bump to 3.2.5

(grafted from devel branch)

CMakeLists.txt

@@ -1,6 +1,6 @@
 project(Eigen)
 
-cmake_minimum_required(VERSION 2.6.2)
+cmake_minimum_required(VERSION 2.8.2)
 
 # guard against in-source builds
 
@@ -107,27 +107,64 @@ endif()
 
 set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320")
 
-if(CMAKE_COMPILER_IS_GNUCXX)
+macro(ei_add_cxx_compiler_flag FLAG)
-  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wnon-virtual-dtor -Wno-long-long -ansi -Wundef -Wcast-align -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -fexceptions -fno-check-new -fno-common -fstrict-aliasing")
+  string(REGEX REPLACE "-" "" SFLAG ${FLAG})
+  check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
+  if(COMPILER_SUPPORT_${SFLAG})
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
+  endif()
+endmacro(ei_add_cxx_compiler_flag)
+
+if(NOT MSVC)
+  # We assume that other compilers are partly compatible with GNUCC
+  
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fexceptions")
   set(CMAKE_CXX_FLAGS_DEBUG "-g3")
   set(CMAKE_CXX_FLAGS_RELEASE "-g0 -O2")
   
-  check_cxx_compiler_flag("-Wno-psabi" COMPILER_SUPPORT_WNOPSABI)
+  # clang outputs some warnings for unknwon flags that are not caught by check_cxx_compiler_flag
-  if(COMPILER_SUPPORT_WNOPSABI)
+  # adding -Werror turns such warnings into errors
-    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-psabi")
+  check_cxx_compiler_flag("-Werror" COMPILER_SUPPORT_WERROR)
+  if(COMPILER_SUPPORT_WERROR)
+    set(CMAKE_REQUIRED_FLAGS "-Werror")
   endif()
-
+  
-  check_cxx_compiler_flag("-Wno-variadic-macros" COMPILER_SUPPORT_WNOVARIADICMACRO)
+  ei_add_cxx_compiler_flag("-pedantic")
-  if(COMPILER_SUPPORT_WNOVARIADICMACRO)
+  ei_add_cxx_compiler_flag("-Wall")
-    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-variadic-macros")
+  ei_add_cxx_compiler_flag("-Wextra")
+  #ei_add_cxx_compiler_flag("-Weverything")              # clang
+  
+  ei_add_cxx_compiler_flag("-Wundef")
+  ei_add_cxx_compiler_flag("-Wcast-align")
+  ei_add_cxx_compiler_flag("-Wchar-subscripts")
+  ei_add_cxx_compiler_flag("-Wnon-virtual-dtor")
+  ei_add_cxx_compiler_flag("-Wunused-local-typedefs")
+  ei_add_cxx_compiler_flag("-Wpointer-arith")
+  ei_add_cxx_compiler_flag("-Wwrite-strings")
+  ei_add_cxx_compiler_flag("-Wformat-security")
+  
+  ei_add_cxx_compiler_flag("-Wno-psabi")
+  ei_add_cxx_compiler_flag("-Wno-variadic-macros")
+  ei_add_cxx_compiler_flag("-Wno-long-long")
+  
+  ei_add_cxx_compiler_flag("-fno-check-new")
+  ei_add_cxx_compiler_flag("-fno-common")
+  ei_add_cxx_compiler_flag("-fstrict-aliasing")
+  ei_add_cxx_compiler_flag("-wd981")                    # disable ICC's "operands are evaluated in unspecified order" remark
+  ei_add_cxx_compiler_flag("-wd2304")                   # disbale ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
+  
+  # The -ansi flag must be added last, otherwise it is also used as a linker flag by check_cxx_compiler_flag making it fails
+  # Moreover we should not set both -strict-ansi and -ansi
+  check_cxx_compiler_flag("-strict-ansi" COMPILER_SUPPORT_STRICTANSI)
+  ei_add_cxx_compiler_flag("-Qunused-arguments")        # disable clang warning: argument unused during compilation: '-ansi'
+  
+  if(COMPILER_SUPPORT_STRICTANSI)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -strict-ansi")
+  else()
+    ei_add_cxx_compiler_flag("-ansi")
   endif()
-
+  
-  check_cxx_compiler_flag("-Wextra" COMPILER_SUPPORT_WEXTRA)
+  set(CMAKE_REQUIRED_FLAGS "")
-  if(COMPILER_SUPPORT_WEXTRA)
-    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wextra")
-  endif()
-
-  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -pedantic")
 
   option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
   if(EIGEN_TEST_SSE2)
@@ -167,7 +204,7 @@ if(CMAKE_COMPILER_IS_GNUCXX)
 
   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()
 
@@ -180,9 +217,8 @@ if(CMAKE_COMPILER_IS_GNUCXX)
     endif()
   endif()
 
-endif(CMAKE_COMPILER_IS_GNUCXX)
+else(NOT MSVC)
 
-if(MSVC)
   # C4127 - conditional expression is constant
   # C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively)
   #         We can disable this warning in the unit tests since it is clear that it occurs
@@ -212,7 +248,7 @@ if(MSVC)
     endif(NOT CMAKE_CL_64)
     message(STATUS "Enabling SSE2 in tests/examples")
   endif(EIGEN_TEST_SSE2)
-endif(MSVC)
+endif(NOT MSVC)
 
 option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
 option(EIGEN_TEST_X87 "Force using X87 instructions. Implies no vectorization." OFF)
@@ -311,6 +347,7 @@ add_subdirectory(Eigen)
 add_subdirectory(doc EXCLUDE_FROM_ALL)
 
 include(EigenConfigureTesting)
+
 # fixme, not sure this line is still needed:
 enable_testing() # must be called from the root CMakeLists, see man page
 
@@ -345,6 +382,8 @@ if(NOT WIN32)
   add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)
 endif(NOT WIN32)
 
+configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)
+
 ei_testing_print_summary()
 
 message(STATUS "")

CTestConfig.cmake

@@ -4,10 +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)

CTestCustom.cmake.in

@@ -1,4 +1,3 @@
 
-## A tribute to Dynamic!
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "2000")
-set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "33331")
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS   "2000")
-set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "33331")

Eigen/Core

@@ -19,6 +19,12 @@
 // defined e.g. EIGEN_DONT_ALIGN) so it needs to be done before we do anything with vectorization.
 #include "src/Core/util/Macros.h"
 
+// Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3)
+// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.
+#if defined(__MINGW32__) && EIGEN_GNUC_AT_LEAST(4,6)
+  #pragma GCC optimize ("-fno-ipa-cp-clone")
+#endif
+
 #include <complex>
 
 // this include file manages BLAS and MKL related macros
@@ -44,7 +50,7 @@
   #endif
 #else
   // Remember that usage of defined() in a #define is undefined by the standard
-  #if (defined __SSE2__) && ( (!defined __GNUC__) || EIGEN_GNUC_AT_LEAST(4,2) )
+  #if (defined __SSE2__) && ( (!defined __GNUC__) || (defined __INTEL_COMPILER) || EIGEN_GNUC_AT_LEAST(4,2) )
     #define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC
   #endif
 #endif
@@ -89,7 +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>
@@ -117,7 +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>
@@ -159,7 +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
 
@@ -245,8 +251,8 @@ using std::ptrdiff_t;
 #include "src/Core/util/Constants.h"
 #include "src/Core/util/ForwardDeclarations.h"
 #include "src/Core/util/Meta.h"
-#include "src/Core/util/XprHelper.h"
 #include "src/Core/util/StaticAssert.h"
+#include "src/Core/util/XprHelper.h"
 #include "src/Core/util/Memory.h"
 
 #include "src/Core/NumTraits.h"
@@ -344,13 +350,6 @@ using std::ptrdiff_t;
 #include "src/Core/ArrayBase.h"
 #include "src/Core/ArrayWrapper.h"
 
-#ifdef EIGEN_ENABLE_EVALUATORS
-#include "src/Core/Product.h"
-#include "src/Core/CoreEvaluators.h"
-#include "src/Core/AssignEvaluator.h"
-#include "src/Core/ProductEvaluators.h"
-#endif
-
 #ifdef EIGEN_USE_BLAS
 #include "src/Core/products/GeneralMatrixMatrix_MKL.h"
 #include "src/Core/products/GeneralMatrixVector_MKL.h"

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/SPQRSupport

@@ -26,4 +26,4 @@
 #include "src/CholmodSupport/CholmodSupport.h"
 #include "src/SPQRSupport/SuiteSparseQRSupport.h"
 
-#endif
+#endif

Eigen/Sparse

@@ -1,13 +1,15 @@
 #ifndef EIGEN_SPARSE_MODULE_H
 #define EIGEN_SPARSE_MODULE_H
 
-/** defgroup Sparse_modules Sparse modules
+/** \defgroup Sparse_Module Sparse meta-module
   *
   * Meta-module including all related modules:
-  * - SparseCore
+  * - \ref SparseCore_Module
-  * - OrderingMethods
+  * - \ref OrderingMethods_Module
-  * - SparseCholesky
+  * - \ref SparseCholesky_Module
-  * - IterativeLinearSolvers
+  * - \ref SparseLU_Module
+  * - \ref SparseQR_Module
+  * - \ref IterativeLinearSolvers_Module
   *
   * \code
   * #include <Eigen/Sparse>
@@ -17,6 +19,8 @@
 #include "SparseCore"
 #include "OrderingMethods"
 #include "SparseCholesky"
+#include "SparseLU"
+#include "SparseQR"
 #include "IterativeLinearSolvers"
 
 #endif // EIGEN_SPARSE_MODULE_H

Eigen/SparseCholesky

@@ -1,7 +1,17 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
 #ifndef EIGEN_SPARSECHOLESKY_MODULE_H
 #define EIGEN_SPARSECHOLESKY_MODULE_H
 
 #include "SparseCore"
+#include "OrderingMethods"
 
 #include "src/Core/util/DisableStupidWarnings.h"
 
@@ -26,7 +36,6 @@
 
 #include "src/misc/Solve.h"
 #include "src/misc/SparseSolve.h"
-
 #include "src/SparseCholesky/SimplicialCholesky.h"
 
 #ifndef EIGEN_MPL2_ONLY

Eigen/SparseLU

@@ -20,6 +20,9 @@
   * Please, see the documentation of the SparseLU class for more details.
   */
 
+#include "src/misc/Solve.h"
+#include "src/misc/SparseSolve.h"
+
 // Ordering interface
 #include "OrderingMethods"
 

Eigen/SparseQR

@@ -20,6 +20,10 @@
   * 
   * 
   */
+
+#include "src/misc/Solve.h"
+#include "src/misc/SparseSolve.h"
+
 #include "OrderingMethods"
 #include "src/SparseCore/SparseColEtree.h"
 #include "src/SparseQR/SparseQR.h"

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;
@@ -258,45 +273,19 @@ template<> struct ldlt_inplace<Lower>
     if (size <= 1)
     {
       transpositions.setIdentity();
-      if(sign)
+      if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef;
-        *sign = real(mat.coeff(0,0))>0 ? 1:-1;
+      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);
-
-        if(sign)
-          *sign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0 ? 1 : -1;
-      }
-      else if(sign)
-      {
-        // LDLT is not guaranteed to work for indefinite matrices, but let's try to get the sign right
-        int newSign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
-        if(newSign != *sign)
-          *sign = 0;
-      }
-
-      // Finish early if the matrix is not full rank.
-      if(biggest_in_corner < cutoff)
-      {
-        for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
-        break;
-      }
-
       transpositions.coeffRef(k) = index_of_biggest_in_corner;
       if(k != index_of_biggest_in_corner)
       {
@@ -309,11 +298,11 @@ template<> struct ldlt_inplace<Lower>
         for(int i=k+1;i<index_of_biggest_in_corner;++i)
         {
           Scalar tmp = mat.coeffRef(i,k);
-          mat.coeffRef(i,k) = conj(mat.coeffRef(index_of_biggest_in_corner,i));
+          mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
-          mat.coeffRef(index_of_biggest_in_corner,i) = conj(tmp);
+          mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
         }
         if(NumTraits<Scalar>::IsComplex)
-          mat.coeffRef(index_of_biggest_in_corner,k) = conj(mat.coeff(index_of_biggest_in_corner,k));
+          mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
       }
 
       // partition the matrix:
@@ -327,13 +316,28 @@ template<> struct ldlt_inplace<Lower>
 
       if(k>0)
       {
-        temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
+        temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
         mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
         if(rs>0)
           A21.noalias() -= A20 * temp.head(k);
       }
-      if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
+      
-        A21 /= mat.coeffRef(k,k);
+      // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
+      // was smaller than the cutoff value. However, soince LDLT is not rank-revealing
+      // we should only make sure we do not introduce INF or NaN values.
+      // LAPACK also uses 0 as the cutoff value.
+      RealScalar realAkk = numext::real(mat.coeffRef(k,k));
+      if((rs>0) && (abs(realAkk) > RealScalar(0)))
+        A21 /= realAkk;
+
+      if (sign == PositiveSemiDef) {
+        if (realAkk < 0) sign = Indefinite;
+      } else if (sign == NegativeSemiDef) {
+        if (realAkk > 0) sign = Indefinite;
+      } else if (sign == ZeroSign) {
+        if (realAkk > 0) sign = PositiveSemiDef;
+        else if (realAkk < 0) sign = NegativeSemiDef;
+      }
     }
 
     return true;
@@ -349,7 +353,7 @@ template<> struct ldlt_inplace<Lower>
   template<typename MatrixType, typename WDerived>
   static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
   {
-    using internal::isfinite;
+    using numext::isfinite;
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
     typedef typename MatrixType::Index Index;
@@ -367,9 +371,9 @@ template<> struct ldlt_inplace<Lower>
         break;
 
       // Update the diagonal terms
-      RealScalar dj = real(mat.coeff(j,j));
+      RealScalar dj = numext::real(mat.coeff(j,j));
       Scalar wj = w.coeff(j);
-      RealScalar swj2 = sigma*abs2(wj);
+      RealScalar swj2 = sigma*numext::abs2(wj);
       RealScalar gamma = dj*alpha + swj2;
 
       mat.coeffRef(j,j) += swj2/alpha;
@@ -380,7 +384,7 @@ template<> struct ldlt_inplace<Lower>
       Index rs = size-j-1;
       w.tail(rs) -= wj * mat.col(j).tail(rs);
       if(gamma != 0)
-        mat.col(j).tail(rs) += (sigma*conj(wj)/gamma)*w.tail(rs);
+        mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
     }
     return true;
   }
@@ -398,7 +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);
@@ -435,6 +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();
 
@@ -443,8 +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;
@@ -472,7 +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;
   }
 
@@ -503,16 +510,21 @@ struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
     using std::abs;
     using std::max;
     typedef typename LDLTType::MatrixType MatrixType;
-    typedef typename LDLTType::Scalar Scalar;
     typedef typename LDLTType::RealScalar RealScalar;
-    const Diagonal<const MatrixType> vectorD = dec().vectorD();
+    const typename Diagonal<const MatrixType>::RealReturnType vectorD(dec().vectorD());
-    RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
+    // In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon
-				 RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
+    // as motivated by LAPACK's xGELSS:
+    // RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() *NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
+    // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
+    // diagonal element is not well justified and to numerical issues in some cases.
+    // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
+    RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest();
+    
     for (Index i = 0; i < vectorD.size(); ++i) {
       if(abs(vectorD(i)) > tolerance)
-	dst.row(i) /= vectorD(i);
+        dst.row(i) /= vectorD(i);
       else
-	dst.row(i).setZero();
+        dst.row(i).setZero();
     }
 
     // dst = L^-T (D^-1 L^-1 P b)
@@ -565,7 +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.
@@ -200,7 +206,7 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
   typedef Matrix<Scalar,Dynamic,1> TempVectorType;
   typedef typename TempVectorType::SegmentReturnType TempVecSegment;
 
-  int n = mat.cols();
+  Index n = mat.cols();
   eigen_assert(mat.rows()==n && vec.size()==n);
 
   TempVectorType temp;
@@ -212,12 +218,12 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
     // i.e., for sigma > 0
     temp = sqrt(sigma) * vec;
 
-    for(int i=0; i<n; ++i)
+    for(Index i=0; i<n; ++i)
     {
       JacobiRotation<Scalar> g;
       g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
 
-      int rs = n-i-1;
+      Index rs = n-i-1;
       if(rs>0)
       {
         ColXprSegment x(mat.col(i).tail(rs));
@@ -230,12 +236,12 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
   {
     temp = vec;
     RealScalar beta = 1;
-    for(int j=0; j<n; ++j)
+    for(Index j=0; j<n; ++j)
     {
-      RealScalar Ljj = real(mat.coeff(j,j));
+      RealScalar Ljj = numext::real(mat.coeff(j,j));
-      RealScalar dj = abs2(Ljj);
+      RealScalar dj = numext::abs2(Ljj);
       Scalar wj = temp.coeff(j);
-      RealScalar swj2 = sigma*abs2(wj);
+      RealScalar swj2 = sigma*numext::abs2(wj);
       RealScalar gamma = dj*beta + swj2;
 
       RealScalar x = dj + swj2/beta;
@@ -251,7 +257,7 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
       {
         temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
         if(gamma != 0)
-          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*conj(wj)/gamma)*temp.tail(rs);
+          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
       }
     }
   }
@@ -277,7 +283,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
       Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
       Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
 
-      RealScalar x = real(mat.coeff(k,k));
+      RealScalar x = numext::real(mat.coeff(k,k));
       if (k>0) x -= A10.squaredNorm();
       if (x<=RealScalar(0))
         return k;
@@ -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

@@ -51,7 +51,6 @@ void cholmod_configure_matrix(CholmodType& mat)
 template<typename _Scalar, int _Options, typename _Index>
 cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
 {
-  typedef SparseMatrix<_Scalar,_Options,_Index> MatrixType;
   cholmod_sparse res;
   res.nzmax   = mat.nonZeros();
   res.nrow    = mat.rows();;
@@ -59,10 +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
   {
@@ -127,7 +128,7 @@ cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
   res.ncol   = mat.cols();
   res.nzmax  = res.nrow * res.ncol;
   res.d      = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
-  res.x      = mat.derived().data();
+  res.x      = (void*)(mat.derived().data());
   res.z      = 0;
 
   internal::cholmod_configure_matrix<Scalar>(res);
@@ -171,6 +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);
     }
 
@@ -242,7 +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.
       * 
@@ -266,7 +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()
       */
@@ -296,13 +298,14 @@ class CholmodBase : internal::noncopyable
       eigen_assert(size==b.rows());
 
       // note: cd stands for Cholmod Dense
-      cholmod_dense b_cd = viewAsCholmod(b.const_cast_derived());
+      Rhs& b_ref(b.const_cast_derived());
+      cholmod_dense b_cd = viewAsCholmod(b_ref);
       cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
       if(!x_cd)
       {
         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);
     }
@@ -313,6 +316,7 @@ class CholmodBase : internal::noncopyable
     {
       eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
       const Index size = m_cholmodFactor->n;
+      EIGEN_UNUSED_VARIABLE(size);
       eigen_assert(size==b.rows());
 
       // note: cs stands for Cholmod Sparse
@@ -322,7 +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);
     }
@@ -345,7 +349,7 @@ class CholmodBase : internal::noncopyable
     }
     
     template<typename Stream>
-    void dumpMemory(Stream& s)
+    void dumpMemory(Stream& /*s*/)
     {}
     
   protected:
@@ -364,8 +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.
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
-  * 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<>
@@ -411,8 +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.
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
-  * 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<>
@@ -457,7 +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<>
@@ -500,7 +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

@@ -107,7 +107,7 @@ class Array
       *
       * \sa resize(Index,Index)
       */
-    EIGEN_STRONG_INLINE explicit Array() : Base()
+    EIGEN_STRONG_INLINE Array() : Base()
     {
       Base::_check_template_params();
       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
@@ -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
+  };
 };
 }
 
@@ -55,7 +60,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     inline Index outerStride() const { return m_expression.outerStride(); }
     inline Index innerStride() const { return m_expression.innerStride(); }
 
-    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
     inline const Scalar* data() const { return m_expression.data(); }
 
     inline CoeffReturnType coeff(Index rowId, Index colId) const
@@ -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
+  };
 };
 }
 
@@ -175,7 +185,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     inline Index outerStride() const { return m_expression.outerStride(); }
     inline Index innerStride() const { return m_expression.innerStride(); }
 
-    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
     inline const Scalar* data() const { return m_expression.data(); }
 
     inline CoeffReturnType coeff(Index rowId, Index colId) const

Eigen/src/Core/Assign.h

@@ -155,7 +155,7 @@ struct assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
 template<typename Derived1, typename Derived2, int Index, int Stop>
 struct assign_DefaultTraversal_InnerUnrolling
 {
-  static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, int outer)
+  static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, typename Derived1::Index outer)
   {
     dst.copyCoeffByOuterInner(outer, Index, src);
     assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src, outer);
@@ -165,7 +165,7 @@ struct assign_DefaultTraversal_InnerUnrolling
 template<typename Derived1, typename Derived2, int Stop>
 struct assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Stop, Stop>
 {
-  static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, int) {}
+  static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, typename Derived1::Index) {}
 };
 
 /***********************
@@ -218,7 +218,7 @@ struct assign_innervec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
 template<typename Derived1, typename Derived2, int Index, int Stop>
 struct assign_innervec_InnerUnrolling
 {
-  static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, int outer)
+  static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, typename Derived1::Index outer)
   {
     dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, Index, src);
     assign_innervec_InnerUnrolling<Derived1, Derived2,
@@ -229,7 +229,7 @@ struct assign_innervec_InnerUnrolling
 template<typename Derived1, typename Derived2, int Stop>
 struct assign_innervec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
 {
-  static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, int) {}
+  static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, typename Derived1::Index) {}
 };
 
 /***************************************************************************
@@ -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)) && (Index(dst_ptr) % sizeof(Scalar))>0)
+    {
+      // the pointer is not aligend-on scalar, so alignment is not possible
+      return assign_impl<Derived1,Derived2,DefaultTraversal,NoUnrolling>::run(dst, src);
+    }
     const Index packetAlignedMask = packetSize - 1;
     const Index innerSize = dst.innerSize();
     const Index outerSize = dst.outerSize();
     const Index alignedStep = alignable ? (packetSize - dst.outerStride() % packetSize) & packetAlignedMask : 0;
-    Index alignedStart = ((!alignable) || assign_traits<Derived1,Derived2>::DstIsAligned) ? 0
+    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, innerSize);
-                       : internal::first_aligned(&dst.coeffRef(0,0), innerSize);
 
     for(Index outer = 0; outer < outerSize; ++outer)
     {
@@ -507,19 +514,19 @@ EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
 namespace internal {
 
 template<typename Derived, typename OtherDerived,
-         bool EvalBeforeAssigning = (int(OtherDerived::Flags) & EvalBeforeAssigningBit) != 0,
+         bool EvalBeforeAssigning = (int(internal::traits<OtherDerived>::Flags) & EvalBeforeAssigningBit) != 0,
-         bool NeedToTranspose = Derived::IsVectorAtCompileTime
+         bool NeedToTranspose = ((int(Derived::RowsAtCompileTime) == 1 && int(OtherDerived::ColsAtCompileTime) == 1)
-                && OtherDerived::IsVectorAtCompileTime
+                              |   // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
-                && ((int(Derived::RowsAtCompileTime) == 1 && int(OtherDerived::ColsAtCompileTime) == 1)
+                                  // revert to || as soon as not needed anymore.
-                      |  // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
+                                  (int(Derived::ColsAtCompileTime) == 1 && int(OtherDerived::RowsAtCompileTime) == 1))
-                         // revert to || as soon as not needed anymore.
+                              && int(Derived::SizeAtCompileTime) != 1>
-                    (int(Derived::ColsAtCompileTime) == 1 && int(OtherDerived::RowsAtCompileTime) == 1))
-                && int(Derived::SizeAtCompileTime) != 1>
 struct assign_selector;
 
 template<typename Derived, typename OtherDerived>
 struct assign_selector<Derived,OtherDerived,false,false> {
   static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
+  template<typename ActualDerived, typename ActualOtherDerived>
+  static EIGEN_STRONG_INLINE Derived& evalTo(ActualDerived& dst, const ActualOtherDerived& other) { other.evalTo(dst); return dst; }
 };
 template<typename Derived, typename OtherDerived>
 struct assign_selector<Derived,OtherDerived,true,false> {
@@ -528,6 +535,8 @@ struct assign_selector<Derived,OtherDerived,true,false> {
 template<typename Derived, typename OtherDerived>
 struct assign_selector<Derived,OtherDerived,false,true> {
   static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose()); }
+  template<typename ActualDerived, typename ActualOtherDerived>
+  static EIGEN_STRONG_INLINE Derived& evalTo(ActualDerived& dst, const ActualOtherDerived& other) { Transpose<ActualDerived> dstTrans(dst); other.evalTo(dstTrans); return dst; }
 };
 template<typename Derived, typename OtherDerived>
 struct assign_selector<Derived,OtherDerived,true,true> {
@@ -566,16 +575,14 @@ template<typename Derived>
 template <typename OtherDerived>
 EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
 {
-  other.derived().evalTo(derived());
+  return internal::assign_selector<Derived,OtherDerived,false>::evalTo(derived(), other.derived());
-  return derived();
 }
 
 template<typename Derived>
 template<typename OtherDerived>
 EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
 {
-  other.evalTo(derived());
+  return internal::assign_selector<Derived,OtherDerived,false>::evalTo(derived(), other.derived());
-  return derived();
 }
 
 } // end namespace Eigen

Eigen/src/Core/AssignEvaluator.h

@@ -1,755 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
-// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_ASSIGN_EVALUATOR_H
-#define EIGEN_ASSIGN_EVALUATOR_H
-
-namespace Eigen {
-
-// This implementation is based on Assign.h
-
-namespace internal {
-  
-/***************************************************************************
-* Part 1 : the logic deciding a strategy for traversal and unrolling       *
-***************************************************************************/
-
-// copy_using_evaluator_traits is based on assign_traits
-
-template <typename Derived, typename OtherDerived>
-struct copy_using_evaluator_traits
-{
-public:
-  enum {
-    DstIsAligned = Derived::Flags & AlignedBit,
-    DstHasDirectAccess = Derived::Flags & DirectAccessBit,
-    SrcIsAligned = OtherDerived::Flags & AlignedBit,
-    JointAlignment = bool(DstIsAligned) && bool(SrcIsAligned) ? Aligned : Unaligned,
-    SrcEvalBeforeAssign = (evaluator_traits<OtherDerived>::HasEvalTo == 1)
-  };
-
-private:
-  enum {
-    InnerSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::SizeAtCompileTime)
-              : int(Derived::Flags)&RowMajorBit ? int(Derived::ColsAtCompileTime)
-              : int(Derived::RowsAtCompileTime),
-    InnerMaxSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::MaxSizeAtCompileTime)
-              : int(Derived::Flags)&RowMajorBit ? int(Derived::MaxColsAtCompileTime)
-              : int(Derived::MaxRowsAtCompileTime),
-    MaxSizeAtCompileTime = Derived::SizeAtCompileTime,
-    PacketSize = packet_traits<typename Derived::Scalar>::size
-  };
-
-  enum {
-    StorageOrdersAgree = (int(Derived::IsRowMajor) == int(OtherDerived::IsRowMajor)),
-    MightVectorize = StorageOrdersAgree
-                  && (int(Derived::Flags) & int(OtherDerived::Flags) & ActualPacketAccessBit),
-    MayInnerVectorize  = MightVectorize && int(InnerSize)!=Dynamic && int(InnerSize)%int(PacketSize)==0
-                       && int(DstIsAligned) && int(SrcIsAligned),
-    MayLinearize = StorageOrdersAgree && (int(Derived::Flags) & int(OtherDerived::Flags) & LinearAccessBit),
-    MayLinearVectorize = MightVectorize && MayLinearize && DstHasDirectAccess
-                       && (DstIsAligned || MaxSizeAtCompileTime == Dynamic),
-      /* If the destination isn't aligned, we have to do runtime checks and we don't unroll,
-         so it's only good for large enough sizes. */
-    MaySliceVectorize  = MightVectorize && DstHasDirectAccess
-                       && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=3*PacketSize)
-      /* slice vectorization can be slow, so we only want it if the slices are big, which is
-         indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block
-         in a fixed-size matrix */
-  };
-
-public:
-  enum {
-    Traversal = int(SrcEvalBeforeAssign) ? int(AllAtOnceTraversal) 
-              : int(MayInnerVectorize)   ? int(InnerVectorizedTraversal)
-              : int(MayLinearVectorize)  ? int(LinearVectorizedTraversal)
-              : int(MaySliceVectorize)   ? int(SliceVectorizedTraversal)
-              : int(MayLinearize)        ? int(LinearTraversal)
-                                         : int(DefaultTraversal),
-    Vectorized = int(Traversal) == InnerVectorizedTraversal
-              || int(Traversal) == LinearVectorizedTraversal
-              || int(Traversal) == SliceVectorizedTraversal
-  };
-
-private:
-  enum {
-    UnrollingLimit      = EIGEN_UNROLLING_LIMIT * (Vectorized ? int(PacketSize) : 1),
-    MayUnrollCompletely = int(Derived::SizeAtCompileTime) != Dynamic
-                       && int(OtherDerived::CoeffReadCost) != Dynamic
-                       && int(Derived::SizeAtCompileTime) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit),
-    MayUnrollInner      = int(InnerSize) != Dynamic
-                       && int(OtherDerived::CoeffReadCost) != Dynamic
-                       && int(InnerSize) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit)
-  };
-
-public:
-  enum {
-    Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal))
-                ? (
- 		    int(MayUnrollCompletely) ? int(CompleteUnrolling)
-                  : int(MayUnrollInner)      ? int(InnerUnrolling)
-                                             : int(NoUnrolling)
-                  )
-              : int(Traversal) == int(LinearVectorizedTraversal)
-                ? ( bool(MayUnrollCompletely) && bool(DstIsAligned) ? int(CompleteUnrolling) 
-                                                                    : int(NoUnrolling) )
-              : int(Traversal) == int(LinearTraversal)
-                ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) 
-                                              : int(NoUnrolling) )
-              : int(NoUnrolling)
-  };
-
-#ifdef EIGEN_DEBUG_ASSIGN
-  static void debug()
-  {
-    EIGEN_DEBUG_VAR(DstIsAligned)
-    EIGEN_DEBUG_VAR(SrcIsAligned)
-    EIGEN_DEBUG_VAR(JointAlignment)
-    EIGEN_DEBUG_VAR(InnerSize)
-    EIGEN_DEBUG_VAR(InnerMaxSize)
-    EIGEN_DEBUG_VAR(PacketSize)
-    EIGEN_DEBUG_VAR(StorageOrdersAgree)
-    EIGEN_DEBUG_VAR(MightVectorize)
-    EIGEN_DEBUG_VAR(MayLinearize)
-    EIGEN_DEBUG_VAR(MayInnerVectorize)
-    EIGEN_DEBUG_VAR(MayLinearVectorize)
-    EIGEN_DEBUG_VAR(MaySliceVectorize)
-    EIGEN_DEBUG_VAR(Traversal)
-    EIGEN_DEBUG_VAR(UnrollingLimit)
-    EIGEN_DEBUG_VAR(MayUnrollCompletely)
-    EIGEN_DEBUG_VAR(MayUnrollInner)
-    EIGEN_DEBUG_VAR(Unrolling)
-  }
-#endif
-};
-
-/***************************************************************************
-* Part 2 : meta-unrollers
-***************************************************************************/
-
-/************************
-*** Default traversal ***
-************************/
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Index, int Stop>
-struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling
-{
-  typedef typename DstEvaluatorType::XprType DstXprType;
-  
-  enum {
-    outer = Index / DstXprType::InnerSizeAtCompileTime,
-    inner = Index % DstXprType::InnerSizeAtCompileTime
-  };
-
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator,
-                                      SrcEvaluatorType &srcEvaluator)
-  {
-    dstEvaluator.copyCoeffByOuterInner(outer, inner, srcEvaluator);
-    copy_using_evaluator_DefaultTraversal_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, Index+1, Stop>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Stop>
-struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling<DstEvaluatorType, SrcEvaluatorType, Stop, Stop>
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType&, SrcEvaluatorType&) { }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Index, int Stop>
-struct copy_using_evaluator_DefaultTraversal_InnerUnrolling
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator,
-                                      SrcEvaluatorType &srcEvaluator, 
-                                      int outer)
-  {
-    dstEvaluator.copyCoeffByOuterInner(outer, Index, srcEvaluator);
-    copy_using_evaluator_DefaultTraversal_InnerUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, Index+1, Stop>
-      ::run(dstEvaluator, srcEvaluator, outer);
-  }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Stop>
-struct copy_using_evaluator_DefaultTraversal_InnerUnrolling<DstEvaluatorType, SrcEvaluatorType, Stop, Stop>
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType&, SrcEvaluatorType&, int) { }
-};
-
-/***********************
-*** Linear traversal ***
-***********************/
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Index, int Stop>
-struct copy_using_evaluator_LinearTraversal_CompleteUnrolling
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator,
-                                      SrcEvaluatorType &srcEvaluator)
-  {
-    dstEvaluator.copyCoeff(Index, srcEvaluator);
-    copy_using_evaluator_LinearTraversal_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, Index+1, Stop>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Stop>
-struct copy_using_evaluator_LinearTraversal_CompleteUnrolling<DstEvaluatorType, SrcEvaluatorType, Stop, Stop>
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType&, SrcEvaluatorType&) { }
-};
-
-/**************************
-*** Inner vectorization ***
-**************************/
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Index, int Stop>
-struct copy_using_evaluator_innervec_CompleteUnrolling
-{
-  typedef typename DstEvaluatorType::XprType DstXprType;
-  typedef typename SrcEvaluatorType::XprType SrcXprType;
-
-  enum {
-    outer = Index / DstXprType::InnerSizeAtCompileTime,
-    inner = Index % DstXprType::InnerSizeAtCompileTime,
-    JointAlignment = copy_using_evaluator_traits<DstXprType,SrcXprType>::JointAlignment
-  };
-
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator,
-                                      SrcEvaluatorType &srcEvaluator)
-  {
-    dstEvaluator.template copyPacketByOuterInner<Aligned, JointAlignment>(outer, inner, srcEvaluator);
-    enum { NextIndex = Index + packet_traits<typename DstXprType::Scalar>::size };
-    copy_using_evaluator_innervec_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, NextIndex, Stop>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Stop>
-struct copy_using_evaluator_innervec_CompleteUnrolling<DstEvaluatorType, SrcEvaluatorType, Stop, Stop>
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType&, SrcEvaluatorType&) { }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Index, int Stop>
-struct copy_using_evaluator_innervec_InnerUnrolling
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator,
-                                      SrcEvaluatorType &srcEvaluator, 
-                                      int outer)
-  {
-    dstEvaluator.template copyPacketByOuterInner<Aligned, Aligned>(outer, Index, srcEvaluator);
-    typedef typename DstEvaluatorType::XprType DstXprType;
-    enum { NextIndex = Index + packet_traits<typename DstXprType::Scalar>::size };
-    copy_using_evaluator_innervec_InnerUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, NextIndex, Stop>
-      ::run(dstEvaluator, srcEvaluator, outer);
-  }
-};
-
-template<typename DstEvaluatorType, typename SrcEvaluatorType, int Stop>
-struct copy_using_evaluator_innervec_InnerUnrolling<DstEvaluatorType, SrcEvaluatorType, Stop, Stop>
-{
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType&, SrcEvaluatorType&, int) { }
-};
-
-/***************************************************************************
-* Part 3 : implementation of all cases
-***************************************************************************/
-
-// copy_using_evaluator_impl is based on assign_impl
-
-template<typename DstXprType, typename SrcXprType,
-         int Traversal = copy_using_evaluator_traits<DstXprType, SrcXprType>::Traversal,
-         int Unrolling = copy_using_evaluator_traits<DstXprType, SrcXprType>::Unrolling>
-struct copy_using_evaluator_impl;
-
-/************************
-*** Default traversal ***
-************************/
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, DefaultTraversal, NoUnrolling>
-{
-  static void run(DstXprType& dst, const SrcXprType& src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    for(Index outer = 0; outer < dst.outerSize(); ++outer) {
-      for(Index inner = 0; inner < dst.innerSize(); ++inner) {
-	dstEvaluator.copyCoeffByOuterInner(outer, inner, srcEvaluator);
-      }
-    }
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, DefaultTraversal, CompleteUnrolling>
-{
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    copy_using_evaluator_DefaultTraversal_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, 0, DstXprType::SizeAtCompileTime>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, DefaultTraversal, InnerUnrolling>
-{
-  typedef typename DstXprType::Index Index;
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    const Index outerSize = dst.outerSize();
-    for(Index outer = 0; outer < outerSize; ++outer)
-      copy_using_evaluator_DefaultTraversal_InnerUnrolling
-        <DstEvaluatorType, SrcEvaluatorType, 0, DstXprType::InnerSizeAtCompileTime>
-        ::run(dstEvaluator, srcEvaluator, outer);
-  }
-};
-
-/***************************
-*** Linear vectorization ***
-***************************/
-
-template <bool IsAligned = false>
-struct unaligned_copy_using_evaluator_impl
-{
-  // if IsAligned = true, then do nothing
-  template <typename SrcEvaluatorType, typename DstEvaluatorType>
-  static EIGEN_STRONG_INLINE void run(const SrcEvaluatorType&, DstEvaluatorType&, 
-                                      typename SrcEvaluatorType::Index, typename SrcEvaluatorType::Index) {}
-};
-
-template <>
-struct unaligned_copy_using_evaluator_impl<false>
-{
-  // MSVC must not inline this functions. If it does, it fails to optimize the
-  // packet access path.
-#ifdef _MSC_VER
-  template <typename DstEvaluatorType, typename SrcEvaluatorType>
-  static EIGEN_DONT_INLINE void run(DstEvaluatorType &dstEvaluator, 
-                                    const SrcEvaluatorType &srcEvaluator,
-                                    typename DstEvaluatorType::Index start,
-                                    typename DstEvaluatorType::Index end)
-#else
-  template <typename DstEvaluatorType, typename SrcEvaluatorType>
-  static EIGEN_STRONG_INLINE void run(DstEvaluatorType &dstEvaluator, 
-                                      const SrcEvaluatorType &srcEvaluator,
-                                      typename DstEvaluatorType::Index start,
-                                      typename DstEvaluatorType::Index end)
-#endif
-  {
-    for (typename DstEvaluatorType::Index index = start; index < end; ++index)
-      dstEvaluator.copyCoeff(index, srcEvaluator);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, LinearVectorizedTraversal, NoUnrolling>
-{
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    const Index size = dst.size();
-    typedef packet_traits<typename DstXprType::Scalar> PacketTraits;
-    enum {
-      packetSize = PacketTraits::size,
-      dstIsAligned = int(copy_using_evaluator_traits<DstXprType,SrcXprType>::DstIsAligned),
-      dstAlignment = PacketTraits::AlignedOnScalar ? Aligned : dstIsAligned,
-      srcAlignment = copy_using_evaluator_traits<DstXprType,SrcXprType>::JointAlignment
-    };
-    const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned(&dstEvaluator.coeffRef(0), size);
-    const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
-
-    unaligned_copy_using_evaluator_impl<dstIsAligned!=0>::run(dstEvaluator, srcEvaluator, 0, alignedStart);
-
-    for(Index index = alignedStart; index < alignedEnd; index += packetSize)
-    {
-      dstEvaluator.template copyPacket<dstAlignment, srcAlignment>(index, srcEvaluator);
-    }
-
-    unaligned_copy_using_evaluator_impl<>::run(dstEvaluator, srcEvaluator, alignedEnd, size);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, LinearVectorizedTraversal, CompleteUnrolling>
-{
-  typedef typename DstXprType::Index Index;
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    enum { size = DstXprType::SizeAtCompileTime,
-           packetSize = packet_traits<typename DstXprType::Scalar>::size,
-           alignedSize = (size/packetSize)*packetSize };
-
-    copy_using_evaluator_innervec_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, 0, alignedSize>
-      ::run(dstEvaluator, srcEvaluator);
-    copy_using_evaluator_DefaultTraversal_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, alignedSize, size>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-/**************************
-*** Inner vectorization ***
-**************************/
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, InnerVectorizedTraversal, NoUnrolling>
-{
-  inline static void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    const Index innerSize = dst.innerSize();
-    const Index outerSize = dst.outerSize();
-    const Index packetSize = packet_traits<typename DstXprType::Scalar>::size;
-    for(Index outer = 0; outer < outerSize; ++outer)
-      for(Index inner = 0; inner < innerSize; inner+=packetSize) {
-	dstEvaluator.template copyPacketByOuterInner<Aligned, Aligned>(outer, inner, srcEvaluator);
-      }
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, InnerVectorizedTraversal, CompleteUnrolling>
-{
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    copy_using_evaluator_innervec_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, 0, DstXprType::SizeAtCompileTime>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, InnerVectorizedTraversal, InnerUnrolling>
-{
-  typedef typename DstXprType::Index Index;
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    const Index outerSize = dst.outerSize();
-    for(Index outer = 0; outer < outerSize; ++outer)
-      copy_using_evaluator_innervec_InnerUnrolling
-        <DstEvaluatorType, SrcEvaluatorType, 0, DstXprType::InnerSizeAtCompileTime>
-        ::run(dstEvaluator, srcEvaluator, outer);
-  }
-};
-
-/***********************
-*** Linear traversal ***
-***********************/
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, LinearTraversal, NoUnrolling>
-{
-  inline static void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    const Index size = dst.size();
-    for(Index i = 0; i < size; ++i)
-      dstEvaluator.copyCoeff(i, srcEvaluator);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, LinearTraversal, CompleteUnrolling>
-{
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    copy_using_evaluator_LinearTraversal_CompleteUnrolling
-      <DstEvaluatorType, SrcEvaluatorType, 0, DstXprType::SizeAtCompileTime>
-      ::run(dstEvaluator, srcEvaluator);
-  }
-};
-
-/**************************
-*** Slice vectorization ***
-***************************/
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, SliceVectorizedTraversal, NoUnrolling>
-{
-  inline static void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    typedef packet_traits<typename DstXprType::Scalar> PacketTraits;
-    enum {
-      packetSize = PacketTraits::size,
-      alignable = PacketTraits::AlignedOnScalar,
-      dstAlignment = alignable ? Aligned : int(copy_using_evaluator_traits<DstXprType,SrcXprType>::DstIsAligned)
-    };
-    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) || copy_using_evaluator_traits<DstXprType,SrcXprType>::DstIsAligned) ? 0
-                       : internal::first_aligned(&dstEvaluator.coeffRef(0,0), innerSize);
-
-    for(Index outer = 0; outer < outerSize; ++outer)
-    {
-      const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);
-      // do the non-vectorizable part of the assignment
-      for(Index inner = 0; inner<alignedStart ; ++inner) {
-        dstEvaluator.copyCoeffByOuterInner(outer, inner, srcEvaluator);
-      }
-
-      // do the vectorizable part of the assignment
-      for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize) {
-        dstEvaluator.template copyPacketByOuterInner<dstAlignment, Unaligned>(outer, inner, srcEvaluator);
-      }
-
-      // do the non-vectorizable part of the assignment
-      for(Index inner = alignedEnd; inner<innerSize ; ++inner) {
-        dstEvaluator.copyCoeffByOuterInner(outer, inner, srcEvaluator);
-      }
-
-      alignedStart = std::min<Index>((alignedStart+alignedStep)%packetSize, innerSize);
-    }
-  }
-};
-
-/****************************
-*** All-at-once traversal ***
-****************************/
-
-template<typename DstXprType, typename SrcXprType>
-struct copy_using_evaluator_impl<DstXprType, SrcXprType, AllAtOnceTraversal, NoUnrolling>
-{
-  inline static void run(DstXprType &dst, const SrcXprType &src)
-  {
-    typedef typename evaluator<DstXprType>::type DstEvaluatorType;
-    typedef typename evaluator<SrcXprType>::type SrcEvaluatorType;
-    typedef typename DstXprType::Index Index;
-
-    DstEvaluatorType dstEvaluator(dst);
-    SrcEvaluatorType srcEvaluator(src);
-
-    // Evaluate rhs in temporary to prevent aliasing problems in a = a * a;
-    // TODO: Do not pass the xpr object to evalTo()
-    srcEvaluator.evalTo(dstEvaluator, dst);
-  }
-};
-
-/***************************************************************************
-* Part 4 : Entry points
-***************************************************************************/
-
-// Based on DenseBase::LazyAssign()
-
-template<typename DstXprType, template <typename> class StorageBase, typename SrcXprType>
-EIGEN_STRONG_INLINE
-const DstXprType& copy_using_evaluator(const NoAlias<DstXprType, StorageBase>& dst, 
-                                       const EigenBase<SrcXprType>& src)
-{
-  return noalias_copy_using_evaluator(dst.expression(), src.derived());
-}
-
-template<typename XprType, int AssumeAliasing = evaluator_traits<XprType>::AssumeAliasing>
-struct AddEvalIfAssumingAliasing;
-
-template<typename XprType>
-struct AddEvalIfAssumingAliasing<XprType, 0>
-{
-  static const XprType& run(const XprType& xpr) 
-  {
-    return xpr;
-  }
-};
-
-template<typename XprType>
-struct AddEvalIfAssumingAliasing<XprType, 1>
-{
-  static const EvalToTemp<XprType> run(const XprType& xpr)
-  {
-    return EvalToTemp<XprType>(xpr);
-  }
-};
-
-template<typename DstXprType, typename SrcXprType>
-EIGEN_STRONG_INLINE
-const DstXprType& copy_using_evaluator(const EigenBase<DstXprType>& dst, const EigenBase<SrcXprType>& src)
-{
-  return noalias_copy_using_evaluator(dst.const_cast_derived(), 
-				      AddEvalIfAssumingAliasing<SrcXprType>::run(src.derived()));
-}
-
-template<typename DstXprType, typename SrcXprType>
-EIGEN_STRONG_INLINE
-const DstXprType& noalias_copy_using_evaluator(const PlainObjectBase<DstXprType>& dst, const EigenBase<SrcXprType>& src)
-{
-#ifdef EIGEN_DEBUG_ASSIGN
-  internal::copy_using_evaluator_traits<DstXprType, SrcXprType>::debug();
-#endif
-#ifdef EIGEN_NO_AUTOMATIC_RESIZING
-  eigen_assert((dst.size()==0 || (IsVectorAtCompileTime ? (dst.size() == src.size())
-				  : (dst.rows() == src.rows() && dst.cols() == src.cols())))
-	       && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
-#else
-  dst.const_cast_derived().resizeLike(src.derived());
-#endif
-  return copy_using_evaluator_without_resizing(dst.const_cast_derived(), src.derived());
-}
-
-template<typename DstXprType, typename SrcXprType>
-EIGEN_STRONG_INLINE
-const DstXprType& noalias_copy_using_evaluator(const EigenBase<DstXprType>& dst, const EigenBase<SrcXprType>& src)
-{
-  return copy_using_evaluator_without_resizing(dst.const_cast_derived(), src.derived());
-}
-
-template<typename DstXprType, typename SrcXprType>
-const DstXprType& copy_using_evaluator_without_resizing(const DstXprType& dst, const SrcXprType& src)
-{
-#ifdef EIGEN_DEBUG_ASSIGN
-  internal::copy_using_evaluator_traits<DstXprType, SrcXprType>::debug();
-#endif
-  eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
-  copy_using_evaluator_impl<DstXprType, SrcXprType>::run(const_cast<DstXprType&>(dst), src);
-  return dst;
-}
-
-// Based on DenseBase::swap()
-// TODO: Chech whether we need to do something special for swapping two
-//       Arrays or Matrices.
-
-template<typename DstXprType, typename SrcXprType>
-void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src)
-{
-  copy_using_evaluator(SwapWrapper<DstXprType>(const_cast<DstXprType&>(dst)), src);
-}
-
-// Based on MatrixBase::operator+= (in CwiseBinaryOp.h)
-template<typename DstXprType, typename SrcXprType>
-void add_assign_using_evaluator(const MatrixBase<DstXprType>& dst, const MatrixBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-// Based on ArrayBase::operator+=
-template<typename DstXprType, typename SrcXprType>
-void add_assign_using_evaluator(const ArrayBase<DstXprType>& dst, const ArrayBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-// TODO: Add add_assign_using_evaluator for EigenBase ?
-
-template<typename DstXprType, typename SrcXprType>
-void subtract_assign_using_evaluator(const MatrixBase<DstXprType>& dst, const MatrixBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-template<typename DstXprType, typename SrcXprType>
-void subtract_assign_using_evaluator(const ArrayBase<DstXprType>& dst, const ArrayBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-template<typename DstXprType, typename SrcXprType>
-void multiply_assign_using_evaluator(const ArrayBase<DstXprType>& dst, const ArrayBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-template<typename DstXprType, typename SrcXprType>
-void divide_assign_using_evaluator(const ArrayBase<DstXprType>& dst, const ArrayBase<SrcXprType>& src)
-{
-  typedef typename DstXprType::Scalar Scalar;
-  SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, DstXprType, SrcXprType> tmp(dst.const_cast_derived());
-  copy_using_evaluator(tmp, src.derived());
-}
-
-
-} // namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_ASSIGN_EVALUATOR_H

Eigen/src/Core/Block.h

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

Eigen/src/Core/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>
@@ -129,6 +129,26 @@ inline typename DenseBase<Derived>::Index DenseBase<Derived>::count() const
   return derived().template cast<bool>().template cast<Index>().sum();
 }
 
+/** \returns true is \c *this contains at least one Not A Number (NaN).
+  *
+  * \sa allFinite()
+  */
+template<typename Derived>
+inline bool DenseBase<Derived>::hasNaN() const
+{
+  return !((derived().array()==derived().array()).all());
+}
+
+/** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values.
+  *
+  * \sa hasNaN()
+  */
+template<typename Derived>
+inline bool DenseBase<Derived>::allFinite() const
+{
+  return !((derived()-derived()).hasNaN());
+}
+    
 } // end namespace Eigen
 
 #endif // EIGEN_ALLANDANY_H

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)
   {
@@ -118,6 +129,8 @@ struct CommaInitializer
   *
   * Example: \include MatrixBase_set.cpp
   * Output: \verbinclude MatrixBase_set.out
+  * 
+  * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
   *
   * \sa CommaInitializer::finished(), class CommaInitializer
   */

Eigen/src/Core/CwiseBinaryOp.h

@@ -94,8 +94,8 @@ struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
 // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
 // add together a float matrix and a double matrix.
 #define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
-  EIGEN_STATIC_ASSERT((internal::functor_allows_mixing_real_and_complex<BINOP>::ret \
+  EIGEN_STATIC_ASSERT((internal::functor_is_product_like<BINOP>::ret \
-                        ? int(internal::is_same<typename NumTraits<LHS>::Real, typename NumTraits<RHS>::Real>::value) \
+                        ? int(internal::scalar_product_traits<LHS, RHS>::Defined) \
                         : int(internal::is_same<LHS, RHS>::value)), \
     YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
 

Eigen/src/Core/CwiseUnaryView.h

@@ -56,8 +56,7 @@ template<typename ViewOp, typename MatrixType, typename StorageKind>
 class CwiseUnaryViewImpl;
 
 template<typename ViewOp, typename MatrixType>
-class CwiseUnaryView : internal::no_assignment_operator,
+class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
-  public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
 {
   public:
 
@@ -99,6 +98,7 @@ class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
     typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
 
     EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
     
     inline Scalar* data() { return &coeffRef(0); }
     inline const Scalar* data() const { return &coeff(0); }

Eigen/src/Core/DenseBase.h

@@ -13,6 +13,16 @@
 
 namespace Eigen {
 
+namespace internal {
+  
+// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
+// This dummy function simply aims at checking that at compile time.
+static inline void check_DenseIndex_is_signed() {
+  EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE); 
+}
+
+} // end namespace internal
+  
 /** \class DenseBase
   * \ingroup Core_Module
   *
@@ -256,11 +266,13 @@ template<typename Derived> class DenseBase
     template<typename OtherDerived>
     Derived& operator=(const ReturnByValue<OtherDerived>& func);
 
-#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal Copies \a other into *this without evaluating other. \returns a reference to *this. */
-    /** Copies \a other into *this without evaluating other. \returns a reference to *this. */
     template<typename OtherDerived>
     Derived& lazyAssign(const DenseBase<OtherDerived>& other);
-#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** \internal Evaluates \a other into *this. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const ReturnByValue<OtherDerived>& other);
 
     CommaInitializer<Derived> operator<< (const Scalar& s);
 
@@ -271,7 +283,7 @@ template<typename Derived> class DenseBase
     CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
 
     Eigen::Transpose<Derived> transpose();
-    typedef const Transpose<const Derived> ConstTransposeReturnType;
+	typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;
     ConstTransposeReturnType transpose() const;
     void transposeInPlace();
 #ifndef EIGEN_NO_DEBUG
@@ -336,6 +348,9 @@ template<typename Derived> class DenseBase
     bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
     bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
     bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    
+    inline bool hasNaN() const;
+    inline bool allFinite() const;
 
     inline Derived& operator*=(const Scalar& other);
     inline Derived& operator/=(const Scalar& other);
@@ -415,8 +430,6 @@ template<typename Derived> class DenseBase
       return derived().coeff(0,0);
     }
 
-/////////// Array module ///////////
-
     bool all(void) const;
     bool any(void) const;
     Index count() const;
@@ -442,17 +455,19 @@ template<typename Derived> class DenseBase
 
     template<typename ThenDerived>
     inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
-    select(const DenseBase<ThenDerived>& thenMatrix, typename ThenDerived::Scalar elseScalar) const;
+    select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;
 
     template<typename ElseDerived>
     inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
-    select(typename ElseDerived::Scalar thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
+    select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
 
     template<int p> RealScalar lpNorm() const;
 
     template<int RowFactor, int ColFactor>
-    const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+    inline const Replicate<Derived,RowFactor,ColFactor> replicate() const;
-    const Replicate<Derived,Dynamic,Dynamic> replicate(Index rowFacor,Index colFactor) const;
+    
+    typedef Replicate<Derived,Dynamic,Dynamic> ReplicateReturnType;
+    inline const ReplicateReturnType replicate(Index rowFacor,Index colFactor) const;
 
     typedef Reverse<Derived, BothDirections> ReverseReturnType;
     typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;

Eigen/src/Core/DenseStorage.h

@@ -24,6 +24,14 @@ namespace internal {
 
 struct constructor_without_unaligned_array_assert {};
 
+template<typename T, int Size> void check_static_allocation_size()
+{
+  // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit
+  #if EIGEN_STACK_ALLOCATION_LIMIT
+  EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+  #endif
+}
+
 /** \internal
   * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
   * to 16 bytes boundary if the total size is a multiple of 16 bytes.
@@ -38,12 +46,12 @@ struct plain_array
 
   plain_array() 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 
   plain_array(constructor_without_unaligned_array_assert) 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 };
 
@@ -76,12 +84,12 @@ struct plain_array<T, Size, MatrixOrArrayOptions, 16>
   plain_array() 
   { 
     EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(0xf);
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 
   plain_array(constructor_without_unaligned_array_assert) 
   { 
-    EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+    check_static_allocation_size<T,Size>();
   }
 };
 
@@ -114,7 +122,7 @@ template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseSt
 {
     internal::plain_array<T,Size,_Options> m_data;
   public:
-    inline explicit DenseStorage() {}
+    inline DenseStorage() {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()) {}
     inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
@@ -131,7 +139,7 @@ template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseSt
 template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
 {
   public:
-    inline explicit DenseStorage() {}
+    inline DenseStorage() {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert) {}
     inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
     inline void swap(DenseStorage& ) {}
@@ -160,7 +168,7 @@ template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic
     DenseIndex m_rows;
     DenseIndex m_cols;
   public:
-    inline explicit DenseStorage() : m_rows(0), m_cols(0) {}
+    inline DenseStorage() : m_rows(0), m_cols(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
     inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex nbCols) : m_rows(nbRows), m_cols(nbCols) {}
@@ -180,7 +188,7 @@ template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Si
     internal::plain_array<T,Size,_Options> m_data;
     DenseIndex m_rows;
   public:
-    inline explicit DenseStorage() : m_rows(0) {}
+    inline DenseStorage() : m_rows(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
     inline DenseStorage(DenseIndex, DenseIndex nbRows, DenseIndex) : m_rows(nbRows) {}
@@ -199,7 +207,7 @@ template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Si
     internal::plain_array<T,Size,_Options> m_data;
     DenseIndex m_cols;
   public:
-    inline explicit DenseStorage() : m_cols(0) {}
+    inline DenseStorage() : m_cols(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert)
       : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
     inline DenseStorage(DenseIndex, DenseIndex, DenseIndex nbCols) : m_cols(nbCols) {}
@@ -219,7 +227,7 @@ template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynam
     DenseIndex m_rows;
     DenseIndex m_cols;
   public:
-    inline explicit DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
+    inline DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert)
        : m_data(0), m_rows(0), m_cols(0) {}
     inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex nbCols)
@@ -260,7 +268,7 @@ template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Ro
     T *m_data;
     DenseIndex m_cols;
   public:
-    inline explicit DenseStorage() : m_data(0), m_cols(0) {}
+    inline DenseStorage() : m_data(0), m_cols(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
     inline DenseStorage(DenseIndex size, DenseIndex, DenseIndex nbCols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(nbCols)
     { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
@@ -296,7 +304,7 @@ template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dyn
     T *m_data;
     DenseIndex m_rows;
   public:
-    inline explicit DenseStorage() : m_data(0), m_rows(0) {}
+    inline DenseStorage() : m_data(0), m_rows(0) {}
     inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
     inline DenseStorage(DenseIndex size, DenseIndex nbRows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(nbRows)
     { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }

Eigen/src/Core/Diagonal.h

@@ -75,7 +75,7 @@ template<typename MatrixType, int _DiagIndex> class Diagonal
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
 
     inline Index rows() const
-    { return m_index.value()<0 ? (std::min)(m_matrix.cols(),m_matrix.rows()+m_index.value()) : (std::min)(m_matrix.rows(),m_matrix.cols()-m_index.value()); }
+    { return m_index.value()<0 ? (std::min<Index>)(m_matrix.cols(),m_matrix.rows()+m_index.value()) : (std::min<Index>)(m_matrix.rows(),m_matrix.cols()-m_index.value()); }
 
     inline Index cols() const { return 1; }
 
@@ -172,7 +172,7 @@ MatrixBase<Derived>::diagonal()
 
 /** This is the const version of diagonal(). */
 template<typename Derived>
-inline const typename MatrixBase<Derived>::ConstDiagonalReturnType
+inline typename MatrixBase<Derived>::ConstDiagonalReturnType
 MatrixBase<Derived>::diagonal() const
 {
   return ConstDiagonalReturnType(derived());
@@ -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

@@ -26,14 +26,15 @@ struct traits<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
     MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
 
     _StorageOrder = MatrixType::Flags & RowMajorBit ? RowMajor : ColMajor,
-    _PacketOnDiag = !((int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
+    _ScalarAccessOnDiag =  !((int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheLeft)
-                    ||(int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheRight)),
+                          ||(int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheRight)),
     _SameTypes = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,
     // FIXME currently we need same types, but in the future the next rule should be the one
-    //_Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagonalType::Flags)&PacketAccessBit))),
+    //_Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagonalType::DiagonalVectorType::Flags)&PacketAccessBit))),
-    _Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && _SameTypes && ((!_PacketOnDiag) || (bool(int(DiagonalType::Flags)&PacketAccessBit))),
+    _Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && _SameTypes && (_ScalarAccessOnDiag || (bool(int(DiagonalType::DiagonalVectorType::Flags)&PacketAccessBit))),
+    _LinearAccessMask = (RowsAtCompileTime==1 || ColsAtCompileTime==1) ? LinearAccessBit : 0,
 
-    Flags = (HereditaryBits & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0),
+    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
   };
 };
@@ -54,13 +55,21 @@ class DiagonalProduct : internal::no_assignment_operator,
       eigen_assert(diagonal.diagonal().size() == (ProductOrder == OnTheLeft ? matrix.rows() : matrix.cols()));
     }
 
-    inline Index rows() const { return m_matrix.rows(); }
+    EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
-    inline Index cols() const { return m_matrix.cols(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
 
-    const Scalar coeff(Index row, Index col) const
+    EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
     {
       return m_diagonal.diagonal().coeff(ProductOrder == OnTheLeft ? row : col) * m_matrix.coeff(row, col);
     }
+    
+    EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const
+    {
+      enum {
+        StorageOrder = int(MatrixType::Flags) & RowMajorBit ? RowMajor : ColMajor
+      };
+      return coeff(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+    }
 
     template<int LoadMode>
     EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
@@ -69,11 +78,19 @@ class DiagonalProduct : internal::no_assignment_operator,
         StorageOrder = Flags & RowMajorBit ? RowMajor : ColMajor
       };
       const Index indexInDiagonalVector = ProductOrder == OnTheLeft ? row : col;
-
       return packet_impl<LoadMode>(row,col,indexInDiagonalVector,typename internal::conditional<
         ((int(StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
        ||(int(StorageOrder) == ColMajor && int(ProductOrder) == OnTheRight)), internal::true_type, internal::false_type>::type());
     }
+    
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index idx) const
+    {
+      enum {
+        StorageOrder = int(MatrixType::Flags) & RowMajorBit ? RowMajor : ColMajor
+      };
+      return packet<LoadMode>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+    }
 
   protected:
     template<int LoadMode>
@@ -88,7 +105,7 @@ class DiagonalProduct : internal::no_assignment_operator,
     {
       enum {
         InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
-        DiagonalVectorPacketLoadMode = (LoadMode == Aligned && ((InnerSize%16) == 0)) ? Aligned : Unaligned
+        DiagonalVectorPacketLoadMode = (LoadMode == Aligned && (((InnerSize%16) == 0) || (int(DiagonalType::DiagonalVectorType::Flags)&AlignedBit)==AlignedBit) ? Aligned : Unaligned)
       };
       return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
                      m_diagonal.diagonal().template packet<DiagonalVectorPacketLoadMode>(id));

Eigen/src/Core/Dot.h

@@ -112,7 +112,7 @@ MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
 template<typename Derived>
 EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
 {
-  return internal::real((*this).cwiseAbs2().sum());
+  return numext::real((*this).cwiseAbs2().sum());
 }
 
 /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
@@ -166,6 +166,7 @@ struct lpNorm_selector
   typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
   static inline RealScalar run(const MatrixBase<Derived>& m)
   {
+    using std::pow;
     return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
   }
 };
@@ -228,7 +229,7 @@ bool MatrixBase<Derived>::isOrthogonal
 {
   typename internal::nested<Derived,2>::type nested(derived());
   typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
-  return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
+  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
 }
 
 /** \returns true if *this is approximately an unitary matrix,

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

@@ -171,7 +171,7 @@ struct functor_traits<scalar_hypot_op<Scalar> > {
   */
 template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
-  inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return internal::pow(a, b); }
+  inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return numext::pow(a, b); }
 };
 template<typename Scalar, typename OtherScalar>
 struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
@@ -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
@@ -310,7 +351,7 @@ struct functor_traits<scalar_abs_op<Scalar> >
 template<typename Scalar> struct scalar_abs2_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs2(a); }
+  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
   template<typename Packet>
   EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
   { return internal::pmul(a,a); }
@@ -326,7 +367,7 @@ struct functor_traits<scalar_abs2_op<Scalar> >
   */
 template<typename Scalar> struct scalar_conjugate_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
-  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using internal::conj; return conj(a); }
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using numext::conj; return conj(a); }
   template<typename Packet>
   EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
 };
@@ -363,7 +404,7 @@ template<typename Scalar>
 struct scalar_real_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::real(a); }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_real_op<Scalar> >
@@ -378,7 +419,7 @@ template<typename Scalar>
 struct scalar_imag_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::imag(a); }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_imag_op<Scalar> >
@@ -393,7 +434,7 @@ template<typename Scalar>
 struct scalar_real_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::real_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_real_ref_op<Scalar> >
@@ -408,7 +449,7 @@ template<typename Scalar>
 struct scalar_imag_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::imag_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_imag_ref_op<Scalar> >
@@ -560,7 +601,7 @@ struct linspaced_op_impl<Scalar,false>
   EIGEN_STRONG_INLINE const Scalar operator() (Index i) const 
   { 
     m_base = padd(m_base, pset1<Packet>(m_step));
-    return m_low+i*m_step; 
+    return m_low+Scalar(i)*m_step; 
   }
 
   template<typename Index>
@@ -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, int 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); }
@@ -648,13 +689,14 @@ template <typename Scalar, bool RandomAccess> struct linspaced_op
 template<typename Functor> struct functor_has_linear_access { enum { ret = 1 }; };
 template<typename Scalar> struct functor_has_linear_access<scalar_identity_op<Scalar> > { enum { ret = 0 }; };
 
-// in CwiseBinaryOp, we require the Lhs and Rhs to have the same scalar type, except for multiplication
+// In Eigen, any binary op (Product, CwiseBinaryOp) require the Lhs and Rhs to have the same scalar type, except for multiplication
-// where we only require them to have the same _real_ scalar type so one may multiply, say, float by complex<float>.
+// where the mixing of different types is handled by scalar_product_traits
+// In particular, real * complex<real> is allowed.
 // FIXME move this to functor_traits adding a functor_default
-template<typename Functor> struct functor_allows_mixing_real_and_complex { enum { ret = 0 }; };
+template<typename Functor> struct functor_is_product_like { enum { ret = 0 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_quotient_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_quotient_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
 
 
 /** \internal
@@ -800,7 +842,7 @@ struct scalar_pow_op {
   // FIXME default copy constructors seems bugged with std::complex<>
   inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
   inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
-  inline Scalar operator() (const Scalar& a) const { return internal::pow(a, m_exponent); }
+  inline Scalar operator() (const Scalar& a) const { return numext::pow(a, m_exponent); }
   const Scalar m_exponent;
 };
 template<typename Scalar>

Eigen/src/Core/Fuzzy.h

@@ -42,7 +42,7 @@ struct isMuchSmallerThan_object_selector
 {
   static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
   {
-    return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum();
+    return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
   }
 };
 
@@ -60,7 +60,7 @@ struct isMuchSmallerThan_scalar_selector
 {
   static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
   {
-    return x.cwiseAbs2().sum() <= abs2(prec * y);
+    return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
   }
 };
 

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>
@@ -435,7 +435,7 @@ template<> struct gemv_selector<OnTheRight,ColMajor,true>
 
     gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
 
-    bool alphaIsCompatible = (!ComplexByReal) || (imag(actualAlpha)==RealScalar(0));
+    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
     bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
     
     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);

Eigen/src/Core/GenericPacketMath.h

@@ -106,7 +106,7 @@ pnegate(const Packet& a) { return -a; }
 
 /** \internal \returns conj(a) (coeff-wise) */
 template<typename Packet> inline Packet
-pconj(const Packet& a) { return conj(a); }
+pconj(const Packet& a) { return numext::conj(a); }
 
 /** \internal \returns a * b (coeff-wise) */
 template<typename Packet> inline Packet
@@ -156,7 +156,11 @@ pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
 template<typename Packet> inline Packet
 ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
 
-/** \internal \returns a packet with elements of \a *from duplicated, e.g.: (from[0],from[0],from[1],from[1]) */
+/** \internal \returns a packet with elements of \a *from duplicated.
+  * For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and
+  * duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]}
+  * Currently, this function is only used for scalar * complex products.
+ */
 template<typename Packet> inline Packet
 ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
 
@@ -307,8 +311,21 @@ struct palign_impl
   static inline void run(PacketType&, const PacketType&) {}
 };
 
-/** \internal update \a first using the concatenation of the \a Offset last elements
+/** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
-  * of \a first and packet_size minus \a Offset first elements of \a second */
+  * of \a first and \a Offset first elements of \a second.
+  * 
+  * This function is currently only used to optimize matrix-vector products on unligned matrices.
+  * It takes 2 packets that represent a contiguous memory array, and returns a packet starting
+  * at the position \a Offset. For instance, for packets of 4 elements, we have:
+  *  Input:
+  *  - first = {f0,f1,f2,f3}
+  *  - second = {s0,s1,s2,s3}
+  * Output: 
+  *   - if Offset==0 then {f0,f1,f2,f3}
+  *   - if Offset==1 then {f1,f2,f3,s0}
+  *   - if Offset==2 then {f2,f3,s0,s1}
+  *   - if Offset==3 then {f3,s0,s1,s3}
+  */
 template<int Offset,typename PacketType>
 inline void palign(PacketType& first, const PacketType& second)
 {

Eigen/src/Core/GlobalFunctions.h

@@ -39,6 +39,7 @@ namespace Eigen
 {
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op)
@@ -70,7 +71,7 @@ namespace Eigen
   **/
   template <typename Derived>
   inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
-    operator/(typename Derived::Scalar s, const Eigen::ArrayBase<Derived>& a)
+    operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
   {
     return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
       a.derived(),
@@ -86,6 +87,6 @@ namespace Eigen
   }
 }
 
-// TODO: cleanly disable those functions that are not supported on Array (internal::real_ref, internal::random, internal::isApprox...)
+// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
 
 #endif // EIGEN_GLOBAL_FUNCTIONS_H

Eigen/src/Core/IO.h

@@ -55,7 +55,7 @@ struct IOFormat
     const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
     const std::string& _matPrefix="", const std::string& _matSuffix="")
   : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
-    coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
+    rowSpacer(""), coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
   {
     int i = int(matSuffix.length())-1;
     while (i>=0 && matSuffix[i]!='\n')
@@ -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

@@ -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

@@ -51,16 +51,15 @@ struct global_math_functions_filtering_base
   typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
 };
 
-#define EIGEN_MATHFUNC_IMPL(func, scalar) func##_impl<typename global_math_functions_filtering_base<scalar>::type>
+#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
-#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename func##_retval<typename global_math_functions_filtering_base<scalar>::type>::type
+#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
-
 
 /****************************************************************************
 * Implementation of real                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
-struct real_impl
+struct real_default_impl
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   static inline RealScalar run(const Scalar& x)
@@ -69,34 +68,32 @@ struct real_impl
   }
 };
 
-template<typename RealScalar>
+template<typename Scalar>
-struct real_impl<std::complex<RealScalar> >
+struct real_default_impl<Scalar,true>
 {
-  static inline RealScalar run(const std::complex<RealScalar>& x)
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
   {
     using std::real;
     return real(x);
   }
 };
 
+template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
+
 template<typename Scalar>
 struct real_retval
 {
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
-}
 
 /****************************************************************************
 * Implementation of imag                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
-struct imag_impl
+struct imag_default_impl
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   static inline RealScalar run(const Scalar&)
@@ -105,28 +102,25 @@ struct imag_impl
   }
 };
 
-template<typename RealScalar>
+template<typename Scalar>
-struct imag_impl<std::complex<RealScalar> >
+struct imag_default_impl<Scalar,true>
 {
-  static inline RealScalar run(const std::complex<RealScalar>& x)
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
   {
     using std::imag;
     return imag(x);
   }
 };
 
+template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
+
 template<typename Scalar>
 struct imag_retval
 {
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of real_ref                                             *
 ****************************************************************************/
@@ -151,18 +145,6 @@ struct real_ref_retval
   typedef typename NumTraits<Scalar>::Real & type;
 };
 
-template<typename Scalar>
-inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
-{
-  return real_ref_impl<Scalar>::run(x);
-}
-
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of imag_ref                                             *
 ****************************************************************************/
@@ -203,23 +185,11 @@ struct imag_ref_retval
   typedef typename NumTraits<Scalar>::Real & type;
 };
 
-template<typename Scalar>
-inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
-{
-  return imag_ref_impl<Scalar>::run(x);
-}
-
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of conj                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
 struct conj_impl
 {
   static inline Scalar run(const Scalar& x)
@@ -228,10 +198,10 @@ struct conj_impl
   }
 };
 
-template<typename RealScalar>
+template<typename Scalar>
-struct conj_impl<std::complex<RealScalar> >
+struct conj_impl<Scalar,true>
 {
-  static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x)
+  static inline Scalar run(const Scalar& x)
   {
     using std::conj;
     return conj(x);
@@ -244,12 +214,6 @@ struct conj_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of abs2                                                 *
 ****************************************************************************/
@@ -279,12 +243,6 @@ struct abs2_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of norm1                                                *
 ****************************************************************************/
@@ -319,12 +277,6 @@ struct norm1_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of hypot                                                *
 ****************************************************************************/
@@ -342,6 +294,7 @@ struct hypot_impl
     RealScalar _x = abs(x);
     RealScalar _y = abs(y);
     RealScalar p = (max)(_x, _y);
+    if(p==RealScalar(0)) return 0;
     RealScalar q = (min)(_x, _y);
     RealScalar qp = q/p;
     return p * sqrt(RealScalar(1) + qp*qp);
@@ -354,12 +307,6 @@ struct hypot_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of cast                                                 *
 ****************************************************************************/
@@ -396,7 +343,7 @@ struct atanh2_default_impl
     using std::log;
     using std::sqrt;
     Scalar z = x / y;
-    if (abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))
+    if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))
       return RealScalar(0.5) * log((y + x) / (y - x));
     else
       return z + z*z*z / RealScalar(3);
@@ -422,12 +369,6 @@ struct atanh2_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of pow                                                  *
 ****************************************************************************/
@@ -471,12 +412,6 @@ struct pow_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of random                                               *
 ****************************************************************************/
@@ -575,11 +510,10 @@ struct random_default_impl<Scalar, false, true>
 #else
     enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,
            scalar_bits = sizeof(Scalar) * CHAR_BIT,
-           shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits))
+           shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
+           offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
     };
-    Scalar x = Scalar(std::rand() >> shift);
+    return Scalar((std::rand() >> shift) - offset);
-    Scalar offset = NumTraits<Scalar>::IsSigned ? Scalar(1 << (rand_bits-1)) : Scalar(0);
-    return x - offset;
 #endif
   }
 };
@@ -611,6 +545,97 @@ inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
   return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
 }
 
+} // end namespace internal
+
+/****************************************************************************
+* Generic math function                                                    *
+****************************************************************************/
+
+namespace numext {
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
+}  
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
+{
+  return internal::real_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
+{
+  return internal::imag_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
+}
+
+// std::isfinite is non standard, so let's define our own version,
+// even though it is not very efficient.
+template<typename T> bool (isfinite)(const T& x)
+{
+  return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
+}
+
+} // end namespace numext
+
+namespace internal {
+
 /****************************************************************************
 * Implementation of fuzzy comparisons                                       *
 ****************************************************************************/
@@ -668,12 +693,12 @@ struct scalar_fuzzy_default_impl<Scalar, true, false>
   template<typename OtherScalar>
   static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
   {
-    return abs2(x) <= abs2(y) * prec * prec;
+    return numext::abs2(x) <= numext::abs2(y) * prec * prec;
   }
   static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
   {
     using std::min;
-    return abs2(x - y) <= (min)(abs2(x), abs2(y)) * prec * prec;
+    return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;
   }
 };
 
@@ -735,17 +760,7 @@ template<> struct scalar_fuzzy_impl<bool>
   
 };
 
-/****************************************************************************
+  
-* Special functions                                                          *
-****************************************************************************/
-
-// std::isfinite is non standard, so let's define our own version,
-// even though it is not very efficient.
-template<typename T> bool (isfinite)(const T& x)
-{
-  return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
-}
-
 } // end namespace internal
 
 } // end namespace Eigen

Eigen/src/Core/Matrix.h

@@ -200,7 +200,7 @@ class Matrix
       *
       * \sa resize(Index,Index)
       */
-    EIGEN_STRONG_INLINE explicit Matrix() : Base()
+    EIGEN_STRONG_INLINE Matrix() : Base()
     {
       Base::_check_template_params();
       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
@@ -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);
@@ -215,24 +213,20 @@ template<typename Derived> class MatrixBase
 
     typedef Diagonal<Derived> DiagonalReturnType;
     DiagonalReturnType diagonal();
-    typedef const Diagonal<const Derived> ConstDiagonalReturnType;
+    typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
-    const ConstDiagonalReturnType diagonal() const;
+    ConstDiagonalReturnType diagonal() const;
 
     template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
     template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
 
     template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
     template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
+    
+    typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
+    typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
 
-    // Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
+    DiagonalDynamicIndexReturnType diagonal(Index index);
-    // On the other hand they confuse MSVC8...
+    ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
-    #if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
-    typename MatrixBase::template DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
-    typename MatrixBase::template ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
-    #else
-    typename DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
-    typename ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
-    #endif
 
     #ifdef EIGEN2_SUPPORT
     template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
@@ -457,7 +451,7 @@ template<typename Derived> class MatrixBase
     const MatrixFunctionReturnValue<Derived> sin() const;
     const MatrixSquareRootReturnValue<Derived> sqrt() const;
     const MatrixLogarithmReturnValue<Derived> log() const;
-    const MatrixPowerReturnValue<Derived> pow(RealScalar p) const;
+    const MatrixPowerReturnValue<Derived> pow(const RealScalar& p) const;
 
 #ifdef EIGEN2_SUPPORT
     template<typename ProductDerived, typename Lhs, typename Rhs>
@@ -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/NoAlias.h

@@ -80,6 +80,10 @@ class NoAlias
     template<typename Lhs, typename Rhs, int NestingFlags>
     EIGEN_STRONG_INLINE ExpressionType& operator-=(const CoeffBasedProduct<Lhs,Rhs,NestingFlags>& other)
     { return m_expression.derived() -= CoeffBasedProduct<Lhs,Rhs,NestByRefBit>(other.lhs(), other.rhs()); }
+    
+    template<typename OtherDerived>
+    ExpressionType& operator=(const ReturnByValue<OtherDerived>& func)
+    { return m_expression = func; }
 #endif
 
     ExpressionType& expression() const

Eigen/src/Core/NumTraits.h

@@ -140,6 +140,9 @@ struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
     AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
     MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
   };
+  
+  static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
+  static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
 };
 
 } // end namespace Eigen

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:
 
@@ -541,24 +570,29 @@ struct permut_matrix_product_retval
  : public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
 {
     typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+    typedef typename MatrixType::Index Index;
 
     permut_matrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
       : m_permutation(perm), m_matrix(matrix)
     {}
 
-    inline int rows() const { return m_matrix.rows(); }
+    inline Index rows() const { return m_matrix.rows(); }
-    inline int cols() const { return m_matrix.cols(); }
+    inline Index cols() const { return m_matrix.cols(); }
 
     template<typename Dest> inline void evalTo(Dest& dst) const
     {
-      const int n = Side==OnTheLeft ? rows() : cols();
+      const Index n = Side==OnTheLeft ? rows() : cols();
-
+      // FIXME we need an is_same for expression that is not sensitive to constness. For instance
-      if(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))
+      // 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());
         mask.fill(false);
-        int r = 0;
+        Index r = 0;
         while(r < m_permutation.size())
         {
           // search for the next seed
@@ -566,10 +600,10 @@ struct permut_matrix_product_retval
           if(r>=m_permutation.size())
             break;
           // we got one, let's follow it until we are back to the seed
-          int k0 = r++;
+          Index k0 = r++;
-          int kPrev = k0;
+          Index kPrev = k0;
           mask.coeffRef(k0) = true;
-          for(int k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
+          for(Index k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
           {
                   Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
             .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>

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;
 
@@ -418,7 +421,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
       return Base::operator=(func);
     }
 
-    EIGEN_STRONG_INLINE explicit PlainObjectBase() : m_storage()
+    EIGEN_STRONG_INLINE PlainObjectBase() : m_storage()
     {
 //       _check_template_params();
 //       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
@@ -570,6 +573,8 @@ 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 +673,10 @@ 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 +736,14 @@ 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/Product.h

@@ -1,107 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_PRODUCT_H
-#define EIGEN_PRODUCT_H
-
-namespace Eigen {
-
-template<typename Lhs, typename Rhs> class Product;
-template<typename Lhs, typename Rhs, typename StorageKind> class ProductImpl;
-
-/** \class Product
-  * \ingroup Core_Module
-  *
-  * \brief Expression of the product of two arbitrary matrices or vectors
-  *
-  * \param Lhs the type of the left-hand side expression
-  * \param Rhs the type of the right-hand side expression
-  *
-  * This class represents an expression of the product of two arbitrary matrices.
-  *
-  */
-
-// Use ProductReturnType to get correct traits, in particular vectorization flags
-namespace internal {
-template<typename Lhs, typename Rhs>
-struct traits<Product<Lhs, Rhs> >
-  : traits<typename ProductReturnType<Lhs, Rhs>::Type>
-{ 
-  // We want A+B*C to be of type Product<Matrix, Sum> and not Product<Matrix, Matrix>
-  // TODO: This flag should eventually go in a separate evaluator traits class
-  enum {
-    Flags = traits<typename ProductReturnType<Lhs, Rhs>::Type>::Flags & ~EvalBeforeNestingBit
-  };
-};
-} // end namespace internal
-
-
-template<typename Lhs, typename Rhs>
-class Product : public ProductImpl<Lhs,Rhs,typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
-                                                                            typename internal::traits<Rhs>::StorageKind>::ret>
-{
-  public:
-    
-    typedef typename ProductImpl<
-        Lhs, Rhs,
-        typename internal::promote_storage_type<typename Lhs::StorageKind,
-                                                typename Rhs::StorageKind>::ret>::Base Base;
-    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
-
-    typedef typename Lhs::Nested LhsNested;
-    typedef typename Rhs::Nested RhsNested;
-    typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
-    typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
-
-    Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
-    {
-      eigen_assert(lhs.cols() == rhs.rows()
-        && "invalid matrix product"
-        && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
-    }
-
-    inline Index rows() const { return m_lhs.rows(); }
-    inline Index cols() const { return m_rhs.cols(); }
-
-    const LhsNestedCleaned& lhs() const { return m_lhs; }
-    const RhsNestedCleaned& rhs() const { return m_rhs; }
-
-  protected:
-
-    LhsNested m_lhs;
-    RhsNested m_rhs;
-};
-
-template<typename Lhs, typename Rhs>
-class ProductImpl<Lhs,Rhs,Dense> : public internal::dense_xpr_base<Product<Lhs,Rhs> >::type
-{
-    typedef Product<Lhs, Rhs> Derived;
-  public:
-
-    typedef typename internal::dense_xpr_base<Product<Lhs, Rhs> >::type Base;
-    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
-};
-
-/***************************************************************************
-* Implementation of matrix base methods
-***************************************************************************/
-
-
-/** \internal used to test the evaluator only
-  */
-template<typename Lhs,typename Rhs>
-const Product<Lhs,Rhs>
-prod(const Lhs& lhs, const Rhs& rhs)
-{
-  return Product<Lhs,Rhs>(lhs,rhs);
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_PRODUCT_H

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;
 };
 }
 
@@ -195,7 +207,7 @@ class ScaledProduct;
 // Also note that here we accept any compatible scalar types
 template<typename Derived,typename Lhs,typename Rhs>
 const ScaledProduct<Derived>
-operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::Scalar x)
+operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::Scalar& x)
 { return ScaledProduct<Derived>(prod.derived(), x); }
 
 template<typename Derived,typename Lhs,typename Rhs>
@@ -207,7 +219,7 @@ operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::Real
 
 template<typename Derived,typename Lhs,typename Rhs>
 const ScaledProduct<Derived>
-operator*(typename Derived::Scalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
+operator*(const typename Derived::Scalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
 { return ScaledProduct<Derived>(prod.derived(), x); }
 
 template<typename Derived,typename Lhs,typename Rhs>

Eigen/src/Core/ProductEvaluators.h

@@ -1,411 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
-// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-
-#ifndef EIGEN_PRODUCTEVALUATORS_H
-#define EIGEN_PRODUCTEVALUATORS_H
-
-namespace Eigen {
-  
-namespace internal {
-  
-// We can evaluate the product either all at once, like GeneralProduct and its evalTo() function, or
-// traverse the matrix coefficient by coefficient, like CoeffBasedProduct.  Use the existing logic
-// in ProductReturnType to decide.
-
-template<typename XprType, typename ProductType>
-struct product_evaluator_dispatcher;
-
-template<typename Lhs, typename Rhs>
-struct evaluator_impl<Product<Lhs, Rhs> >
-  : product_evaluator_dispatcher<Product<Lhs, Rhs>, typename ProductReturnType<Lhs, Rhs>::Type> 
-{
-  typedef Product<Lhs, Rhs> XprType;
-  typedef product_evaluator_dispatcher<XprType, typename ProductReturnType<Lhs, Rhs>::Type> Base;
-
-  evaluator_impl(const XprType& xpr) : Base(xpr) 
-  { }
-};
-
-template<typename XprType, typename ProductType>
-struct product_evaluator_traits_dispatcher;
-
-template<typename Lhs, typename Rhs>
-struct evaluator_traits<Product<Lhs, Rhs> >
-  : product_evaluator_traits_dispatcher<Product<Lhs, Rhs>, typename ProductReturnType<Lhs, Rhs>::Type> 
-{ 
-  static const int AssumeAliasing = 1;
-};
-
-// Case 1: Evaluate all at once
-//
-// We can view the GeneralProduct class as a part of the product evaluator. 
-// Four sub-cases: InnerProduct, OuterProduct, GemmProduct and GemvProduct.
-// InnerProduct is special because GeneralProduct does not have an evalTo() method in this case.
-
-template<typename Lhs, typename Rhs>
-struct product_evaluator_traits_dispatcher<Product<Lhs, Rhs>, GeneralProduct<Lhs, Rhs, InnerProduct> > 
-{
-  static const int HasEvalTo = 0;
-};
-
-template<typename Lhs, typename Rhs>
-struct product_evaluator_dispatcher<Product<Lhs, Rhs>, GeneralProduct<Lhs, Rhs, InnerProduct> > 
-  : public evaluator<typename Product<Lhs, Rhs>::PlainObject>::type
-{
-  typedef Product<Lhs, Rhs> XprType;
-  typedef typename XprType::PlainObject PlainObject;
-  typedef typename evaluator<PlainObject>::type evaluator_base;
-
-  // TODO: Computation is too early (?)
-  product_evaluator_dispatcher(const XprType& xpr) : evaluator_base(m_result)
-  {
-    m_result.coeffRef(0,0) = (xpr.lhs().transpose().cwiseProduct(xpr.rhs())).sum();
-  }
-  
-protected:  
-  PlainObject m_result;
-};
-
-// For the other three subcases, simply call the evalTo() method of GeneralProduct
-// TODO: GeneralProduct should take evaluators, not expression objects.
-
-template<typename Lhs, typename Rhs, int ProductType>
-struct product_evaluator_traits_dispatcher<Product<Lhs, Rhs>, GeneralProduct<Lhs, Rhs, ProductType> > 
-{
-  static const int HasEvalTo = 1;
-};
-
-template<typename Lhs, typename Rhs, int ProductType>
-struct product_evaluator_dispatcher<Product<Lhs, Rhs>, GeneralProduct<Lhs, Rhs, ProductType> > 
-{
-  typedef Product<Lhs, Rhs> XprType;
-  typedef typename XprType::PlainObject PlainObject;
-  typedef typename evaluator<PlainObject>::type evaluator_base;
-  
-  product_evaluator_dispatcher(const XprType& xpr) : m_xpr(xpr)
-  { }
-  
-  template<typename DstEvaluatorType, typename DstXprType>
-  void evalTo(DstEvaluatorType /* not used */, DstXprType& dst)
-  {
-    dst.resize(m_xpr.rows(), m_xpr.cols());
-    GeneralProduct<Lhs, Rhs, ProductType>(m_xpr.lhs(), m_xpr.rhs()).evalTo(dst);
-  }
-  
-protected: 
-  const XprType& m_xpr;
-};
-
-// Case 2: Evaluate coeff by coeff
-//
-// This is mostly taken from CoeffBasedProduct.h
-// The main difference is that we add an extra argument to the etor_product_*_impl::run() function
-// for the inner dimension of the product, because evaluator object do not know their size.
-
-template<int Traversal, int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
-struct etor_product_coeff_impl;
-
-template<int StorageOrder, int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_product_packet_impl;
-
-template<typename Lhs, typename Rhs, typename LhsNested, typename RhsNested, int Flags>
-struct product_evaluator_traits_dispatcher<Product<Lhs, Rhs>, CoeffBasedProduct<LhsNested, RhsNested, Flags> >
-{
-  static const int HasEvalTo = 0;
-};
-
-template<typename Lhs, typename Rhs, typename LhsNested, typename RhsNested, int Flags>
-struct product_evaluator_dispatcher<Product<Lhs, Rhs>, CoeffBasedProduct<LhsNested, RhsNested, Flags> >
-  : evaluator_impl_base<Product<Lhs, Rhs> >
-{
-  typedef Product<Lhs, Rhs> XprType;
-  typedef CoeffBasedProduct<LhsNested, RhsNested, Flags> CoeffBasedProductType;
-
-  product_evaluator_dispatcher(const XprType& xpr) 
-    : m_lhsImpl(xpr.lhs()), 
-      m_rhsImpl(xpr.rhs()),  
-      m_innerDim(xpr.lhs().cols())
-  { }
-
-  typedef typename XprType::Index Index;
-  typedef typename XprType::Scalar Scalar;
-  typedef typename XprType::CoeffReturnType CoeffReturnType;
-  typedef typename XprType::PacketScalar PacketScalar;
-  typedef typename XprType::PacketReturnType PacketReturnType;
-
-  // Everything below here is taken from CoeffBasedProduct.h
-
-  enum {
-    RowsAtCompileTime = traits<CoeffBasedProductType>::RowsAtCompileTime,
-    PacketSize = packet_traits<Scalar>::size,
-    InnerSize  = traits<CoeffBasedProductType>::InnerSize,
-    CoeffReadCost = traits<CoeffBasedProductType>::CoeffReadCost,
-    Unroll = CoeffReadCost != Dynamic && CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
-    CanVectorizeInner = traits<CoeffBasedProductType>::CanVectorizeInner
-  };
-
-  typedef typename evaluator<Lhs>::type LhsEtorType;
-  typedef typename evaluator<Rhs>::type RhsEtorType;
-  typedef etor_product_coeff_impl<CanVectorizeInner ? InnerVectorizedTraversal : DefaultTraversal,
-                                  Unroll ? InnerSize-1 : Dynamic,
-                                  LhsEtorType, RhsEtorType, Scalar> CoeffImpl;
-
-  const CoeffReturnType coeff(Index row, Index col) const
-  {
-    Scalar res;
-    CoeffImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);
-    return res;
-  }
-
-  /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,
-   * which is why we don't set the LinearAccessBit.
-   */
-  const CoeffReturnType coeff(Index index) const
-  {
-    Scalar res;
-    const Index row = RowsAtCompileTime == 1 ? 0 : index;
-    const Index col = RowsAtCompileTime == 1 ? index : 0;
-    CoeffImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);
-    return res;
-  }
-
-  template<int LoadMode>
-  const PacketReturnType packet(Index row, Index col) const
-  {
-    PacketScalar res;
-    typedef etor_product_packet_impl<Flags&RowMajorBit ? RowMajor : ColMajor,
-				     Unroll ? InnerSize-1 : Dynamic,
-				     LhsEtorType, RhsEtorType, PacketScalar, LoadMode> PacketImpl;
-    PacketImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);
-    return res;
-  }
-
-protected:
-  typename evaluator<Lhs>::type m_lhsImpl;
-  typename evaluator<Rhs>::type m_rhsImpl;
-
-  // TODO: Get rid of m_innerDim if known at compile time
-  Index m_innerDim;
-};
-
-/***************************************************************************
-* Normal product .coeff() implementation (with meta-unrolling)
-***************************************************************************/
-
-/**************************************
-*** Scalar path  - no vectorization ***
-**************************************/
-
-template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
-struct etor_product_coeff_impl<DefaultTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
-{
-  typedef typename Lhs::Index Index;
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, RetScalar &res)
-  {
-    etor_product_coeff_impl<DefaultTraversal, UnrollingIndex-1, Lhs, Rhs, RetScalar>::run(row, col, lhs, rhs, innerDim, res);
-    res += lhs.coeff(row, UnrollingIndex) * rhs.coeff(UnrollingIndex, col);
-  }
-};
-
-template<typename Lhs, typename Rhs, typename RetScalar>
-struct etor_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, Index /*innerDim*/, RetScalar &res)
-  {
-    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
-  }
-};
-
-template<typename Lhs, typename Rhs, typename RetScalar>
-struct etor_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, Index innerDim, RetScalar& res)
-  {
-    eigen_assert(innerDim>0 && "you are using a non initialized matrix");
-    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
-    for(Index i = 1; i < innerDim; ++i)
-      res += lhs.coeff(row, i) * rhs.coeff(i, col);
-  }
-};
-
-/*******************************************
-*** Scalar path with inner vectorization ***
-*******************************************/
-
-template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet>
-struct etor_product_coeff_vectorized_unroller
-{
-  typedef typename Lhs::Index Index;
-  enum { PacketSize = packet_traits<typename Lhs::Scalar>::size };
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, typename Lhs::PacketScalar &pres)
-  {
-    etor_product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, innerDim, pres);
-    pres = padd(pres, pmul( lhs.template packet<Aligned>(row, UnrollingIndex) , rhs.template packet<Aligned>(UnrollingIndex, col) ));
-  }
-};
-
-template<typename Lhs, typename Rhs, typename Packet>
-struct etor_product_coeff_vectorized_unroller<0, Lhs, Rhs, Packet>
-{
-  typedef typename Lhs::Index Index;
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, typename Lhs::PacketScalar &pres)
-  {
-    pres = pmul(lhs.template packet<Aligned>(row, 0) , rhs.template packet<Aligned>(0, col));
-  }
-};
-
-template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
-struct etor_product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
-{
-  typedef typename Lhs::PacketScalar Packet;
-  typedef typename Lhs::Index Index;
-  enum { PacketSize = packet_traits<typename Lhs::Scalar>::size };
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, RetScalar &res)
-  {
-    Packet pres;
-    etor_product_coeff_vectorized_unroller<UnrollingIndex+1-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, innerDim, pres);
-    etor_product_coeff_impl<DefaultTraversal,UnrollingIndex,Lhs,Rhs,RetScalar>::run(row, col, lhs, rhs, innerDim, res);
-    res = predux(pres);
-  }
-};
-
-template<typename Lhs, typename Rhs, int LhsRows = Lhs::RowsAtCompileTime, int RhsCols = Rhs::ColsAtCompileTime>
-struct etor_product_coeff_vectorized_dyn_selector
-{
-  typedef typename Lhs::Index Index;
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, typename Lhs::Scalar &res)
-  {
-    res = lhs.row(row).transpose().cwiseProduct(rhs.col(col)).sum();
-  }
-};
-
-// NOTE the 3 following specializations are because taking .col(0) on a vector is a bit slower
-// NOTE maybe they are now useless since we have a specialization for Block<Matrix>
-template<typename Lhs, typename Rhs, int RhsCols>
-struct etor_product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,RhsCols>
-{
-  typedef typename Lhs::Index Index;
-  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, typename Lhs::Scalar &res)
-  {
-    res = lhs.transpose().cwiseProduct(rhs.col(col)).sum();
-  }
-};
-
-template<typename Lhs, typename Rhs, int LhsRows>
-struct etor_product_coeff_vectorized_dyn_selector<Lhs,Rhs,LhsRows,1>
-{
-  typedef typename Lhs::Index Index;
-  static EIGEN_STRONG_INLINE void run(Index row, Index /*col*/, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, typename Lhs::Scalar &res)
-  {
-    res = lhs.row(row).transpose().cwiseProduct(rhs).sum();
-  }
-};
-
-template<typename Lhs, typename Rhs>
-struct etor_product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,1>
-{
-  typedef typename Lhs::Index Index;
-  EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, typename Lhs::Scalar &res)
-  {
-    res = lhs.transpose().cwiseProduct(rhs).sum();
-  }
-};
-
-template<typename Lhs, typename Rhs, typename RetScalar>
-struct etor_product_coeff_impl<InnerVectorizedTraversal, 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, Index innerDim, typename Lhs::Scalar &res)
-  {
-    etor_product_coeff_vectorized_dyn_selector<Lhs,Rhs>::run(row, col, lhs, rhs, innerDim, res);
-  }
-};
-
-/*******************
-*** Packet path  ***
-*******************/
-
-template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_product_packet_impl<RowMajor, UnrollingIndex, 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, Index innerDim, Packet &res)
-  {
-    etor_product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
-    res =  pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex)), rhs.template packet<LoadMode>(UnrollingIndex, col), res);
-  }
-};
-
-template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_product_packet_impl<ColMajor, UnrollingIndex, 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, Index innerDim, Packet &res)
-  {
-    etor_product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
-    res =  pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex), pset1<Packet>(rhs.coeff(UnrollingIndex, col)), res);
-  }
-};
-
-template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_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, Index /*innerDim*/, Packet &res)
-  {
-    res = pmul(pset1<Packet>(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
-  }
-};
-
-template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_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, Index /*innerDim*/, Packet &res)
-  {
-    res = pmul(lhs.template packet<LoadMode>(row, 0), pset1<Packet>(rhs.coeff(0, col)));
-  }
-};
-
-template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_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, Index innerDim, Packet& res)
-  {
-    eigen_assert(innerDim>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 < innerDim; ++i)
-      res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
-  }
-};
-
-template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct etor_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, Index innerDim, Packet& res)
-  {
-    eigen_assert(innerDim>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 < innerDim; ++i)
-      res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
-  }
-};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_PRODUCT_EVALUATORS_H

Eigen/src/Core/Redux.h

@@ -330,7 +330,8 @@ DenseBase<Derived>::redux(const Func& func) const
             ::run(derived(), func);
 }
 
-/** \returns the minimum of all coefficients of *this
+/** \returns the minimum of all coefficients of \c *this.
+  * \warning the result is undefined if \c *this contains NaN.
   */
 template<typename Derived>
 EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
@@ -339,7 +340,8 @@ DenseBase<Derived>::minCoeff() const
   return this->redux(Eigen::internal::scalar_min_op<Scalar>());
 }
 
-/** \returns the maximum of all coefficients of *this
+/** \returns the maximum of all coefficients of \c *this.
+  * \warning the result is undefined if \c *this contains NaN.
   */
 template<typename Derived>
 EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar

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,
+               typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
-               int = Derived::ThisConstantIsPrivateInPlainObjectBase)
     #else
     template<typename Derived>
     inline Ref(DenseBase<Derived>& expr)
     #endif
     {
+      EIGEN_STATIC_ASSERT(static_cast<bool>(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+      EIGEN_STATIC_ASSERT(static_cast<bool>(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+      enum { THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY = Derived::ThisConstantIsPrivateInPlainObjectBase};
       Base::construct(expr.const_cast_derived());
     }
 
@@ -223,7 +236,8 @@ 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";

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

@@ -48,7 +48,7 @@ struct nested<ReturnByValue<Derived>, n, PlainObject>
 } // end namespace internal
 
 template<typename Derived> class ReturnByValue
-  : public internal::dense_xpr_base< ReturnByValue<Derived> >::type
+  : internal::no_assignment_operator, public internal::dense_xpr_base< ReturnByValue<Derived> >::type
 {
   public:
     typedef typename internal::traits<Derived>::ReturnType ReturnType;
@@ -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/Select.h

@@ -136,7 +136,7 @@ template<typename Derived>
 template<typename ThenDerived>
 inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
 DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
-                            typename ThenDerived::Scalar elseScalar) const
+                           const typename ThenDerived::Scalar& elseScalar) const
 {
   return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
     derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
@@ -150,8 +150,8 @@ DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
 template<typename Derived>
 template<typename ElseDerived>
 inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
-DenseBase<Derived>::select(typename ElseDerived::Scalar thenScalar,
+DenseBase<Derived>::select(const typename ElseDerived::Scalar& thenScalar,
-                            const DenseBase<ElseDerived>& elseMatrix) const
+                           const DenseBase<ElseDerived>& elseMatrix) const
 {
   return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
     derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());

Eigen/src/Core/SelfAdjointView.h

@@ -132,7 +132,7 @@ template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
       * \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
       */
     template<typename DerivedU, typename DerivedV>
-    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, Scalar alpha = Scalar(1));
+    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha = Scalar(1));
 
     /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
       * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
@@ -145,7 +145,7 @@ template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
       * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
       */
     template<typename DerivedU>
-    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, Scalar alpha = Scalar(1));
+    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
 
 /////////// Cholesky module ///////////
 
@@ -214,9 +214,9 @@ struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), U
     triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
 
     if(row == col)
-      dst.coeffRef(row, col) = real(src.coeff(row, col));
+      dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
     else if(row < col)
-      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+      dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
   }
 };
 
@@ -239,9 +239,9 @@ struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), U
     triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
 
     if(row == col)
-      dst.coeffRef(row, col) = real(src.coeff(row, col));
+      dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
     else if(row > col)
-      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+      dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
   }
 };
 
@@ -262,7 +262,7 @@ struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dyn
       for(Index i = 0; i < j; ++i)
       {
         dst.copyCoeff(i, j, src);
-        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+        dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
       }
       dst.copyCoeff(j, j, src);
     }
@@ -280,7 +280,7 @@ struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dyn
       for(Index j = 0; j < i; ++j)
       {
         dst.copyCoeff(i, j, src);
-        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+        dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
       }
       dst.copyCoeff(i, i, src);
     }

Eigen/src/Core/StableNorm.h

@@ -13,26 +13,39 @@
 namespace Eigen { 
 
 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();
+  using std::max;
-  if (max>scale)
+  Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
+  
+  if (maxCoeff>scale)
   {
-    ssq = ssq * abs2(scale/max);
+    ssq = ssq * numext::abs2(scale/maxCoeff);
-    scale = max;
+    Scalar tmp = Scalar(1)/maxCoeff;
-    invScale = Scalar(1)/scale;
+    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>
 inline typename NumTraits<typename traits<Derived>::Scalar>::Real
 blueNorm_impl(const EigenBase<Derived>& _vec)
 {
-  typedef typename Derived::Scalar Scalar;
   typedef typename Derived::RealScalar RealScalar;  
   typedef typename Derived::Index Index;
   using std::pow;
@@ -41,43 +54,40 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   using std::sqrt;
   using std::abs;
   const Derived& vec(_vec.derived());
-  static Index nmax = -1;
+  static bool initialized = false;
   static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
-  if(nmax <= 0)
+  if(!initialized)
   {
-    int nbig, ibeta, it, iemin, iemax, iexp;
+    int ibeta, it, iemin, iemax, iexp;
-    RealScalar abig, eps;
+    RealScalar eps;
     // This program calculates the machine-dependent constants
-    // bl, b2, slm, s2m, relerr overfl, nmax
+    // bl, b2, slm, s2m, relerr overfl
     // from the "basic" machine-dependent numbers
     // nbig, ibeta, it, iemin, iemax, rbig.
     // The following define the basic machine-dependent constants.
     // For portability, the PORT subprograms "ilmaeh" and "rlmach"
     // are used. For any specific computer, each of the assignment
     // statements can be replaced
-    nbig  = (std::numeric_limits<Index>::max)();            // largest integer
+    ibeta = std::numeric_limits<RealScalar>::radix;                 // base for floating-point numbers
-    ibeta = std::numeric_limits<RealScalar>::radix;         // base for floating-point numbers
+    it    = std::numeric_limits<RealScalar>::digits;                // number of base-beta digits in mantissa
-    it    = std::numeric_limits<RealScalar>::digits;        // number of base-beta digits in mantissa
+    iemin = std::numeric_limits<RealScalar>::min_exponent;          // minimum exponent
-    iemin = std::numeric_limits<RealScalar>::min_exponent;  // minimum exponent
+    iemax = std::numeric_limits<RealScalar>::max_exponent;          // maximum exponent
-    iemax = std::numeric_limits<RealScalar>::max_exponent;  // maximum exponent
+    rbig  = (std::numeric_limits<RealScalar>::max)();               // largest floating-point number
-    rbig  = (std::numeric_limits<RealScalar>::max)();         // largest floating-point number
 
     iexp  = -((1-iemin)/2);
-    b1    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));  // lower boundary of midrange
+    b1    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // lower boundary of midrange
     iexp  = (iemax + 1 - it)/2;
-    b2    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));   // upper boundary of midrange
+    b2    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // upper boundary of midrange
 
     iexp  = (2-iemin)/2;
-    s1m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));   // scaling factor for lower range
+    s1m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for lower range
     iexp  = - ((iemax+it)/2);
-    s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));   // scaling factor for upper range
+    s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for upper range
 
-    overfl  = rbig*s2m;             // overflow boundary for abig
+    overfl  = rbig*s2m;                                             // overflow boundary for abig
     eps     = RealScalar(pow(double(ibeta), 1-it));
-    relerr  = sqrt(eps);         // tolerance for neglecting asml
+    relerr  = sqrt(eps);                                            // tolerance for neglecting asml
-    abig    = RealScalar(1.0/eps - 1.0);
+    initialized = true;
-    if (RealScalar(nbig)>abig)  nmax = int(abig);  // largest safe n
-    else                        nmax = nbig;
   }
   Index n = vec.size();
   RealScalar ab2 = b2 / RealScalar(n);
@@ -87,9 +97,9 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   for(typename Derived::InnerIterator it(vec, 0); it; ++it)
   {
     RealScalar ax = abs(it.value());
-    if(ax > ab2)     abig += internal::abs2(ax*s2m);
+    if(ax > ab2)     abig += numext::abs2(ax*s2m);
-    else if(ax < b1) asml += internal::abs2(ax*s1m);
+    else if(ax < b1) asml += numext::abs2(ax*s1m);
-    else             amed += internal::abs2(ax);
+    else             amed += numext::abs2(ax);
   }
   if(abig > RealScalar(0))
   {
@@ -123,8 +133,9 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   if(asml <= abig*relerr)
     return abig;
   else
-    return abig * sqrt(RealScalar(1) + internal::abs2(asml/abig));
+    return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
 }
+
 } // end namespace internal
 
 /** \returns the \em l2 norm of \c *this avoiding underflow and overflow.

Eigen/src/Core/Transpose.h

@@ -104,6 +104,7 @@ template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
 
     typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
     EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)
 
     inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
     inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
@@ -206,7 +207,7 @@ DenseBase<Derived>::transpose()
   *
   * \sa transposeInPlace(), adjoint() */
 template<typename Derived>
-inline const typename DenseBase<Derived>::ConstTransposeReturnType
+inline typename DenseBase<Derived>::ConstTransposeReturnType
 DenseBase<Derived>::transpose() const
 {
   return ConstTransposeReturnType(derived());
@@ -252,7 +253,7 @@ struct inplace_transpose_selector;
 template<typename MatrixType>
 struct inplace_transpose_selector<MatrixType,true> { // square matrix
   static void run(MatrixType& m) {
-    m.template triangularView<StrictlyUpper>().swap(m.transpose());
+    m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
   }
 };
 
@@ -260,7 +261,7 @@ template<typename MatrixType>
 struct inplace_transpose_selector<MatrixType,false> { // non square matrix
   static void run(MatrixType& m) {
     if (m.rows()==m.cols())
-      m.template triangularView<StrictlyUpper>().swap(m.transpose());
+      m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
     else
       m = m.transpose().eval();
   }
@@ -283,7 +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>
@@ -314,6 +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>
@@ -387,7 +390,7 @@ struct checkTransposeAliasing_impl
         eigen_assert((!check_transpose_aliasing_run_time_selector
                       <typename Derived::Scalar,blas_traits<Derived>::IsTransposed,OtherDerived>
                       ::run(extract_data(dst), other))
-          && "aliasing detected during tranposition, use transposeInPlace() "
+          && "aliasing detected during transposition, use transposeInPlace() "
              "or evaluate the rhs into a temporary using .eval()");
 
     }

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)
   };
 };
 }
@@ -233,6 +234,28 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
                        Direction==Vertical   ? 1 : m_matrix.rows(),
                        Direction==Horizontal ? 1 : m_matrix.cols());
     }
+    
+    template<typename OtherDerived> struct OppositeExtendedType {
+      typedef Replicate<OtherDerived,
+                        Direction==Horizontal ? 1 : ExpressionType::RowsAtCompileTime,
+                        Direction==Vertical   ? 1 : ExpressionType::ColsAtCompileTime> Type;
+    };
+
+    /** \internal
+      * Replicates a vector in the opposite direction to match the size of \c *this */
+    template<typename OtherDerived>
+    typename OppositeExtendedType<OtherDerived>::Type
+    extendedToOpposite(const DenseBase<OtherDerived>& other) const
+    {
+      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxColsAtCompileTime==1),
+                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxRowsAtCompileTime==1),
+                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+      return typename OppositeExtendedType<OtherDerived>::Type
+                      (other.derived(),
+                       Direction==Horizontal  ? 1 : m_matrix.rows(),
+                       Direction==Vertical    ? 1 : m_matrix.cols());
+    }
 
   public:
 
@@ -255,6 +278,8 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
 
     /** \returns a row (or column) vector expression of the smallest coefficient
       * of each column (or row) of the referenced expression.
+      * 
+      * \warning the result is undefined if \c *this contains NaN.
       *
       * Example: \include PartialRedux_minCoeff.cpp
       * Output: \verbinclude PartialRedux_minCoeff.out
@@ -265,6 +290,8 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
 
     /** \returns a row (or column) vector expression of the largest coefficient
       * of each column (or row) of the referenced expression.
+      * 
+      * \warning the result is undefined if \c *this contains NaN.
       *
       * Example: \include PartialRedux_maxCoeff.cpp
       * Output: \verbinclude PartialRedux_maxCoeff.out
@@ -504,6 +531,23 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
       return m_matrix / extendedTo(other.derived());
     }
+    
+    /** \returns an expression where each column of row of the referenced matrix are normalized.
+      * The referenced matrix is \b not modified.
+      * \sa MatrixBase::normalized(), normalize()
+      */
+    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+                  const ExpressionTypeNestedCleaned,
+                  const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>
+    normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
+    
+    
+    /** Normalize in-place each row or columns of the referenced matrix.
+      * \sa MatrixBase::normalize(), normalized()
+      */
+    void normalize() {
+      m_matrix = this->normalized();
+    }
 
 /////////// Geometry module ///////////
 

Eigen/src/Core/Visitor.h

@@ -164,8 +164,8 @@ struct functor_traits<max_coeff_visitor<Scalar> > {
 
 } // end namespace internal
 
-/** \returns the minimum of all coefficients of *this
+/** \returns the minimum of all coefficients of *this and puts in *row and *col its location.
-  * and puts in *row and *col its location.
+  * \warning the result is undefined if \c *this contains NaN.
   *
   * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
   */
@@ -181,8 +181,8 @@ DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
   return minVisitor.res;
 }
 
-/** \returns the minimum of all coefficients of *this
+/** \returns the minimum of all coefficients of *this and puts in *index its location.
-  * and puts in *index its location.
+  * \warning the result is undefined if \c *this contains NaN. 
   *
   * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
   */
@@ -198,8 +198,8 @@ DenseBase<Derived>::minCoeff(IndexType* index) const
   return minVisitor.res;
 }
 
-/** \returns the maximum of all coefficients of *this
+/** \returns the maximum of all coefficients of *this and puts in *row and *col its location.
-  * and puts in *row and *col its location.
+  * \warning the result is undefined if \c *this contains NaN. 
   *
   * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
   */
@@ -215,8 +215,8 @@ DenseBase<Derived>::maxCoeff(IndexType* rowPtr, IndexType* colPtr) const
   return maxVisitor.res;
 }
 
-/** \returns the maximum of all coefficients of *this
+/** \returns the maximum of all coefficients of *this and puts in *index its location.
-  * and puts in *index its location.
+  * \warning the result is undefined if \c *this contains NaN.
   *
   * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
   */

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

@@ -173,6 +173,9 @@ template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const
 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return psub<Packet4f>(p4f_ZERO, a); }
 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub<Packet4i>(p4i_ZERO, a); }
 
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b,p4f_ZERO); }
 /* Commented out: it's actually slower than processing it scalar
  *

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

@@ -68,7 +68,6 @@ template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
 {
   Packet4f v1, v2;
-  float32x2_t a_lo, a_hi;
 
   // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
   v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));
@@ -81,9 +80,7 @@ template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, con
   // Conjugate v2 
   v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR));
   // Swap real/imag elements in v2.
-  a_lo = vrev64_f32(vget_low_f32(v2));
+  v2 = vrev64q_f32(v2);
-  a_hi = vrev64_f32(vget_high_f32(v2));
-  v2 = vcombine_f32(a_lo, a_hi);
   // Add and return the result
   return Packet2cf(vaddq_f32(v1, v2));
 }
@@ -113,7 +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)
 {
@@ -241,13 +238,10 @@ template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, con
   // TODO optimize it for AltiVec
   Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
   Packet4f s, rev_s;
-  float32x2_t a_lo, a_hi;
 
   // this computes the norm
   s = vmulq_f32(b.v, b.v);
-  a_lo = vrev64_f32(vget_low_f32(s));
+  rev_s = vrev64q_f32(s);
-  a_hi = vrev64_f32(vget_high_f32(s));
-  rev_s = vcombine_f32(a_lo, a_hi);
 
   return Packet2cf(pdiv(res.v, vaddq_f32(s,rev_s)));
 }

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

@@ -48,9 +48,18 @@ typedef uint32x4_t  Packet4ui;
   #define EIGEN_INIT_NEON_PACKET2(X, Y)       {X, Y}
   #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
 #endif
-    
+
-#ifndef __pld
+// arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
-#define __pld(x) asm volatile ( "   pld [%[addr]]\n" :: [addr] "r" (x) : "cc" );
+// which available on LLVM and GCC (at least)
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__)
+  #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#elif defined __pld
+  #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
+#elif !defined(__aarch64__)
+  #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( "   pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#else
+  // by default no explicit prefetching
+  #define EIGEN_ARM_PREFETCH(ADDR)
 #endif
 
 template<> struct packet_traits<float>  : default_packet_traits
@@ -115,6 +124,9 @@ template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const
 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }
 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }
 
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }
 
@@ -188,15 +200,15 @@ template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)   { EI
 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
 {
   float32x2_t lo, hi;
-  lo = vdup_n_f32(*from);
+  lo = vld1_dup_f32(from);
-  hi = vdup_n_f32(*(from+1));
+  hi = vld1_dup_f32(from+1);
   return vcombine_f32(lo, hi);
 }
 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
 {
   int32x2_t lo, hi;
-  lo = vdup_n_s32(*from);
+  lo = vld1_dup_s32(from);
-  hi = vdup_n_s32(*(from+1));
+  hi = vld1_dup_s32(from+1);
   return vcombine_s32(lo, hi);
 }
 
@@ -206,8 +218,8 @@ template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& f
 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }
 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }
 
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { __pld(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { __pld(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { EIGEN_ARM_PREFETCH(addr); }
 
 // FIXME only store the 2 first elements ?
 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }

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

@@ -81,8 +81,8 @@ template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a,
 template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(a.v,b.v)); }
 
-template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&numext::real_ref(*from))); }
-template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&numext::real_ref(*from))); }
 
 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
 {
@@ -104,8 +104,8 @@ template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<flo
 
 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
 
-template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
-template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
 
 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
 

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.
@@ -442,21 +442,32 @@ 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)
 {
   Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
 
   /* select only the inverse sqrt of non-zero inputs */
-  Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
+  Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));
   Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
 
   x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,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
@@ -141,6 +142,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
   return psub(_mm_setr_epi32(0,0,0,0), a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
@@ -173,18 +178,26 @@ template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const
 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
 {
+#ifdef EIGEN_VECTORIZE_SSE4_1
+  return _mm_min_epi32(a,b);
+#else
   // after some bench, this version *is* faster than a scalar implementation
   Packet4i mask = _mm_cmplt_epi32(a,b);
   return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
 {
+#ifdef EIGEN_VECTORIZE_SSE4_1
+  return _mm_max_epi32(a,b);
+#else
   // after some bench, this version *is* faster than a scalar implementation
   Packet4i mask = _mm_cmpgt_epi32(a,b);
   return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
@@ -495,8 +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];
+  int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
-  register int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
+  int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
   return aux0<aux2 ? aux0 : aux2;
 }
 
@@ -516,8 +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];
+  int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
-  register int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
+  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;
@@ -150,7 +151,7 @@ class CoeffBasedProduct
     {
       // we don't allow taking products of matrices of different real types, as that wouldn't be vectorizable.
       // We still allow to mix T and complex<T>.
-      EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
+      EIGEN_STATIC_ASSERT((internal::scalar_product_traits<typename Lhs::RealScalar, typename Rhs::RealScalar>::Defined),
         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
       eigen_assert(lhs.cols() == rhs.rows()
         && "invalid matrix product"
@@ -184,7 +185,7 @@ class CoeffBasedProduct
     {
       PacketScalar res;
       internal::product_packet_impl<Flags&RowMajorBit ? RowMajor : ColMajor,
-                              Unroll ? InnerSize-1 : Dynamic,
+                              Unroll ? InnerSize : Dynamic,
                               _LhsNested, _RhsNested, PacketScalar, LoadMode>
         ::run(row, col, m_lhs, m_rhs, res);
       return res;
@@ -242,12 +243,12 @@ struct product_coeff_impl<DefaultTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
   {
     product_coeff_impl<DefaultTraversal, UnrollingIndex-1, Lhs, Rhs, RetScalar>::run(row, col, lhs, rhs, res);
-    res += lhs.coeff(row, UnrollingIndex) * rhs.coeff(UnrollingIndex, col);
+    res += lhs.coeff(row, UnrollingIndex-1) * rhs.coeff(UnrollingIndex-1, col);
   }
 };
 
 template<typename Lhs, typename Rhs, typename RetScalar>
-struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
+struct product_coeff_impl<DefaultTraversal, 1, Lhs, Rhs, RetScalar>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
@@ -256,16 +257,23 @@ struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
   }
 };
 
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<DefaultTraversal, 0, Lhs, Rhs, RetScalar>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+  {
+    res = RetScalar(0);
+  }
+};
+
 template<typename Lhs, typename Rhs, typename RetScalar>
 struct product_coeff_impl<DefaultTraversal, Dynamic, Lhs, Rhs, RetScalar>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = (lhs.row(row).transpose().cwiseProduct( rhs.col(col) )).sum();
-    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
-      for(Index i = 1; i < lhs.cols(); ++i)
-        res += lhs.coeff(row, i) * rhs.coeff(i, col);
   }
 };
 
@@ -295,6 +303,16 @@ struct product_coeff_vectorized_unroller<0, Lhs, Rhs, Packet>
   }
 };
 
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct product_coeff_impl<InnerVectorizedTraversal, 0, Lhs, Rhs, RetScalar>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, RetScalar &res)
+  {
+    res = 0;
+  }
+};
+
 template<int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
 struct product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, RetScalar>
 {
@@ -304,8 +322,7 @@ struct product_coeff_impl<InnerVectorizedTraversal, UnrollingIndex, Lhs, Rhs, Re
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
   {
     Packet pres;
-    product_coeff_vectorized_unroller<UnrollingIndex+1-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
+    product_coeff_vectorized_unroller<UnrollingIndex-PacketSize, Lhs, Rhs, Packet>::run(row, col, lhs, rhs, pres);
-    product_coeff_impl<DefaultTraversal,UnrollingIndex,Lhs,Rhs,RetScalar>::run(row, col, lhs, rhs, res);
     res = predux(pres);
   }
 };
@@ -373,7 +390,7 @@ struct product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
   {
     product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
-    res =  pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex)), rhs.template packet<LoadMode>(UnrollingIndex, col), res);
+    res =  pmadd(pset1<Packet>(lhs.coeff(row, UnrollingIndex-1)), rhs.template packet<LoadMode>(UnrollingIndex-1, col), res);
   }
 };
 
@@ -384,12 +401,12 @@ struct product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
   {
     product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, res);
-    res =  pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex), pset1<Packet>(rhs.coeff(UnrollingIndex, col)), res);
+    res =  pmadd(lhs.template packet<LoadMode>(row, UnrollingIndex-1), pset1<Packet>(rhs.coeff(UnrollingIndex-1, col)), res);
   }
 };
 
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+struct product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
@@ -399,7 +416,7 @@ struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
 };
 
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
-struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+struct product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet &res)
@@ -408,16 +425,35 @@ struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
   }
 };
 
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+  {
+    res = pset1<Packet>(0);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+  typedef typename Lhs::Index Index;
+  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Packet &res)
+  {
+    res = pset1<Packet>(0);
+  }
+};
+
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
 {
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = pset1<Packet>(0);
-    res = pmul(pset1<Packet>(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
+    for(Index i = 0; i < lhs.cols(); ++i)
-      for(Index i = 1; i < lhs.cols(); ++i)
+      res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
-        res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
   }
 };
 
@@ -427,10 +463,9 @@ struct product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
   typedef typename Lhs::Index Index;
   static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Packet& res)
   {
-    eigen_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = pset1<Packet>(0);
-    res = pmul(lhs.template packet<LoadMode>(row, 0), pset1<Packet>(rhs.coeff(0, col)));
+    for(Index i = 0; i < lhs.cols(); ++i)
-      for(Index i = 1; i < lhs.cols(); ++i)
+      res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
-        res =  pmadd(lhs.template packet<LoadMode>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
   }
 };
 

Eigen/src/Core/products/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/GeneralMatrixMatrixTriangular.h

@@ -238,7 +238,6 @@ struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
 {
   static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
   {
-    typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::Index Index;
     
     typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;

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
+  ResScalar* res, Index resIncr, RhsScalar alpha);
-  #ifdef EIGEN_INTERNAL_DEBUGGING
-    resIncr
-  #endif
-  , 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
+  ResScalar* res, Index resIncr, RhsScalar alpha)
-  #ifdef EIGEN_INTERNAL_DEBUGGING
-    resIncr
-  #endif
-  , RhsScalar alpha)
 {
+  EIGEN_UNUSED_VARIABLE(resIncr)
   eigen_internal_assert(resIncr==1);
   #ifdef _EIGEN_ACCUMULATE_PACKETS
   #error _EIGEN_ACCUMULATE_PACKETS has already been defined
@@ -86,7 +79,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,Co
   conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
   conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
   if(ConjugateRhs)
-    alpha = conj(alpha);
+    alpha = numext::conj(alpha);
 
   enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };
   const Index columnsAtOnce = 4;
@@ -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)
+  #pragma omp parallel num_threads(threads)
-  for(Index i=0; i<threads; ++i)
   {
+    Index i = omp_get_thread_num();
+    // Note that the actual number of threads might be lower than the number of request ones.
+    Index actual_threads = omp_get_num_threads();
+    
+    Index blockCols = (cols / actual_threads) & ~Index(0x3);
+    Index blockRows = (rows / actual_threads) & ~Index(0x7);
+    
     Index r0 = i*blockRows;
-    Index actualBlockRows = (i+1==threads) ? rows-r0 : blockRows;
+    Index actualBlockRows = (i+1==actual_threads) ? rows-r0 : blockRows;
 
     Index c0 = i*blockCols;
-    Index actualBlockCols = (i+1==threads) ? cols-c0 : blockCols;
+    Index actualBlockCols = (i+1==actual_threads) ? cols-c0 : blockCols;
 
     info[i].rhs_start = c0;
     info[i].rhs_length = actualBlockCols;

Eigen/src/Core/products/SelfadjointMatrixMatrix.h

@@ -30,9 +30,9 @@ struct symm_pack_lhs
     for(Index k=i; k<i+BlockRows; k++)
     {
       for(Index w=0; w<h; w++)
-        blockA[count++] = conj(lhs(k, i+w)); // transposed
+        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
 
-      blockA[count++] = real(lhs(k,k));   // real (diagonal)
+      blockA[count++] = numext::real(lhs(k,k));   // real (diagonal)
 
       for(Index w=h+1; w<BlockRows; w++)
         blockA[count++] = lhs(i+w, k);          // normal
@@ -41,7 +41,7 @@ struct symm_pack_lhs
     // transposed copy
     for(Index k=i+BlockRows; k<cols; k++)
       for(Index w=0; w<BlockRows; w++)
-        blockA[count++] = conj(lhs(k, i+w)); // transposed
+        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
   }
   void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
   {
@@ -65,10 +65,10 @@ struct symm_pack_lhs
       for(Index k=0; k<i; k++)
         blockA[count++] = lhs(i, k);              // normal
 
-      blockA[count++] = real(lhs(i, i));       // real (diagonal)
+      blockA[count++] = numext::real(lhs(i, i));       // real (diagonal)
 
       for(Index k=i+1; k<cols; k++)
-        blockA[count++] = conj(lhs(k, i));     // transposed
+        blockA[count++] = numext::conj(lhs(k, i));     // transposed
     }
   }
 };
@@ -107,12 +107,12 @@ struct symm_pack_rhs
       // transpose
       for(Index k=k2; k<j2; k++)
       {
-        blockB[count+0] = conj(rhs(j2+0,k));
+        blockB[count+0] = numext::conj(rhs(j2+0,k));
-        blockB[count+1] = conj(rhs(j2+1,k));
+        blockB[count+1] = numext::conj(rhs(j2+1,k));
         if (nr==4)
         {
-          blockB[count+2] = conj(rhs(j2+2,k));
+          blockB[count+2] = numext::conj(rhs(j2+2,k));
-          blockB[count+3] = conj(rhs(j2+3,k));
+          blockB[count+3] = numext::conj(rhs(j2+3,k));
         }
         count += nr;
       }
@@ -124,11 +124,11 @@ struct symm_pack_rhs
         for (Index w=0 ; w<h; ++w)
           blockB[count+w] = rhs(k,j2+w);
 
-        blockB[count+h] = real(rhs(k,k));
+        blockB[count+h] = numext::real(rhs(k,k));
 
         // transpose
         for (Index w=h+1 ; w<nr; ++w)
-          blockB[count+w] = conj(rhs(j2+w,k));
+          blockB[count+w] = numext::conj(rhs(j2+w,k));
         count += nr;
         ++h;
       }
@@ -151,12 +151,12 @@ struct symm_pack_rhs
     {
       for(Index k=k2; k<end_k; k++)
       {
-        blockB[count+0] = conj(rhs(j2+0,k));
+        blockB[count+0] = numext::conj(rhs(j2+0,k));
-        blockB[count+1] = conj(rhs(j2+1,k));
+        blockB[count+1] = numext::conj(rhs(j2+1,k));
         if (nr==4)
         {
-          blockB[count+2] = conj(rhs(j2+2,k));
+          blockB[count+2] = numext::conj(rhs(j2+2,k));
-          blockB[count+3] = conj(rhs(j2+3,k));
+          blockB[count+3] = numext::conj(rhs(j2+3,k));
         }
         count += nr;
       }
@@ -169,13 +169,13 @@ struct symm_pack_rhs
       Index half = (std::min)(end_k,j2);
       for(Index k=k2; k<half; k++)
       {
-        blockB[count] = conj(rhs(j2,k));
+        blockB[count] = numext::conj(rhs(j2,k));
         count += 1;
       }
 
       if(half==j2 && half<k2+rows)
       {
-        blockB[count] = real(rhs(j2,j2));
+        blockB[count] = numext::real(rhs(j2,j2));
         count += 1;
       }
       else

Eigen/src/Core/products/SelfadjointMatrixVector.h

@@ -44,7 +44,6 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
   Scalar alpha)
 {
   typedef typename packet_traits<Scalar>::type Packet;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
   const Index PacketSize = sizeof(Packet)/sizeof(Scalar);
 
   enum {
@@ -60,7 +59,7 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
   conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs,  IsRowMajor), ConjugateRhs> pcj0;
   conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
 
-  Scalar cjAlpha = ConjugateRhs ? conj(alpha) : alpha;
+  Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
 
   // FIXME this copy is now handled outside product_selfadjoint_vector, so it could probably be removed.
   // if the rhs is not sequentially stored in memory we copy it to a temporary buffer,
@@ -80,8 +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;
+    const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
-    register const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
+    const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
 
     Scalar t0 = cjAlpha * rhs[j];
     Packet ptmp0 = pset1<Packet>(t0);
@@ -99,8 +98,8 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
     size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
 
     // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
-    res[j]   += cjd.pmul(internal::real(A0[j]), t0);
+    res[j]   += cjd.pmul(numext::real(A0[j]), t0);
-    res[j+1] += cjd.pmul(internal::real(A1[j+1]), t1);
+    res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
     if(FirstTriangular)
     {
       res[j]   += cj0.pmul(A1[j],   t1);
@@ -115,8 +114,8 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
     for (size_t i=starti; i<alignedStart; ++i)
     {
       res[i] += t0 * A0[i] + t1 * A1[i];
-      t2 += conj(A0[i]) * rhs[i];
+      t2 += numext::conj(A0[i]) * rhs[i];
-      t3 += conj(A1[i]) * rhs[i];
+      t3 += numext::conj(A1[i]) * rhs[i];
     }
     // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
     // gcc 4.2 does this optimization automatically.
@@ -148,12 +147,12 @@ 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);
     // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
-    res[j] += cjd.pmul(internal::real(A0[j]), t1);
+    res[j] += cjd.pmul(numext::real(A0[j]), t1);
     for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
     {
       res[i] += cj0.pmul(A0[i], t1);

Eigen/src/Core/products/SelfadjointProduct.h

@@ -111,7 +111,7 @@ struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,false>
 template<typename MatrixType, unsigned int UpLo>
 template<typename DerivedU>
 SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
-::rankUpdate(const MatrixBase<DerivedU>& u, Scalar alpha)
+::rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha)
 {
   selfadjoint_product_selector<MatrixType,DerivedU,UpLo>::run(_expression().const_cast_derived(), u.derived(), alpha);
 

Eigen/src/Core/products/SelfadjointRank2Update.h

@@ -30,8 +30,8 @@ struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>
     for (Index i=0; i<size; ++i)
     {
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
-                        (conj(alpha)  * conj(u.coeff(i))) * v.tail(size-i)
+                        (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)
-                      + (alpha * conj(v.coeff(i))) * u.tail(size-i);
+                      + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);
     }
   }
 };
@@ -44,8 +44,8 @@ struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>
     const Index size = u.size();
     for (Index i=0; i<size; ++i)
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
-                        (conj(alpha)  * conj(u.coeff(i))) * v.head(i+1)
+                        (numext::conj(alpha)  * numext::conj(u.coeff(i))) * v.head(i+1)
-                      + (alpha * conj(v.coeff(i))) * u.head(i+1);
+                      + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);
   }
 };
 
@@ -58,7 +58,7 @@ template<bool Cond, typename T> struct conj_expr_if
 template<typename MatrixType, unsigned int UpLo>
 template<typename DerivedU, typename DerivedV>
 SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
-::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, Scalar alpha)
+::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha)
 {
   typedef internal::blas_traits<DerivedU> UBlasTraits;
   typedef typename UBlasTraits::DirectLinearAccessType ActualUType;
@@ -75,9 +75,9 @@ SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
 
   enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
   Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())
-                             * internal::conj(VBlasTraits::extractScalarFactor(v.derived()));
+                             * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));
   if (IsRowMajor)
-    actualAlpha = internal::conj(actualAlpha);
+    actualAlpha = numext::conj(actualAlpha);
 
   internal::selfadjoint_rank2_update_selector<Scalar, Index,
     typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ UBlasTraits::NeedToConjugate,_ActualUType>::type>::type,

Eigen/src/Core/products/TriangularMatrixVector.h

@@ -245,7 +245,7 @@ template<> struct trmv_selector<ColMajor>
 
     gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
 
-    bool alphaIsCompatible = (!ComplexByReal) || (imag(actualAlpha)==RealScalar(0));
+    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
     bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
     
     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
@@ -256,7 +256,7 @@ template<> struct trmv_selector<ColMajor>
     if(!evalToDest)
     {
       #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
-      int size = dest.size();
+      Index size = dest.size();
       EIGEN_DENSE_STORAGE_CTOR_PLUGIN
       #endif
       if(!alphaIsCompatible)

Eigen/src/Core/util/BlasUtil.h

@@ -42,7 +42,7 @@ template<bool Conjugate> struct conj_if;
 
 template<> struct conj_if<true> {
   template<typename T>
-  inline T operator()(const T& x) { return conj(x); }
+  inline T operator()(const T& x) { return numext::conj(x); }
   template<typename T>
   inline T pconj(const T& x) { return internal::pconj(x); }
 };
@@ -67,7 +67,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) + imag(x)*imag(y), imag(x)*real(y) - real(x)*imag(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::imag(x)*numext::real(y) - numext::real(x)*numext::imag(y)); }
 };
 
 template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,false>
@@ -77,7 +77,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) + imag(x)*imag(y), real(x)*imag(y) - imag(x)*real(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
 };
 
 template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,true>
@@ -87,7 +87,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) - imag(x)*imag(y), - real(x)*imag(y) - imag(x)*real(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) - numext::imag(x)*numext::imag(y), - numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
 };
 
 template<typename RealScalar,bool Conj> struct conj_helper<std::complex<RealScalar>, RealScalar, Conj,false>
@@ -113,7 +113,7 @@ template<typename From,typename To> struct get_factor {
 };
 
 template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
-  static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return real(x); }
+  static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
 };
 
 // Lightweight helper class to access matrix coefficients.

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

@@ -54,8 +54,25 @@
 #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
 

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_MAJOR_VERSION 2
-#define EIGEN_MINOR_VERSION 91
+#define EIGEN_MINOR_VERSION 5
 
 #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:
@@ -238,12 +245,19 @@
 #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) && (defined __GNUC__)
+#if !defined(EIGEN_ASM_COMMENT)
-#define EIGEN_ASM_COMMENT(X)  asm("#" X)
+  #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
-#else
+    #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
-#define EIGEN_ASM_COMMENT(X)
+  #else
+    #define EIGEN_ASM_COMMENT(X)
+  #endif
 #endif
 
 /* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
@@ -264,6 +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
@@ -282,7 +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
@@ -298,7 +314,7 @@
 // just an empty macro !
 #define EIGEN_EMPTY
 
-#if defined(_MSC_VER) && (!defined(__INTEL_COMPILER))
+#if defined(_MSC_VER) && (_MSC_VER < 1800) && (!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)
@@ -317,8 +333,11 @@
   }
 #endif
 
-#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+/** \internal
-  EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
 
 /**
 * Just a side note. Commenting within defines works only by documenting

Eigen/src/Core/util/Memory.h

@@ -58,10 +58,17 @@
 
 #endif
 
-#if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) \
+// See bug 554 (http://eigen.tuxfamily.org/bz/show_bug.cgi?id=554)
- && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+// It seems to be unsafe to check _POSIX_ADVISORY_INFO without including unistd.h first.
-  #define EIGEN_HAS_POSIX_MEMALIGN 1
+// Currently, let's include it only on unix systems:
-#else
+#if defined(__unix__) || defined(__unix)
+  #include <unistd.h>
+  #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || (defined __PGI) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+    #define EIGEN_HAS_POSIX_MEMALIGN 1
+  #endif
+#endif
+
+#ifndef EIGEN_HAS_POSIX_MEMALIGN
   #define EIGEN_HAS_POSIX_MEMALIGN 0
 #endif
 
@@ -94,11 +101,11 @@ inline void throw_std_bad_alloc()
 /** \internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
   * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.
   */
-inline void* handmade_aligned_malloc(size_t size)
+inline void* handmade_aligned_malloc(std::size_t size)
 {
   void *original = std::malloc(size+16);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<size_t>(original) & ~(size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
   *(reinterpret_cast<void**>(aligned) - 1) = original;
   return aligned;
 }
@@ -114,13 +121,18 @@ inline void handmade_aligned_free(void *ptr)
   * Since we know that our handmade version is based on std::realloc
   * we can use std::realloc to implement efficient reallocation.
   */
-inline void* handmade_aligned_realloc(void* ptr, size_t size, size_t = 0)
+inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
 {
   if (ptr == 0) return handmade_aligned_malloc(size);
   void *original = *(reinterpret_cast<void**>(ptr) - 1);
+  std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);
   original = std::realloc(original,size+16);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<size_t>(original) & ~(size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+  void *previous_aligned = static_cast<char *>(original)+previous_offset;
+  if(aligned!=previous_aligned)
+    std::memmove(aligned, previous_aligned, size);
+  
   *(reinterpret_cast<void**>(aligned) - 1) = original;
   return aligned;
 }
@@ -129,7 +141,7 @@ inline void* handmade_aligned_realloc(void* ptr, size_t size, size_t = 0)
 *** Implementation of generic aligned realloc (when no realloc can be used)***
 *****************************************************************************/
 
-void* aligned_malloc(size_t size);
+void* aligned_malloc(std::size_t size);
 void  aligned_free(void *ptr);
 
 /** \internal
@@ -210,7 +222,7 @@ inline void* aligned_malloc(size_t size)
     if(posix_memalign(&result, 16, size)) result = 0;
   #elif EIGEN_HAS_MM_MALLOC
     result = _mm_malloc(size, 16);
-#elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
+  #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
     result = _aligned_malloc(size, 16);
   #else
     result = handmade_aligned_malloc(size);
@@ -260,12 +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);
@@ -405,6 +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)
@@ -452,10 +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)
 {
-  typedef typename packet_traits<Scalar>::type Packet;
+  static const Index PacketSize = packet_traits<Scalar>::size;
-  enum { PacketSize = packet_traits<Scalar>::size,
+  static const Index PacketAlignedMask = PacketSize-1;
-         PacketAlignedMask = PacketSize-1
-  };
 
   if(PacketSize==1)
   {
@@ -511,7 +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
@@ -567,7 +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
@@ -601,7 +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) \
@@ -623,7 +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() { \
@@ -718,15 +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();
@@ -751,11 +755,16 @@ public:
 #    if defined(__PIC__) && defined(__i386__)
        // Case for x86 with PIC
 #      define EIGEN_CPUID(abcd,func,id) \
-         __asm__ __volatile__ ("xchgl %%ebx, %%esi;cpuid; xchgl %%ebx,%%esi": "=a" (abcd[0]), "=S" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id));
+         __asm__ __volatile__ ("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id));
+#    elif defined(__PIC__) && defined(__x86_64__)
+       // Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.
+       // However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.
+#      define EIGEN_CPUID(abcd,func,id) \
+        __asm__ __volatile__ ("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id));
 #    else
        // Case for x86_64 or x86 w/o PIC
 #      define EIGEN_CPUID(abcd,func,id) \
-         __asm__ __volatile__ ("cpuid": "=a" (abcd[0]), "=b" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id) );
+         __asm__ __volatile__ ("cpuid": "=a" (abcd[0]), "=b" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id) );
 #    endif
 #  elif defined(_MSC_VER)
 #    if (_MSC_VER > 1500) && ( defined(_M_IX86) || defined(_M_X64) )
@@ -768,9 +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)
@@ -912,13 +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/Meta.h

@@ -186,23 +186,35 @@ template<int Y, int InfX, int SupX>
 class meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
 
 /** \internal determines whether the product of two numeric types is allowed and what the return type is */
-template<typename T, typename U> struct scalar_product_traits;
+template<typename T, typename U> struct scalar_product_traits
+{
+  enum { Defined = 0 };
+};
 
 template<typename T> struct scalar_product_traits<T,T>
 {
-  //enum { Cost = NumTraits<T>::MulCost };
+  enum {
+    // Cost = NumTraits<T>::MulCost,
+    Defined = 1
+  };
   typedef T ReturnType;
 };
 
 template<typename T> struct scalar_product_traits<T,std::complex<T> >
 {
-  //enum { Cost = 2*NumTraits<T>::MulCost };
+  enum {
+    // Cost = 2*NumTraits<T>::MulCost,
+    Defined = 1
+  };
   typedef std::complex<T> ReturnType;
 };
 
 template<typename T> struct scalar_product_traits<std::complex<T>, T>
 {
-  //enum { Cost = 2*NumTraits<T>::MulCost  };
+  enum {
+    // Cost = 2*NumTraits<T>::MulCost,
+    Defined = 1
+  };
   typedef std::complex<T> ReturnType;
 };
 

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

@@ -91,7 +91,8 @@ template<typename T> struct functor_traits
   enum
   {
     Cost = 10,
-    PacketAccess = false
+    PacketAccess = false,
+    IsRepeatable = false
   };
 };
 
@@ -340,7 +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/Geometry/AlignedBox.h

@@ -34,7 +34,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==
   typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
 
   /** Default constructor initializing a null box. */
-  inline explicit AlignedBox()
+  inline AlignedBox()
   { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
 
   /** Constructs a null box with \a _dim the dimension of the ambient space. */

Eigen/src/Eigen2Support/Geometry/Hyperplane.h

@@ -44,7 +44,7 @@ public:
   typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
 
   /** Default constructor without initialization */
-  inline explicit Hyperplane() {}
+  inline Hyperplane() {}
 
   /** Constructs a dynamic-size hyperplane with \a _dim the dimension
     * of the ambient space */

Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h

@@ -36,7 +36,7 @@ public:
   typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
 
   /** Default constructor without initialization */
-  inline explicit ParametrizedLine() {}
+  inline ParametrizedLine() {}
 
   /** Constructs a dynamic-size line with \a _dim the dimension
     * of the ambient space */

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/MathFunctions.h

@@ -12,18 +12,18 @@
 
 namespace Eigen { 
 
-template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return internal::real(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return numext::real(x); }
-template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return internal::imag(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return numext::imag(x); }
-template<typename T> inline T ei_conj(const T& x) { return internal::conj(x); }
+template<typename T> inline T ei_conj(const T& x) { return numext::conj(x); }
 template<typename T> inline typename NumTraits<T>::Real ei_abs (const T& x) { using std::abs; return abs(x); }
-template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return internal::abs2(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return numext::abs2(x); }
 template<typename T> inline T ei_sqrt(const T& x) { using std::sqrt; return sqrt(x); }
 template<typename T> inline T ei_exp (const T& x) { using std::exp;  return exp(x); }
 template<typename T> inline T ei_log (const T& x) { using std::log;  return log(x); }
 template<typename T> inline T ei_sin (const T& x) { using std::sin;  return sin(x); }
 template<typename T> inline T ei_cos (const T& x) { using std::cos;  return cos(x); }
 template<typename T> inline T ei_atan2(const T& x,const T& y) { using std::atan2; return atan2(x,y); }
-template<typename T> inline T ei_pow (const T& x,const T& y) { return internal::pow(x,y); }
+template<typename T> inline T ei_pow (const T& x,const T& y) { return numext::pow(x,y); }
 template<typename T> inline T ei_random () { return internal::random<T>(); }
 template<typename T> inline T ei_random (const T& x, const T& y) { return internal::random(x, y); }
 

Eigen/src/Eigen2Support/SVD.h

@@ -315,7 +315,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
         e[p-2] = 0.0;
         for (j = p-2; j >= k; --j)
         {
-          Scalar t(internal::hypot(m_sigma[j],f));
+          Scalar t(numext::hypot(m_sigma[j],f));
           Scalar cs(m_sigma[j]/t);
           Scalar sn(f/t);
           m_sigma[j] = t;
@@ -344,7 +344,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
         e[k-1] = 0.0;
         for (j = k; j < p; ++j)
         {
-          Scalar t(internal::hypot(m_sigma[j],f));
+          Scalar t(numext::hypot(m_sigma[j],f));
           Scalar cs( m_sigma[j]/t);
           Scalar sn(f/t);
           m_sigma[j] = t;
@@ -392,7 +392,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
 
         for (j = k; j < p-1; ++j)
         {
-          Scalar t = internal::hypot(f,g);
+          Scalar t = numext::hypot(f,g);
           Scalar cs = f/t;
           Scalar sn = g/t;
           if (j != k)
@@ -410,7 +410,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
               m_matV(i,j) = t;
             }
           }
-          t = internal::hypot(f,g);
+          t = numext::hypot(f,g);
           cs = f/t;
           sn = g/t;
           m_sigma[j] = t;
@@ -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() == m_matU.rows());
-  ei_assert(b.rows() == 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());
 
@@ -294,7 +302,7 @@ void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(const RealScalar& mat
       {
         // If the i-th and k-th eigenvalue are equal, then z equals 0.
         // Use a small value instead, to prevent division by zero.
-        internal::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
+        numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
       }
       m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
     }

Eigen/src/Eigenvalues/ComplexSchur.h

@@ -263,8 +263,8 @@ template<typename _MatrixType> class ComplexSchur
 template<typename MatrixType>
 inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
 {
-  RealScalar d = internal::norm1(m_matT.coeff(i,i)) + internal::norm1(m_matT.coeff(i+1,i+1));
+  RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
-  RealScalar sd = internal::norm1(m_matT.coeff(i+1,i));
+  RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
   if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
   {
     m_matT.coeffRef(i+1,i) = ComplexScalar(0);
@@ -282,7 +282,7 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
   if (iter == 10 || iter == 20) 
   {
     // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
-    return abs(internal::real(m_matT.coeff(iu,iu-1))) + abs(internal::real(m_matT.coeff(iu-1,iu-2)));
+    return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
   }
 
   // compute the shift as one of the eigenvalues of t, the 2x2
@@ -299,13 +299,13 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
   ComplexScalar eival1 = (trace + disc) / RealScalar(2);
   ComplexScalar eival2 = (trace - disc) / RealScalar(2);
 
-  if(internal::norm1(eival1) > internal::norm1(eival2))
+  if(numext::norm1(eival1) > numext::norm1(eival2))
     eival2 = det / eival1;
   else
     eival1 = det / eival2;
 
   // choose the eigenvalue closest to the bottom entry of the diagonal
-  if(internal::norm1(eival1-t.coeff(1,1)) < internal::norm1(eival2-t.coeff(1,1)))
+  if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
     return normt * eival1;
   else
     return normt * eival2;
@@ -364,7 +364,6 @@ struct complex_schur_reduce_to_hessenberg<MatrixType, false>
   static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
   {
     typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
-    typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
 
     // Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar
     _this.m_hess.compute(matrix);

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;
@@ -317,12 +324,12 @@ MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
   MatrixType matD = MatrixType::Zero(n,n);
   for (Index i=0; i<n; ++i)
   {
-    if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i))))
+    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i))))
-      matD.coeffRef(i,i) = internal::real(m_eivalues.coeff(i));
+      matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
     else
     {
-      matD.template block<2,2>(i,i) <<  internal::real(m_eivalues.coeff(i)), internal::imag(m_eivalues.coeff(i)),
+      matD.template block<2,2>(i,i) <<  numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
-                                       -internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i));
+                                       -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
       ++i;
     }
   }
@@ -338,7 +345,7 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige
   EigenvectorsType matV(n,n);
   for (Index j=0; j<n; ++j)
   {
-    if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(j)), internal::real(m_eivalues.coeff(j))) || j+1==n)
+    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j))) || j+1==n)
     {
       // we have a real eigen value
       matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
@@ -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());
@@ -515,8 +524,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
       else
       {
         std::complex<Scalar> cc = cdiv<Scalar>(0.0,-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q);
-        m_matT.coeffRef(n-1,n-1) = internal::real(cc);
+        m_matT.coeffRef(n-1,n-1) = numext::real(cc);
-        m_matT.coeffRef(n-1,n) = internal::imag(cc);
+        m_matT.coeffRef(n-1,n) = numext::imag(cc);
       }
       m_matT.coeffRef(n,n-1) = 0.0;
       m_matT.coeffRef(n,n) = 1.0;
@@ -538,8 +547,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
           if (m_eivalues.coeff(i).imag() == RealScalar(0))
           {
             std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
-            m_matT.coeffRef(i,n-1) = internal::real(cc);
+            m_matT.coeffRef(i,n-1) = numext::real(cc);
-            m_matT.coeffRef(i,n) = internal::imag(cc);
+            m_matT.coeffRef(i,n) = numext::imag(cc);
           }
           else
           {
@@ -552,8 +561,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
               vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
 
             std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
-            m_matT.coeffRef(i,n-1) = internal::real(cc);
+            m_matT.coeffRef(i,n-1) = numext::real(cc);
-            m_matT.coeffRef(i,n) = internal::imag(cc);
+            m_matT.coeffRef(i,n) = numext::imag(cc);
             if (abs(x) > (abs(lastw) + abs(q)))
             {
               m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
@@ -562,8 +571,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
             else
             {
               cc = cdiv(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n),lastw,q);
-              m_matT.coeffRef(i+1,n-1) = internal::real(cc);
+              m_matT.coeffRef(i+1,n-1) = numext::real(cc);
-              m_matT.coeffRef(i+1,n) = internal::imag(cc);
+              m_matT.coeffRef(i+1,n) = numext::imag(cc);
             }
           }
 

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/HessenbergDecomposition.h

@@ -82,7 +82,7 @@ template<typename _MatrixType> class HessenbergDecomposition
     typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
 
     /** \brief Return type of matrixQ() */
-    typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
     
     typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
 
@@ -313,7 +313,7 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
 
     // A = A H'
     matA.rightCols(remainingSize)
-        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), internal::conj(h), &temp.coeffRef(0));
+        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));
   }
 }
 

Eigen/src/Eigenvalues/RealQZ.h

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

Eigen/src/Eigenvalues/RealSchur.h

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

Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h

@@ -351,6 +351,11 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     #endif // EIGEN2_SUPPORT
 
   protected:
+    static void check_template_parameters()
+    {
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+    }
+    
     MatrixType m_eivec;
     RealVectorType m_eivalues;
     typename TridiagonalizationType::SubDiagonalType m_subdiag;
@@ -384,6 +389,8 @@ 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
@@ -395,7 +402,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
 
   if(n==1)
   {
-    m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0));
+    m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0));
     if(computeEigenvectors)
       m_eivec.setOnes(n,n);
     m_info = Success;
@@ -490,7 +497,12 @@ 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;
   
+  /** \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;
@@ -510,39 +522,48 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
     // Construct the parameters used in classifying the roots of the equation
     // and in solving the equation for the roots in closed form.
     Scalar c2_over_3 = c2*s_inv3;
-    Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3;
+    Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;
-    if (a_over_3 > Scalar(0))
+    if(a_over_3<Scalar(0))
       a_over_3 = Scalar(0);
 
     Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
 
-    Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3;
+    Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
-    if (q > Scalar(0))
+    if(q<Scalar(0))
       q = Scalar(0);
 
     // Compute the eigenvalues by solving for the roots of the polynomial.
-    Scalar rho = sqrt(-a_over_3);
+    Scalar rho = sqrt(a_over_3);
-    Scalar theta = atan2(sqrt(-q),half_b)*s_inv3;
+    Scalar theta = atan2(sqrt(q),half_b)*s_inv3;  // since sqrt(q) > 0, atan2 is in [0, pi] and theta is in [0, pi/3]
     Scalar cos_theta = cos(theta);
     Scalar sin_theta = sin(theta);
-    roots(0) = c2_over_3 + Scalar(2)*rho*cos_theta;
+    // roots are already sorted, since cos is monotonically decreasing on [0, pi]
-    roots(1) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
+    roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)
-    roots(2) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);
+    roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); // == 2*rho*cos(theta+ pi/3)
-
+    roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;
-    // Sort in increasing order.
-    if (roots(0) >= roots(1))
-      std::swap(roots(0),roots(1));
-    if (roots(1) >= roots(2))
-    {
-      std::swap(roots(1),roots(2));
-      if (roots(0) >= roots(1))
-        std::swap(roots(0),roots(1));
-    }
   }
-  
+
+  static inline bool extract_kernel(MatrixType& mat, Ref<VectorType> res, Ref<VectorType> representative)
+  {
+    using std::abs;
+    Index i0;
+    // Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):
+    mat.diagonal().cwiseAbs().maxCoeff(&i0);
+    // mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,
+    // so let's save it:
+    representative = mat.col(i0);
+    Scalar n0, n1;
+    VectorType c0, c1;
+    n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();
+    n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();
+    if(n0>n1) res = c0/std::sqrt(n0);
+    else      res = c1/std::sqrt(n1);
+
+    return true;
+  }
+
   static inline void run(SolverType& solver, const MatrixType& mat, int options)
   {
-    using std::sqrt;
     eigen_assert(mat.cols() == 3 && mat.cols() == mat.rows());
     eigen_assert((options&~(EigVecMask|GenEigMask))==0
             && (options&EigVecMask)!=EigVecMask
@@ -552,106 +573,72 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
     MatrixType& eivecs = solver.m_eivec;
     VectorType& eivals = solver.m_eivalues;
   
-    // map the matrix coefficients to [-1:1] to avoid over- and underflow.
+    // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
-    Scalar scale = mat.cwiseAbs().maxCoeff();
+    Scalar shift = mat.trace() / Scalar(3);
-    MatrixType scaledMat = mat / scale;
+    // TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later
+    MatrixType scaledMat = mat.template selfadjointView<Lower>();
+    scaledMat.diagonal().array() -= shift;
+    Scalar scale = scaledMat.cwiseAbs().maxCoeff();
+    if(scale > 0) scaledMat /= scale;   // TODO for scale==0 we could save the remaining operations
 
     // compute the eigenvalues
     computeRoots(scaledMat,eivals);
 
-    // compute the eigen vectors
+    // compute the eigenvectors
     if(computeEigenvectors)
     {
-      Scalar safeNorm2 = Eigen::NumTraits<Scalar>::epsilon();
-      safeNorm2 *= safeNorm2;
       if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
       {
+        // All three eigenvalues are numerically the same
         eivecs.setIdentity();
       }
       else
       {
-        scaledMat = scaledMat.template selfadjointView<Lower>();
         MatrixType tmp;
         tmp = scaledMat;
 
+        // Compute the eigenvector of the most distinct eigenvalue
         Scalar d0 = eivals(2) - eivals(1);
         Scalar d1 = eivals(1) - eivals(0);
-        int k =  d0 > d1 ? 2 : 0;
+        Index k(0), l(2);
-        d0 = d0 > d1 ? d1 : d0;
+        if(d0 > d1)
-
-        tmp.diagonal().array () -= eivals(k);
-        VectorType cross;
-        Scalar n;
-        n = (cross = tmp.row(0).cross(tmp.row(1))).squaredNorm();
-
-        if(n>safeNorm2)
-          eivecs.col(k) = cross / sqrt(n);
-        else
         {
-          n = (cross = tmp.row(0).cross(tmp.row(2))).squaredNorm();
+          std::swap(k,l);
-
+          d0 = d1;
-          if(n>safeNorm2)
-            eivecs.col(k) = cross / sqrt(n);
-          else
-          {
-            n = (cross = tmp.row(1).cross(tmp.row(2))).squaredNorm();
-
-            if(n>safeNorm2)
-              eivecs.col(k) = cross / sqrt(n);
-            else
-            {
-              // the input matrix and/or the eigenvaues probably contains some inf/NaN,
-              // => exit
-              // scale back to the original size.
-              eivals *= scale;
-
-              solver.m_info = NumericalIssue;
-              solver.m_isInitialized = true;
-              solver.m_eigenvectorsOk = computeEigenvectors;
-              return;
-            }
-          }
         }
 
-        tmp = scaledMat;
+        // Compute the eigenvector of index k
-        tmp.diagonal().array() -= eivals(1);
-
-        if(d0<=Eigen::NumTraits<Scalar>::epsilon())
-          eivecs.col(1) = eivecs.col(k).unitOrthogonal();
-        else
         {
-          n = (cross = eivecs.col(k).cross(tmp.row(0).normalized())).squaredNorm();
+          tmp.diagonal().array () -= eivals(k);
-          if(n>safeNorm2)
+          // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.
-            eivecs.col(1) = cross / sqrt(n);
+          extract_kernel(tmp, eivecs.col(k), eivecs.col(l));
-          else
-          {
-            n = (cross = eivecs.col(k).cross(tmp.row(1))).squaredNorm();
-            if(n>safeNorm2)
-              eivecs.col(1) = cross / sqrt(n);
-            else
-            {
-              n = (cross = eivecs.col(k).cross(tmp.row(2))).squaredNorm();
-              if(n>safeNorm2)
-                eivecs.col(1) = cross / sqrt(n);
-              else
-              {
-                // we should never reach this point,
-                // if so the last two eigenvalues are likely to ve very closed to each other
-                eivecs.col(1) = eivecs.col(k).unitOrthogonal();
-              }
-            }
-          }
-
-          // make sure that eivecs[1] is orthogonal to eivecs[2]
-          Scalar d = eivecs.col(1).dot(eivecs.col(k));
-          eivecs.col(1) = (eivecs.col(1) - d * eivecs.col(k)).normalized();
         }
 
-        eivecs.col(k==2 ? 0 : 2) = eivecs.col(k).cross(eivecs.col(1)).normalized();
+        // Compute eigenvector of index l
+        if(d0<=2*Eigen::NumTraits<Scalar>::epsilon()*d1)
+        {
+          // If d0 is too small, then the two other eigenvalues are numerically the same,
+          // and thus we only have to ortho-normalize the near orthogonal vector we saved above.
+          eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);
+          eivecs.col(l).normalize();
+        }
+        else
+        {
+          tmp = scaledMat;
+          tmp.diagonal().array () -= eivals(l);
+
+          VectorType dummy;
+          extract_kernel(tmp, eivecs.col(l), dummy);
+        }
+
+        // Compute last eigenvector from the other two
+        eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();
       }
     }
+
     // Rescale back to the original size.
     eivals *= scale;
+    eivals.array() += shift;
     
     solver.m_info = Success;
     solver.m_isInitialized = true;
@@ -669,7 +656,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
   static inline void computeRoots(const MatrixType& m, VectorType& roots)
   {
     using std::sqrt;
-    const Scalar t0 = Scalar(0.5) * sqrt( 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;
@@ -678,6 +665,8 @@ 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
@@ -698,22 +687,29 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
     // compute the eigen vectors
     if(computeEigenvectors)
     {
-      scaledMat.diagonal().array () -= eivals(1);
+      if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())
-      Scalar a2 = abs2(scaledMat(0,0));
-      Scalar c2 = abs2(scaledMat(1,1));
-      Scalar b2 = abs2(scaledMat(1,0));
-      if(a2>c2)
       {
-        eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+        eivecs.setIdentity();
-        eivecs.col(1) /= sqrt(a2+b2);
       }
       else
       {
-        eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+        scaledMat.diagonal().array () -= eivals(1);
-        eivecs.col(1) /= sqrt(c2+b2);
+        Scalar a2 = numext::abs2(scaledMat(0,0));
-      }
+        Scalar c2 = numext::abs2(scaledMat(1,1));
+        Scalar b2 = numext::abs2(scaledMat(1,0));
+        if(a2>c2)
+        {
+          eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+          eivecs.col(1) /= sqrt(a2+b2);
+        }
+        else
+        {
+          eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+          eivecs.col(1) /= sqrt(c2+b2);
+        }
 
-      eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+        eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+      }
     }
     
     // Rescale back to the original size.
@@ -744,7 +740,7 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
   RealScalar e = subdiag[end-1];
   // Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
   // underflow thus leading to inf/NaN values when using the following commented code:
-//   RealScalar e2 = abs2(subdiag[end-1]);
+//   RealScalar e2 = numext::abs2(subdiag[end-1]);
 //   RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
   // This explain the following, somewhat more complicated, version:
   RealScalar mu = diag[end];
@@ -752,8 +748,8 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
     mu -= abs(e);
   else
   {
-    RealScalar e2 = abs2(subdiag[end-1]);
+    RealScalar e2 = numext::abs2(subdiag[end-1]);
-    RealScalar h = hypot(td,e);
+    RealScalar h = numext::hypot(td,e);
     if(e2==0)  mu -= (e / (td + (td>0 ? 1 : -1))) * (e / h);
     else       mu -= e2 / (td + (td>0 ? h : -h));
   }

Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h

@@ -56,7 +56,7 @@ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(c
 \
   if(n==1) \
   { \
-    m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0)); \
+    m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0)); \
     if(computeEigenvectors) m_eivec.setOnes(n,n); \
     m_info = Success; \
     m_isInitialized = true; \

Eigen/src/Eigenvalues/Tridiagonalization.h

@@ -96,7 +96,7 @@ template<typename _MatrixType> class Tridiagonalization
             >::type SubDiagonalReturnType;
 
     /** \brief Return type of matrixQ() */
-    typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
 
     /** \brief Default constructor.
       *
@@ -345,7 +345,7 @@ namespace internal {
 template<typename MatrixType, typename CoeffVectorType>
 void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
 {
-  using internal::conj;
+  using numext::conj;
   typedef typename MatrixType::Index Index;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::RealScalar RealScalar;
@@ -426,8 +426,6 @@ struct tridiagonalization_inplace_selector;
 template<typename MatrixType, typename DiagonalType, typename SubDiagonalType>
 void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
 {
-  typedef typename MatrixType::Index Index;
-  //Index n = mat.rows();
   eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);
   tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);
 }
@@ -470,7 +468,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
   {
     using std::sqrt;
     diag[0] = mat(0,0);
-    RealScalar v1norm2 = abs2(mat(2,0));
+    RealScalar v1norm2 = numext::abs2(mat(2,0));
     if(v1norm2 == RealScalar(0))
     {
       diag[1] = mat(1,1);
@@ -482,7 +480,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
     }
     else
     {
-      RealScalar beta = sqrt(abs2(mat(1,0)) + v1norm2);
+      RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
       RealScalar invBeta = RealScalar(1)/beta;
       Scalar m01 = mat(1,0) * invBeta;
       Scalar m02 = mat(2,0) * invBeta;
@@ -512,7 +510,7 @@ struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
   template<typename DiagonalType, typename SubDiagonalType>
   static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
   {
-    diag(0,0) = real(mat(0,0));
+    diag(0,0) = numext::real(mat(0,0));
     if(extractQ)
       mat(0,0) = Scalar(1);
   }

Eigen/src/Geometry/AlignedBox.h

@@ -19,10 +19,12 @@ namespace Eigen {
   *
   * \brief An axis aligned box
   *
-  * \param _Scalar the type of the scalar coefficients
+  * \tparam _Scalar the type of the scalar coefficients
-  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
   *
   * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+  * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
+  * \sa alignedboxtypedefs
   */
 template <typename _Scalar, int _AmbientDim>
 class AlignedBox
@@ -40,57 +42,59 @@ 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
+    /** @} */
   };
 
 
   /** Default constructor initializing a null box. */
-  inline explicit AlignedBox()
+  inline AlignedBox()
   { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
 
   /** Constructs a null box with \a _dim the dimension of the ambient space. */
   inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
   { setEmpty(); }
 
-  /** Constructs a box with extremities \a _min and \a _max. */
+  /** Constructs a box with extremities \a _min and \a _max.
+   * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
   template<typename OtherVectorType1, typename OtherVectorType2>
   inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
 
   /** Constructs a box containing a single point \a p. */
   template<typename Derived>
-  inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
+  inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
-  {
+  { }
-    typename internal::nested<Derived,2>::type p(a_p.derived());
-    m_min = p;
-    m_max = p;
-  }
 
   ~AlignedBox() {}
 
   /** \returns the dimension in which the box holds */
   inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
 
-  /** \deprecated use isEmpty */
+  /** \deprecated use isEmpty() */
   inline bool isNull() const { return isEmpty(); }
 
-  /** \deprecated use setEmpty */
+  /** \deprecated use setEmpty() */
   inline void setNull() { setEmpty(); }
 
-  /** \returns true if the box is empty. */
+  /** \returns true if the box is empty.
+   * \sa setEmpty */
   inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
 
-  /** Makes \c *this an empty box. */
+  /** Makes \c *this an empty box.
+   * \sa isEmpty */
   inline void setEmpty()
   {
     m_min.setConstant( ScalarTraits::highest() );
@@ -175,27 +179,34 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns true if the point \a p is inside the box \c *this. */
   template<typename Derived>
-  inline bool contains(const MatrixBase<Derived>& a_p) const
+  inline bool contains(const MatrixBase<Derived>& p) const
   {
-    typename internal::nested<Derived,2>::type p(a_p.derived());
+    typename internal::nested<Derived,2>::type p_n(p.derived());
-    return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
+    return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
   }
 
   /** \returns true if the box \a b is entirely inside the box \c *this. */
   inline bool contains(const AlignedBox& b) const
   { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
 
-  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
+  /** \returns true if the box \a b is intersecting the box \c *this.
+   * \sa intersection, clamp */
+  inline bool intersects(const AlignedBox& b) const
+  { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
+
+  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
+   * \sa extend(const AlignedBox&) */
   template<typename Derived>
-  inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
+  inline AlignedBox& extend(const MatrixBase<Derived>& p)
   {
-    typename internal::nested<Derived,2>::type p(a_p.derived());
+    typename internal::nested<Derived,2>::type p_n(p.derived());
-    m_min = m_min.cwiseMin(p);
+    m_min = m_min.cwiseMin(p_n);
-    m_max = m_max.cwiseMax(p);
+    m_max = m_max.cwiseMax(p_n);
     return *this;
   }
 
-  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
+  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
+   * \sa merged, extend(const MatrixBase&) */
   inline AlignedBox& extend(const AlignedBox& b)
   {
     m_min = m_min.cwiseMin(b.m_min);
@@ -203,7 +214,9 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     return *this;
   }
 
-  /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
+  /** Clamps \c *this by the box \a b and returns a reference to \c *this.
+   * \note If the boxes don't intersect, the resulting box is empty.
+   * \sa intersection(), intersects() */
   inline AlignedBox& clamp(const AlignedBox& b)
   {
     m_min = m_min.cwiseMax(b.m_min);
@@ -211,11 +224,15 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     return *this;
   }
 
-  /** Returns an AlignedBox that is the intersection of \a b and \c *this */
+  /** Returns an AlignedBox that is the intersection of \a b and \c *this
+   * \note If the boxes don't intersect, the resulting box is empty.
+   * \sa intersects(), clamp, contains()  */
   inline AlignedBox intersection(const AlignedBox& b) const
   {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
 
-  /** Returns an AlignedBox that is the union of \a b and \c *this */
+  /** Returns an AlignedBox that is the union of \a b and \c *this.
+   * \note Merging with an empty box may result in a box bigger than \c *this. 
+   * \sa extend(const AlignedBox&) */
   inline AlignedBox merged(const AlignedBox& b) const
   { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
 
@@ -231,20 +248,20 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns the squared distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
-    * \sa exteriorDistance()
+    * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
     */
   template<typename Derived>
-  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;
+  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
 
   /** \returns the squared distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
-    * \sa exteriorDistance()
+    * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
     */
   inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
 
   /** \returns the distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
-    * \sa squaredExteriorDistance()
+    * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
     */
   template<typename Derived>
   inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
@@ -252,7 +269,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns the distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
-    * \sa squaredExteriorDistance()
+    * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
     */
   inline NonInteger exteriorDistance(const AlignedBox& b) const
   { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }

Eigen/src/Geometry/EulerAngles.h

@@ -27,56 +27,75 @@ namespace Eigen {
   *      * AngleAxisf(ea[1], Vector3f::UnitX())
   *      * 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[-pi:pi]x[-pi:pi].
+  * 
+  * \sa class AngleAxis
   */
 template<typename Derived>
 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
 MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
 {
   using std::atan2;
+  using std::sin;
+  using std::cos;
   /* Implemented from Graphics Gems IV */
   EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
 
   Matrix<Scalar,3,1> res;
   typedef Matrix<typename Derived::Scalar,2,1> Vector2;
-  const Scalar epsilon = NumTraits<Scalar>::dummy_precision();
 
   const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
   const Index i = a0;
   const Index j = (a0 + 1 + odd)%3;
   const Index k = (a0 + 2 - odd)%3;
-
+  
   if (a0==a2)
   {
-    Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
+    res[0] = atan2(coeff(j,i), coeff(k,i));
-    res[1] = atan2(s, coeff(i,i));
+    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
-    if (s > epsilon)
     {
-      res[0] = atan2(coeff(j,i), coeff(k,i));
+      res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
-      res[2] = atan2(coeff(i,j),-coeff(i,k));
+      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+      res[1] = -atan2(s2, coeff(i,i));
     }
     else
     {
-      res[0] = Scalar(0);
+      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
-      res[2] = (coeff(i,i)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
+      res[1] = atan2(s2, coeff(i,i));
     }
-  }
+    
+    // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
+    // we can compute their respective rotation, and apply its inverse to M. Since the result must
+    // be a rotation around x, we have:
+    //
+    //  c2  s1.s2 c1.s2                   1  0   0 
+    //  0   c1    -s1       *    M    =   0  c3  s3
+    //  -s2 s1.c2 c1.c2                   0 -s3  c3
+    //
+    //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3
+    
+    Scalar s1 = sin(res[0]);
+    Scalar c1 = cos(res[0]);
+    res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
+  } 
   else
   {
-    Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
+    res[0] = atan2(coeff(j,k), coeff(k,k));
-    res[1] = atan2(-coeff(i,k), c);
+    Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
-    if (c > epsilon)
+    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
-    {
+      res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
-      res[0] = atan2(coeff(j,k), coeff(k,k));
+      res[1] = atan2(-coeff(i,k), -c2);
-      res[2] = atan2(coeff(i,j), coeff(i,i));
     }
     else
-    {
+      res[1] = atan2(-coeff(i,k), c2);
-      res[0] = Scalar(0);
+    Scalar s1 = sin(res[0]);
-      res[2] = (coeff(i,k)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
+    Scalar c1 = cos(res[0]);
-    }
+    res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
   }
   if (!odd)
     res = -res;
+  
   return res;
 }