     cset = col; 
     root(cset) = col; 
@@ -105,6 +106,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
       Index i = col;
       if(it) i = it.index();
       if (i == col) found_diag = true;
+      
       row = firstRowElt(i);
       if (row >= col) continue; 
       rset = internal::etree_find(row, pp); // Find the name of the set containing row

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)
     {}
 };

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 {
@@ -114,18 +120,31 @@ 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 col() const { return Transpose ? m_outer : Base::row(); }
+    inline Index row() const { return Transpose ? m_outer : Base::index(); }
+    inline Index col() const { return Transpose ? Base::index() : m_outer; }
 
     inline Scalar value() const { return Base::value() * m_factor; }
 
   protected:
-    int m_outer;
+    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;
 };
 
@@ -155,13 +174,13 @@ struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, R
   {
     for(Index c=0; c<rhs.cols(); ++c)
     {
-      int n = lhs.outerSize();
+      Index n = lhs.outerSize();
       for(Index j=0; j<n; ++j)
       {
         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

@@ -223,7 +223,7 @@ class SparseMatrix
       
       if(isCompressed())
       {
-        reserve(VectorXi::Constant(outerSize(), 2));
+        reserve(Matrix<Index,Dynamic,1>::Constant(outerSize(), 2));
       }
       return insertUncompressed(row,col);
     }
@@ -402,7 +402,7 @@ class SparseMatrix
       * \sa insertBack, insertBackByOuterInner */
     inline void startVec(Index outer)
     {
-      eigen_assert(m_outerIndex[outer]==int(m_data.size()) && "You must call startVec for each inner vector sequentially");
+      eigen_assert(m_outerIndex[outer]==Index(m_data.size()) && "You must call startVec for each inner vector sequentially");
       eigen_assert(m_outerIndex[outer+1]==0 && "You must call startVec for each inner vector sequentially");
       m_outerIndex[outer+1] = m_outerIndex[outer];
     }
@@ -480,7 +480,7 @@ class SparseMatrix
       if(m_innerNonZeros != 0)
         return; 
       m_innerNonZeros = static_cast<Index*>(std::malloc(m_outerSize * sizeof(Index)));
-      for (int i = 0; i < m_outerSize; i++)
+      for (Index i = 0; i < m_outerSize; i++)
       {
         m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i]; 
       }
@@ -752,8 +752,8 @@ class SparseMatrix
         else
           for (Index i=0; i<m.outerSize(); ++i)
           {
-            int p = m.m_outerIndex[i];
-            int pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];
+            Index p = m.m_outerIndex[i];
+            Index pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];
             Index k=p;
             for (; k<pe; ++k)
               s << "(" << m.m_data.value(k) << "," << m.m_data.index(k) << ") ";
@@ -939,12 +939,13 @@ void set_from_triplets(const InputIterator& begin, const InputIterator& end, Spa
   EIGEN_UNUSED_VARIABLE(Options);
   enum { IsRowMajor = SparseMatrixType::IsRowMajor };
   typedef typename SparseMatrixType::Scalar Scalar;
-  SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor> trMat(mat.rows(),mat.cols());
+  typedef typename SparseMatrixType::Index Index;
+  SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor,Index> trMat(mat.rows(),mat.cols());
 
-  if(begin<end)
+  if(begin!=end)
   {
     // pass 1: count the nnz per inner-vector
-    VectorXi wi(trMat.outerSize());
+    Matrix<Index,Dynamic,1> wi(trMat.outerSize());
     wi.setZero();
     for(InputIterator it(begin); it!=end; ++it)
     {
@@ -1018,11 +1019,11 @@ void SparseMatrix<Scalar,_Options,_Index>::sumupDuplicates()
 {
   eigen_assert(!isCompressed());
   // TODO, in practice we should be able to use m_innerNonZeros for that task
-  VectorXi wi(innerSize());
+  Matrix<Index,Dynamic,1> wi(innerSize());
   wi.fill(-1);
   Index count = 0;
   // for each inner-vector, wi[inner_index] will hold the position of first element into the index/value buffers
-  for(int j=0; j<outerSize(); ++j)
+  for(Index j=0; j<outerSize(); ++j)
   {
     Index start   = count;
     Index oldEnd  = m_outerIndex[j]+m_innerNonZeros[j];
@@ -1081,7 +1082,7 @@ EIGEN_DONT_INLINE SparseMatrix<Scalar,_Options,_Index>& SparseMatrix<Scalar,_Opt
 
     // prefix sum
     Index count = 0;
-    VectorXi positions(dest.outerSize());
+    Matrix<Index,Dynamic,1> positions(dest.outerSize());
     for (Index j=0; j<dest.outerSize(); ++j)
     {
       Index tmp = dest.m_outerIndex[j];
@@ -1177,7 +1178,7 @@ 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
@@ -1189,13 +1190,13 @@ 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
-      float nnzEstimate = float(m_outerIndex[outer])*float(m_outerSize)/float(outer+1);
-      reallocRatio = (nnzEstimate-float(m_data.size()))/float(m_data.size());
+      // in addition, we use double to avoid integers overflows
+      double nnzEstimate = double(m_outerIndex[outer])*double(m_outerSize)/double(outer+1);
+      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

@@ -105,7 +105,7 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
                      >::type AdjointReturnType;
 
 
-    typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor> PlainObject;
+    typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor, Index> PlainObject;
 
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
@@ -302,8 +302,8 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
         }
         else
         {
-          SparseMatrix<Scalar, RowMajorBit> trans = m;
-          s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit> >&>(trans);
+          SparseMatrix<Scalar, RowMajorBit, Index> trans = m;
+          s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit, Index> >&>(trans);
         }
       }
       return s;
@@ -358,7 +358,8 @@ 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 +404,10 @@ 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);
-    const Block<const Derived,Dynamic,Dynamic,true> innerVectors(Index outerStart, Index outerSize) const;
+    typedef Block<Derived,Dynamic,Dynamic,true> InnerVectorsReturnType;
+    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

@@ -57,11 +57,11 @@ struct permut_sparsematrix_product_retval
       if(MoveOuter)
       {
         SparseMatrix<Scalar,SrcStorageOrder,Index> tmp(m_matrix.rows(), m_matrix.cols());
-        VectorXi sizes(m_matrix.outerSize());
+        Matrix<Index,Dynamic,1> sizes(m_matrix.outerSize());
         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)
@@ -77,7 +77,7 @@ struct permut_sparsematrix_product_retval
       else
       {
         SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,Index> tmp(m_matrix.rows(), m_matrix.cols());
-        VectorXi sizes(tmp.outerSize());
+        Matrix<Index,Dynamic,1> sizes(tmp.outerSize());
         sizes.setZero();
         PermutationMatrix<Dynamic,Dynamic,Index> perm;
         if((Side==OnTheLeft) ^ Transposed)

Eigen/src/SparseCore/SparseProduct.h

@@ -16,6 +16,7 @@ template<typename Lhs, typename Rhs>
 struct SparseSparseProductReturnType
 {
   typedef typename internal::traits<Lhs>::Scalar Scalar;
+  typedef typename internal::traits<Lhs>::Index Index;
   enum {
     LhsRowMajor = internal::traits<Lhs>::Flags & RowMajorBit,
     RhsRowMajor = internal::traits<Rhs>::Flags & RowMajorBit,
@@ -24,11 +25,11 @@ struct SparseSparseProductReturnType
   };
 
   typedef typename internal::conditional<TransposeLhs,
-    SparseMatrix<Scalar,0>,
+    SparseMatrix<Scalar,0,Index>,
     typename internal::nested<Lhs,Rhs::RowsAtCompileTime>::type>::type LhsNested;
 
   typedef typename internal::conditional<TransposeRhs,
-    SparseMatrix<Scalar,0>,
+    SparseMatrix<Scalar,0,Index>,
     typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type>::type RhsNested;
 
   typedef SparseSparseProduct<LhsNested, RhsNested> Type;

Eigen/src/SparseCore/SparseSelfAdjointView.h

@@ -75,22 +75,22 @@ template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView
       * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
       */
     template<typename OtherDerived>
-    SparseSparseProduct<SparseMatrix<Scalar,  ((internal::traits<OtherDerived>::Flags&RowMajorBit) ? RowMajor : ColMajor),Index>, OtherDerived>
+    SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>
     operator*(const SparseMatrixBase<OtherDerived>& rhs) const
     {
-      return SparseSparseProduct<SparseMatrix<Scalar, (internal::traits<OtherDerived>::Flags&RowMajorBit) ? RowMajor : ColMajor, Index>, OtherDerived>(*this, rhs.derived());
+      return SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>(*this, rhs.derived());
     }
-    
+
     /** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
       *
       * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
       * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
       */
     template<typename OtherDerived> friend
-    SparseSparseProduct<OtherDerived, SparseMatrix<Scalar,  ((internal::traits<OtherDerived>::Flags&RowMajorBit) ? RowMajor : ColMajor),Index> >
+    SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject >
     operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
     {
-      return SparseSparseProduct< OtherDerived, SparseMatrix<Scalar, (internal::traits<OtherDerived>::Flags&RowMajorBit) ? RowMajor : ColMajor, Index> >(lhs.derived(), rhs.derived());
+      return SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject>(lhs.derived(), rhs);
     }
     
     /** Efficient sparse self-adjoint matrix times dense vector/matrix product */

Eigen/src/SparseCore/SparseSparseProductWithPruning.h

@@ -27,7 +27,7 @@ static void sparse_sparse_product_with_pruning_impl(const Lhs& lhs, const Rhs& r
   // make sure to call innerSize/outerSize since we fake the storage order.
   Index rows = lhs.innerSize();
   Index cols = rhs.outerSize();
-  //int size = lhs.outerSize();
+  //Index size = lhs.outerSize();
   eigen_assert(lhs.outerSize() == rhs.innerSize());
 
   // allocate a temporary buffer
@@ -100,7 +100,7 @@ struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,C
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
   {
     // we need a col-major matrix to hold the result
-    typedef SparseMatrix<typename ResultType::Scalar> SparseTemporaryType;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> SparseTemporaryType;
     SparseTemporaryType _res(res.rows(), res.cols());
     internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,SparseTemporaryType>(lhs, rhs, _res, tolerance);
     res = _res;
@@ -126,10 +126,11 @@ struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,R
   typedef typename ResultType::RealScalar RealScalar;
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
   {
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor> ColMajorMatrix;
-    ColMajorMatrix colLhs(lhs);
-    ColMajorMatrix colRhs(rhs);
-    internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrix,ColMajorMatrix,ResultType>(colLhs, colRhs, res, tolerance);
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename Lhs::Index> ColMajorMatrixLhs;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename Lhs::Index> ColMajorMatrixRhs;
+    ColMajorMatrixLhs colLhs(lhs);
+    ColMajorMatrixRhs colRhs(rhs);
+    internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,ColMajorMatrixRhs,ResultType>(colLhs, colRhs, res, tolerance);
 
     // let's transpose the product to get a column x column product
 //     typedef SparseMatrix<typename ResultType::Scalar> SparseTemporaryType;

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(); }
-    Index col() const { return Base::row(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
+    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(); }
-    Index col() const { return Base::row(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index row() const { return Base::col(); }
+    typename TransposeImpl<MatrixType,Sparse>::Index col() const { return Base::row(); }
 };
 
 } // end namespace Eigen