Get docs to build

(Nov 10th, 2009)

.gitignore

@@ -0,0 +1,41 @@
+qrc_*cxx
+*.orig
+*.pyc
+*.diff
+diff
+*.save
+save
+*.old
+*.gmo
+*.qm
+core
+core.*
+*.bak
+*~
+*.build*
+*.moc.*
+*.moc
+ui_*
+CMakeCache.txt
+tags
+.*.swp
+activity.png
+*.out
+*.php*
+*.log
+*.orig
+*.rej
+log
+patch
+*.patch
+a
+a.*
+lapack/testing
+lapack/reference
+.*project
+.settings
+Makefile
+!ci/build.gitlab-ci.yml
+!scripts/buildtests.in
+!Eigen/Core
+!Eigen/src/Core

.gitlab-ci.yml

@@ -0,0 +1,28 @@
+# This file is part of Eigen, a lightweight C++ template library
+# for linear algebra.
+#
+# Copyright (C) 2023, The Eigen Authors
+#
+# 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/.
+
+stages:
+  - build
+  - deploy
+
+variables:
+  # CMake build directory.
+  EIGEN_CI_BUILDDIR: .build
+  # Specify the CMake build target.
+  EIGEN_CI_BUILD_TARGET: ""
+  # If a test regex is specified, that will be selected.
+  # Otherwise, we will try a label if specified.
+  EIGEN_CI_CTEST_REGEX: ""
+  EIGEN_CI_CTEST_LABEL: ""
+  EIGEN_CI_CTEST_ARGS: ""
+
+include:
+  - "/ci/common.gitlab-ci.yml"
+  - "/ci/build.linux.gitlab-ci.yml"
+  - "/ci/deploy.gitlab-ci.yml"

.hgeol

@@ -0,0 +1,3 @@
+[patterns]
+**.* = native
+eigen_autoexp_part.dat = CRLF

.hgignore

@@ -0,0 +1,32 @@
+syntax: glob
+qrc_*cxx
+*.orig
+*.pyc
+*.diff
+diff
+*.save
+save
+*.old
+*.gmo
+*.qm
+core
+core.*
+*.bak
+*~
+build*
+*.moc.*
+*.moc
+ui_*
+CMakeCache.txt
+tags
+.*.swp
+activity.png
+*.out
+*.php*
+*.log
+*.orig
+*.rej
+log
+patch
+a
+a.*

.krazy

@@ -0,0 +1,3 @@
+SKIP /disabled/
+SKIP /bench/
+SKIP /build/

CMakeLists.txt

@@ -1,18 +1,405 @@
 project(Eigen)
 
-OPTION(BUILD_TESTS "Build tests"  OFF)
-OPTION(BUILD_EXAMPLES "Build examples"  OFF)
+cmake_minimum_required(VERSION 2.6.2)
+
+# guard against in-source builds
+
+if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR})
+  message(FATAL_ERROR "In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. ")
+endif()
+
+# guard against bad build-type strings
+
+if (NOT CMAKE_BUILD_TYPE)
+  set(CMAKE_BUILD_TYPE "Release")
+endif()
+
+string(TOLOWER "${CMAKE_BUILD_TYPE}" cmake_build_type_tolower)
+if(    NOT cmake_build_type_tolower STREQUAL "debug"
+   AND NOT cmake_build_type_tolower STREQUAL "release"
+   AND NOT cmake_build_type_tolower STREQUAL "relwithdebinfo")
+  message(FATAL_ERROR "Unknown build type \"${CMAKE_BUILD_TYPE}\". Allowed values are Debug, Release, RelWithDebInfo (case-insensitive).")
+endif()
+
+
+#############################################################################
+# retrieve version infomation                                               #
+#############################################################################
+
+# automatically parse the version number
+file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header)
+string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
+set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
+string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
+set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
+string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
+set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
+set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})
+
+# if the mercurial program is absent, this will leave the EIGEN_HG_CHANGESET string empty,
+# but won't stop CMake.
+execute_process(COMMAND hg tip -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_HGTIP_OUTPUT)
+execute_process(COMMAND hg branch -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_BRANCH_OUTPUT)
+
+# if this is the default (aka development) branch, extract the mercurial changeset number from the hg tip output...
+if(EIGEN_BRANCH_OUTPUT MATCHES "default")
+string(REGEX MATCH "^changeset: *[0-9]*:([0-9;a-f]+).*" EIGEN_HG_CHANGESET_MATCH "${EIGEN_HGTIP_OUTPUT}")
+set(EIGEN_HG_CHANGESET "${CMAKE_MATCH_1}")
+endif(EIGEN_BRANCH_OUTPUT MATCHES "default")
+#...and show it next to the version number
+if(EIGEN_HG_CHANGESET)
+  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (mercurial changeset ${EIGEN_HG_CHANGESET})")
+else(EIGEN_HG_CHANGESET)
+  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
+endif(EIGEN_HG_CHANGESET)
+
+
+include(CheckCXXCompilerFlag)
+
+set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
+
+#############################################################################
+# find how to link to the standard libraries                                #
+#############################################################################
+
+find_package(StandardMathLibrary)
+
+set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
+
+if(NOT STANDARD_MATH_LIBRARY_FOUND)
+
+  message(FATAL_ERROR
+    "Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
+
+else()
+
+  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+    set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}")
+  else()
+    set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}")
+  endif()
+
+endif()
+
+if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+  message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}")
+else()
+  message(STATUS "Standard libraries to link to explicitly: none")
+endif()
+
+option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
+if(NOT WIN32)
+  option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON)
+endif(NOT WIN32)
 
 set(CMAKE_INCLUDE_CURRENT_DIR ON)
 
+option(EIGEN_SPLIT_LARGE_TESTS "Split large tests into smaller executables" ON)
+
+option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF)
+if(EIGEN_DEFAULT_TO_ROW_MAJOR)
+  add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR")
+endif()
+
+add_definitions("-DEIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS")
+
 if(CMAKE_COMPILER_IS_GNUCXX)
-   if (CMAKE_SYSTEM_NAME MATCHES Linux)
-     set ( CMAKE_C_FLAGS     "${CMAKE_C_FLAGS} -Wno-long-long -ansi -Wundef -Wcast-align -Werror-implicit-function-declaration -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -Wmissing-format-attribute -fno-common")
-     set ( CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wnon-virtual-dtor -Wno-long-long -ansi -Wundef -Wcast-align -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -fno-exceptions -fno-check-new -fno-common")
-   endif (CMAKE_SYSTEM_NAME MATCHES Linux)
-endif (CMAKE_COMPILER_IS_GNUCXX)
+  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")
+  set(CMAKE_CXX_FLAGS_DEBUG "-g3")
+  set(CMAKE_CXX_FLAGS_RELEASE "-g0 -O2")
 
-include_directories( ${CMAKE_SOURCE_DIR} ${CMAKE_BINARY_DIR} )
+  check_cxx_compiler_flag("-Wno-variadic-macros" COMPILER_SUPPORT_WNOVARIADICMACRO)
+  if(COMPILER_SUPPORT_WNOVARIADICMACRO)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-variadic-macros")
+  endif()
 
-add_subdirectory(src)
-add_subdirectory(test)
+  check_cxx_compiler_flag("-Wextra" COMPILER_SUPPORT_WEXTRA)
+  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)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2")
+    message(STATUS "Enabling SSE2 in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF)
+  if(EIGEN_TEST_SSE3)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3")
+    message(STATUS "Enabling SSE3 in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF)
+  if(EIGEN_TEST_SSSE3)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3")
+    message(STATUS "Enabling SSSE3 in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_SSE4_1 "Enable/Disable SSE4.1 in tests/examples" OFF)
+  if(EIGEN_TEST_SSE4_1)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.1")
+    message(STATUS "Enabling SSE4.1 in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_SSE4_2 "Enable/Disable SSE4.2 in tests/examples" OFF)
+  if(EIGEN_TEST_SSE4_2)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.2")
+    message(STATUS "Enabling SSE4.2 in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_ALTIVEC "Enable/Disable AltiVec in tests/examples" OFF)
+  if(EIGEN_TEST_ALTIVEC)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec")
+    message(STATUS "Enabling AltiVec in tests/examples")
+  endif()
+
+  option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
+  if(EIGEN_TEST_NEON)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=softfp -mfpu=neon -mcpu=cortex-a8")
+    message(STATUS "Enabling NEON in tests/examples")
+  endif()
+
+  check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP)
+  if(COMPILER_SUPPORT_OPENMP)
+    option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
+    if(EIGEN_TEST_OPENMP)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
+      message(STATUS "Enabling OpenMP in tests/examples")
+    endif()
+  endif()
+
+endif(CMAKE_COMPILER_IS_GNUCXX)
+
+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
+  #         because we are oftentimes returning objects that have a destructor or may
+  #         throw exceptions - in particular in the unit tests we are throwing extra many
+  #         exceptions to cover indexing errors.
+  # C4505 - unreferenced local function has been removed (impossible to deactive selectively)
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714")
+
+  # replace all /Wx by /W4
+  string(REGEX REPLACE "/W[0-9]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+
+  check_cxx_compiler_flag("/openmp" COMPILER_SUPPORT_OPENMP)
+  if(COMPILER_SUPPORT_OPENMP)
+    option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
+    if(EIGEN_TEST_OPENMP)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /openmp")
+      message(STATUS "Enabling OpenMP in tests/examples")
+    endif()
+  endif()
+
+  option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
+  if(EIGEN_TEST_SSE2)
+    if(NOT CMAKE_CL_64)
+      # arch is not supported on 64 bit systems, SSE is enabled automatically.
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
+    endif(NOT CMAKE_CL_64)
+    message(STATUS "Enabling SSE2 in tests/examples")
+  endif(EIGEN_TEST_SSE2)
+endif(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)
+option(EIGEN_TEST_32BIT "Force generating 32bit code." OFF)
+
+if(EIGEN_TEST_X87)
+  set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON)
+  if(CMAKE_COMPILER_IS_GNUCXX)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpmath=387")
+    message(STATUS "Forcing use of x87 instructions in tests/examples")
+  else()
+    message(STATUS "EIGEN_TEST_X87 ignored on your compiler")
+  endif()
+endif()
+
+if(EIGEN_TEST_32BIT)
+  if(CMAKE_COMPILER_IS_GNUCXX)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m32")
+    message(STATUS "Forcing generation of 32-bit code in tests/examples")
+  else()
+    message(STATUS "EIGEN_TEST_32BIT ignored on your compiler")
+  endif()
+endif()
+
+if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
+  add_definitions(-DEIGEN_DONT_VECTORIZE=1)
+  message(STATUS "Disabling vectorization in tests/examples")
+endif()
+
+option(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT "Disable explicit alignment (hence vectorization) in tests/examples" OFF)
+if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)
+  add_definitions(-DEIGEN_DONT_ALIGN=1)
+  message(STATUS "Disabling alignment in tests/examples")
+endif()
+
+option(EIGEN_TEST_C++0x "Enables all C++0x features." OFF)
+
+include_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})
+
+# the user modifiable install path for header files
+set(EIGEN_INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR} CACHE PATH "The directory where we install the header files (optional)")
+
+# set the internal install path for header files which depends on wether the user modifiable
+# EIGEN_INCLUDE_INSTALL_DIR has been set by the user or not.
+if(EIGEN_INCLUDE_INSTALL_DIR)
+  set(INCLUDE_INSTALL_DIR
+    ${EIGEN_INCLUDE_INSTALL_DIR}
+    CACHE INTERNAL
+    "The directory where we install the header files (internal)"
+  )
+else()
+  set(INCLUDE_INSTALL_DIR
+    "${CMAKE_INSTALL_PREFIX}/include/eigen3"
+    CACHE INTERNAL
+    "The directory where we install the header files (internal)"
+  )
+endif()
+
+# similar to set_target_properties but append the property instead of overwriting it
+macro(ei_add_target_property target prop value)
+
+  get_target_property(previous ${target} ${prop})
+  # if the property wasn't previously set, ${previous} is now "previous-NOTFOUND" which cmake allows catching with plain if()
+  if(NOT previous)
+    set(previous "")
+  endif(NOT previous)
+  set_target_properties(${target} PROPERTIES ${prop} "${previous} ${value}")
+endmacro(ei_add_target_property)
+
+install(FILES
+  signature_of_eigen3_matrix_library
+  DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel
+  )
+
+if(EIGEN_BUILD_PKGCONFIG)
+    SET(path_separator ":")
+    STRING(REPLACE ${path_separator} ";" pkg_config_libdir_search "$ENV{PKG_CONFIG_LIBDIR}")
+    message(STATUS "searching for 'pkgconfig' directory in PKG_CONFIG_LIBDIR ( $ENV{PKG_CONFIG_LIBDIR} ), ${CMAKE_INSTALL_PREFIX}/share, and ${CMAKE_INSTALL_PREFIX}/lib")
+    FIND_PATH(pkg_config_libdir pkgconfig ${pkg_config_libdir_search} ${CMAKE_INSTALL_PREFIX}/share ${CMAKE_INSTALL_PREFIX}/lib ${pkg_config_libdir_search})
+    if(pkg_config_libdir)
+        SET(pkg_config_install_dir ${pkg_config_libdir})
+        message(STATUS "found ${pkg_config_libdir}/pkgconfig" )
+    else(pkg_config_libdir)
+        SET(pkg_config_install_dir ${CMAKE_INSTALL_PREFIX}/share)
+        message(STATUS "pkgconfig not found; installing in ${pkg_config_install_dir}" )
+    endif(pkg_config_libdir)
+
+    configure_file(eigen3.pc.in eigen3.pc)
+    install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
+        DESTINATION ${pkg_config_install_dir}/pkgconfig
+        )
+endif(EIGEN_BUILD_PKGCONFIG)
+
+add_subdirectory(Eigen)
+
+add_subdirectory(doc EXCLUDE_FROM_ALL)
+
+add_custom_target(buildtests)
+add_custom_target(check COMMAND "ctest")
+add_dependencies(check buildtests)
+
+# CMake/Ctest does not allow us to change the build command,
+# so we have to workaround by directly editing the generated DartConfiguration.tcl file
+# save CMAKE_MAKE_PROGRAM
+set(CMAKE_MAKE_PROGRAM_SAVE ${CMAKE_MAKE_PROGRAM})
+# and set a fake one
+set(CMAKE_MAKE_PROGRAM "@EIGEN_MAKECOMMAND_PLACEHOLDER@")
+
+include(CTest)
+enable_testing() # must be called from the root CMakeLists, see man page
+include(EigenTesting)
+ei_init_testing()
+
+# overwrite default DartConfiguration.tcl
+# The worarounds are different for each version of the MSVC IDE
+if(MSVC_IDE)
+  if(MSVC_VERSION EQUAL 1600) # MSVC 2010
+    set(EIGEN_MAKECOMMAND_PLACEHOLDER "${CMAKE_MAKE_PROGRAM_SAVE} buildtests.vcxproj /p:Configuration=\${CTEST_CONFIGURATION_TYPE} \n # ")
+  else() # MSVC 2008 (TODO check MSVC 2005)
+    set(EIGEN_MAKECOMMAND_PLACEHOLDER "${CMAKE_MAKE_PROGRAM_SAVE} /project buildtests")
+  endif()
+else()
+  # for make and nmake
+  set(EIGEN_MAKECOMMAND_PLACEHOLDER "${CMAKE_MAKE_PROGRAM_SAVE} buildtests")
+endif()
+
+configure_file(${CMAKE_BINARY_DIR}/DartConfiguration.tcl ${CMAKE_BINARY_DIR}/DartConfiguration.tcl)
+# restore default CMAKE_MAKE_PROGRAM
+set(CMAKE_MAKE_PROGRAM ${CMAKE_MAKE_PROGRAM_SAVE})
+# un-set temporary variables so that it is like they never existed.
+# CMake 2.6.3 introduces the more logical unset() syntax for this.
+set(CMAKE_MAKE_PROGRAM_SAVE)
+set(EIGEN_MAKECOMMAND_PLACEHOLDER)
+
+configure_file(${CMAKE_SOURCE_DIR}/CTestCustom.cmake.in ${CMAKE_BINARY_DIR}/CTestCustom.cmake)
+
+
+if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+  add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
+else()
+  add_subdirectory(test EXCLUDE_FROM_ALL)
+endif()
+
+if(NOT MSVC)
+  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+    add_subdirectory(blas)
+    add_subdirectory(lapack)
+  else()
+    add_subdirectory(blas EXCLUDE_FROM_ALL)
+    add_subdirectory(lapack EXCLUDE_FROM_ALL)
+  endif()
+endif(NOT MSVC)
+
+add_subdirectory(unsupported)
+
+add_subdirectory(demos EXCLUDE_FROM_ALL)
+
+# must be after test and unsupported, for configuring buildtests.in
+add_subdirectory(scripts EXCLUDE_FROM_ALL)
+
+# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target "make btl"?
+if(EIGEN_BUILD_BTL)
+  add_subdirectory(bench/btl EXCLUDE_FROM_ALL)
+endif(EIGEN_BUILD_BTL)
+
+ei_testing_print_summary()
+
+message(STATUS "")
+message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
+message(STATUS "")
+
+option(EIGEN_FAILTEST "Enable failtests." OFF)
+if(EIGEN_FAILTEST)
+  add_subdirectory(failtest)
+endif()
+
+string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower)
+if(cmake_generator_tolower MATCHES "makefile")
+  message(STATUS "Some things you can do now:")
+  message(STATUS "--------------+--------------------------------------------------------------")
+  message(STATUS "Command       |   Description")
+  message(STATUS "--------------+--------------------------------------------------------------")
+  message(STATUS "make install  | Install to ${CMAKE_INSTALL_PREFIX}. To change that:")
+  message(STATUS "              |     cmake . -DCMAKE_INSTALL_PREFIX=yourpath")
+  message(STATUS "              |   Eigen headers will then be installed to:")
+  message(STATUS "              |     ${INCLUDE_INSTALL_DIR}")
+  message(STATUS "              |   To install Eigen headers to a separate location, do:")
+  message(STATUS "              |     cmake . -DEIGEN_INCLUDE_INSTALL_DIR=yourpath")
+  message(STATUS "make doc      | Generate the API documentation, requires Doxygen & LaTeX")
+  message(STATUS "make check    | Build and run the unit-tests. Read this page:")
+  message(STATUS "              |   http://eigen.tuxfamily.org/index.php?title=Tests")
+  message(STATUS "make blas     | Build BLAS library (not the same thing as Eigen)")
+  message(STATUS "--------------+--------------------------------------------------------------")
+else()
+  message(STATUS "To build/run the unit tests, read this page:")
+  message(STATUS "  http://eigen.tuxfamily.org/index.php?title=Tests")
+endif()
+
+message(STATUS "")

COPYING.GPL

@@ -0,0 +1,674 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+the GNU General Public License is intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.  We, the Free Software Foundation, use the
+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors.  You can apply it to
+your programs, too.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights.  Therefore, you have
+certain responsibilities if you distribute copies of the software, or if
+you modify it: responsibilities to respect the freedom of others.
+
+  For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must pass on to the recipients the same
+freedoms that you received.  You must make sure that they, too, receive
+or can get the source code.  And you must show them these terms so they
+know their rights.
+
+  Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+  For the developers' and authors' protection, the GPL clearly explains
+that there is no warranty for this free software.  For both users' and
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+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

COPYING.LGPL

@@ -0,0 +1,165 @@
+                  GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions. 
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
+engineering for debugging such modifications, if you also do each of
+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
+   execution, include the copyright notice for the Library among
+   these notices, as well as a reference directing the user to the
+   copies of the GNU GPL and this license document.
+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
+       License, and the Corresponding Application Code in a form
+       suitable for, and under terms that permit, the user to
+       recombine or relink the Application with a modified version of
+       the Linked Version to produce a modified Combined Work, in the
+       manner specified by section 6 of the GNU GPL for conveying
+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
+       Version. 
+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.

CTestConfig.cmake

@@ -0,0 +1,13 @@
+## This file should be placed in the root directory of your project.
+## Then modify the CMakeLists.txt file in the root directory of your
+## project to incorporate the testing dashboard.
+## # The following are required to uses Dart and the Cdash dashboard
+##   ENABLE_TESTING()
+##   INCLUDE(CTest)
+set(CTEST_PROJECT_NAME "Eigen")
+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_SITE_CDASH TRUE)

CTestCustom.cmake.in

@@ -0,0 +1,4 @@
+
+## A tribute to Dynamic!
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "33331")
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "33331")

Eigen/Array

@@ -0,0 +1,11 @@
+#ifndef EIGEN_ARRAY_MODULE_H
+#define EIGEN_ARRAY_MODULE_H
+
+// include Core first to handle Eigen2 support macros
+#include "Core"
+
+#ifndef EIGEN2_SUPPORT
+  #error The Eigen/Array header does no longer exist in Eigen3. All that functionality has moved to Eigen/Core.
+#endif
+
+#endif // EIGEN_ARRAY_MODULE_H

Eigen/CMakeLists.txt

@@ -0,0 +1,19 @@
+include(RegexUtils)
+test_escape_string_as_regex()
+
+file(GLOB Eigen_directory_files "*")
+
+escape_string_as_regex(ESCAPED_CMAKE_CURRENT_SOURCE_DIR "${CMAKE_CURRENT_SOURCE_DIR}")
+
+foreach(f ${Eigen_directory_files})
+  if(NOT f MATCHES "\\.txt" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/[.].+" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/src")
+    list(APPEND Eigen_directory_files_to_install ${f})
+  endif()
+endforeach(f ${Eigen_directory_files})
+
+install(FILES
+  ${Eigen_directory_files_to_install}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel
+  )
+
+add_subdirectory(src)

Eigen/Cholesky

@@ -0,0 +1,33 @@
+#ifndef EIGEN_CHOLESKY_MODULE_H
+#define EIGEN_CHOLESKY_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup Cholesky_Module Cholesky module
+  *
+  *
+  *
+  * This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
+  * Those decompositions are accessible via the following MatrixBase methods:
+  *  - MatrixBase::llt(),
+  *  - MatrixBase::ldlt()
+  *
+  * \code
+  * #include <Eigen/Cholesky>
+  * \endcode
+  */
+
+#include "src/misc/Solve.h"
+#include "src/Cholesky/LLT.h"
+#include "src/Cholesky/LDLT.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CHOLESKY_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/Core

@@ -0,0 +1,360 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CORE_H
+#define EIGEN_CORE_H
+
+// first thing Eigen does: stop the compiler from committing suicide
+#include "src/Core/util/DisableStupidWarnings.h"
+
+// then include this file where all our macros are defined. It's really important to do it first because
+// it's where we do all the alignment settings (platform detection and honoring the user's will if he
+// defined e.g. EIGEN_DONT_ALIGN) so it needs to be done before we do anything with vectorization.
+#include "src/Core/util/Macros.h"
+
+// if alignment is disabled, then disable vectorization. Note: EIGEN_ALIGN is the proper check, it takes into
+// account both the user's will (EIGEN_DONT_ALIGN) and our own platform checks
+#if !EIGEN_ALIGN
+  #ifndef EIGEN_DONT_VECTORIZE
+    #define EIGEN_DONT_VECTORIZE
+  #endif
+#endif
+
+#ifdef _MSC_VER
+  #include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled
+  #if (_MSC_VER >= 1500) // 2008 or later
+    // Remember that usage of defined() in a #define is undefined by the standard.
+    // a user reported that in 64-bit mode, MSVC doesn't care to define _M_IX86_FP.
+    #if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(_M_X64)
+      #define EIGEN_SSE2_ON_MSVC_2008_OR_LATER
+    #endif
+  #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) )
+    #define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC
+  #endif
+#endif
+
+#ifndef EIGEN_DONT_VECTORIZE
+
+  #if defined (EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC) || defined(EIGEN_SSE2_ON_MSVC_2008_OR_LATER)
+
+    // Defines symbols for compile-time detection of which instructions are
+    // used.
+    // EIGEN_VECTORIZE_YY is defined if and only if the instruction set YY is used
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_SSE
+    #define EIGEN_VECTORIZE_SSE2
+
+    // Detect sse3/ssse3/sse4:
+    // gcc and icc defines __SSE3__, ...
+    // there is no way to know about this on msvc. You can define EIGEN_VECTORIZE_SSE* if you
+    // want to force the use of those instructions with msvc.
+    #ifdef __SSE3__
+      #define EIGEN_VECTORIZE_SSE3
+    #endif
+    #ifdef __SSSE3__
+      #define EIGEN_VECTORIZE_SSSE3
+    #endif
+    #ifdef __SSE4_1__
+      #define EIGEN_VECTORIZE_SSE4_1
+    #endif
+    #ifdef __SSE4_2__
+      #define EIGEN_VECTORIZE_SSE4_2
+    #endif
+
+    // include files
+
+    // This extern "C" works around a MINGW-w64 compilation issue
+    // https://sourceforge.net/tracker/index.php?func=detail&aid=3018394&group_id=202880&atid=983354
+    // In essence, intrin.h is included by windows.h and also declares intrinsics (just as emmintrin.h etc. below do).
+    // However, intrin.h uses an extern "C" declaration, and g++ thus complains of duplicate declarations
+    // with conflicting linkage.  The linkage for intrinsics doesn't matter, but at that stage the compiler doesn't know;
+    // so, to avoid compile errors when windows.h is included after Eigen/Core, ensure intrinsics are extern "C" here too.
+    // notice that since these are C headers, the extern "C" is theoretically needed anyways.
+    extern "C" {
+      #include <emmintrin.h>
+      #include <xmmintrin.h>
+      #ifdef  EIGEN_VECTORIZE_SSE3
+      #include <pmmintrin.h>
+      #endif
+      #ifdef EIGEN_VECTORIZE_SSSE3
+      #include <tmmintrin.h>
+      #endif
+      #ifdef EIGEN_VECTORIZE_SSE4_1
+      #include <smmintrin.h>
+      #endif
+      #ifdef EIGEN_VECTORIZE_SSE4_2
+      #include <nmmintrin.h>
+      #endif
+    } // end extern "C"
+  #elif defined __ALTIVEC__
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_ALTIVEC
+    #include <altivec.h>
+    // We need to #undef all these ugly tokens defined in <altivec.h>
+    // => use __vector instead of vector
+    #undef bool
+    #undef vector
+    #undef pixel
+  #elif defined  __ARM_NEON__
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_NEON
+    #include <arm_neon.h>
+  #endif
+#endif
+
+#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
+  #define EIGEN_HAS_OPENMP
+#endif
+
+#ifdef EIGEN_HAS_OPENMP
+#include <omp.h>
+#endif
+
+// MSVC for windows mobile does not have the errno.h file
+#if !(defined(_MSC_VER) && defined(_WIN32_WCE)) && !defined(__ARMCC_VERSION)
+#define EIGEN_HAS_ERRNO
+#endif
+
+#ifdef EIGEN_HAS_ERRNO
+#include <cerrno>
+#endif
+#include <cstddef>
+#include <cstdlib>
+#include <cmath>
+#include <complex>
+#include <cassert>
+#include <functional>
+#include <iosfwd>
+#include <cstring>
+#include <string>
+#include <limits>
+#include <climits> // for CHAR_BIT
+// for min/max:
+#include <algorithm>
+
+// for outputting debug info
+#ifdef EIGEN_DEBUG_ASSIGN
+#include <iostream>
+#endif
+
+// required for __cpuid, needs to be included after cmath
+#if defined(_MSC_VER) && (defined(_M_IX86)||defined(_M_X64))
+  #include <intrin.h>
+#endif
+
+#if defined(_CPPUNWIND) || defined(__EXCEPTIONS)
+  #define EIGEN_EXCEPTIONS
+#endif
+
+#ifdef EIGEN_EXCEPTIONS
+  #include <new>
+#endif
+
+// defined in bits/termios.h
+#undef B0
+
+/** \brief Namespace containing all symbols from the %Eigen library. */
+namespace Eigen {
+
+inline static const char *SimdInstructionSetsInUse(void) {
+#if defined(EIGEN_VECTORIZE_SSE4_2)
+  return "SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
+#elif defined(EIGEN_VECTORIZE_SSE4_1)
+  return "SSE, SSE2, SSE3, SSSE3, SSE4.1";
+#elif defined(EIGEN_VECTORIZE_SSSE3)
+  return "SSE, SSE2, SSE3, SSSE3";
+#elif defined(EIGEN_VECTORIZE_SSE3)
+  return "SSE, SSE2, SSE3";
+#elif defined(EIGEN_VECTORIZE_SSE2)
+  return "SSE, SSE2";
+#elif defined(EIGEN_VECTORIZE_ALTIVEC)
+  return "AltiVec";
+#elif defined(EIGEN_VECTORIZE_NEON)
+  return "ARM NEON";
+#else
+  return "None";
+#endif
+}
+
+#define STAGE10_FULL_EIGEN2_API             10
+#define STAGE20_RESOLVE_API_CONFLICTS       20
+#define STAGE30_FULL_EIGEN3_API             30
+#define STAGE40_FULL_EIGEN3_STRICTNESS      40
+#define STAGE99_NO_EIGEN2_SUPPORT           99
+
+#if   defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS
+  #define EIGEN2_SUPPORT
+  #define EIGEN2_SUPPORT_STAGE STAGE40_FULL_EIGEN3_STRICTNESS
+#elif defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API
+  #define EIGEN2_SUPPORT
+  #define EIGEN2_SUPPORT_STAGE STAGE30_FULL_EIGEN3_API
+#elif defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS
+  #define EIGEN2_SUPPORT
+  #define EIGEN2_SUPPORT_STAGE STAGE20_RESOLVE_API_CONFLICTS
+#elif defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API
+  #define EIGEN2_SUPPORT
+  #define EIGEN2_SUPPORT_STAGE STAGE10_FULL_EIGEN2_API
+#elif defined EIGEN2_SUPPORT
+  // default to stage 3, that's what it's always meant
+  #define EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API
+  #define EIGEN2_SUPPORT_STAGE STAGE30_FULL_EIGEN3_API
+#else
+  #define EIGEN2_SUPPORT_STAGE STAGE99_NO_EIGEN2_SUPPORT
+#endif
+
+#ifdef EIGEN2_SUPPORT
+#undef minor
+#endif
+
+// we use size_t frequently and we'll never remember to prepend it with std:: everytime just to
+// ensure QNX/QCC support
+using std::size_t;
+// gcc 4.6.0 wants std:: for ptrdiff_t 
+using std::ptrdiff_t;
+
+/** \defgroup Core_Module Core module
+  * This is the main module of Eigen providing dense matrix and vector support
+  * (both fixed and dynamic size) with all the features corresponding to a BLAS library
+  * and much more...
+  *
+  * \code
+  * #include <Eigen/Core>
+  * \endcode
+  */
+
+#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/Memory.h"
+
+#include "src/Core/NumTraits.h"
+#include "src/Core/MathFunctions.h"
+#include "src/Core/GenericPacketMath.h"
+
+#if defined EIGEN_VECTORIZE_SSE
+  #include "src/Core/arch/SSE/PacketMath.h"
+  #include "src/Core/arch/SSE/MathFunctions.h"
+  #include "src/Core/arch/SSE/Complex.h"
+#elif defined EIGEN_VECTORIZE_ALTIVEC
+  #include "src/Core/arch/AltiVec/PacketMath.h"
+  #include "src/Core/arch/AltiVec/Complex.h"
+#elif defined EIGEN_VECTORIZE_NEON
+  #include "src/Core/arch/NEON/PacketMath.h"
+  #include "src/Core/arch/NEON/Complex.h"
+#endif
+
+#include "src/Core/arch/Default/Settings.h"
+
+#include "src/Core/Functors.h"
+#include "src/Core/DenseCoeffsBase.h"
+#include "src/Core/DenseBase.h"
+#include "src/Core/MatrixBase.h"
+#include "src/Core/EigenBase.h"
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874
+                                // at least confirmed with Doxygen 1.5.5 and 1.5.6
+  #include "src/Core/Assign.h"
+#endif
+
+#include "src/Core/util/BlasUtil.h"
+#include "src/Core/DenseStorage.h"
+#include "src/Core/NestByValue.h"
+#include "src/Core/ForceAlignedAccess.h"
+#include "src/Core/ReturnByValue.h"
+#include "src/Core/NoAlias.h"
+#include "src/Core/PlainObjectBase.h"
+#include "src/Core/Matrix.h"
+#include "src/Core/Array.h"
+#include "src/Core/CwiseBinaryOp.h"
+#include "src/Core/CwiseUnaryOp.h"
+#include "src/Core/CwiseNullaryOp.h"
+#include "src/Core/CwiseUnaryView.h"
+#include "src/Core/SelfCwiseBinaryOp.h"
+#include "src/Core/Dot.h"
+#include "src/Core/StableNorm.h"
+#include "src/Core/MapBase.h"
+#include "src/Core/Stride.h"
+#include "src/Core/Map.h"
+#include "src/Core/Block.h"
+#include "src/Core/VectorBlock.h"
+#include "src/Core/Transpose.h"
+#include "src/Core/DiagonalMatrix.h"
+#include "src/Core/Diagonal.h"
+#include "src/Core/DiagonalProduct.h"
+#include "src/Core/PermutationMatrix.h"
+#include "src/Core/Transpositions.h"
+#include "src/Core/Redux.h"
+#include "src/Core/Visitor.h"
+#include "src/Core/Fuzzy.h"
+#include "src/Core/IO.h"
+#include "src/Core/Swap.h"
+#include "src/Core/CommaInitializer.h"
+#include "src/Core/Flagged.h"
+#include "src/Core/ProductBase.h"
+#include "src/Core/Product.h"
+#include "src/Core/TriangularMatrix.h"
+#include "src/Core/SelfAdjointView.h"
+#include "src/Core/SolveTriangular.h"
+#include "src/Core/products/Parallelizer.h"
+#include "src/Core/products/CoeffBasedProduct.h"
+#include "src/Core/products/GeneralBlockPanelKernel.h"
+#include "src/Core/products/GeneralMatrixVector.h"
+#include "src/Core/products/GeneralMatrixMatrix.h"
+#include "src/Core/products/GeneralMatrixMatrixTriangular.h"
+#include "src/Core/products/SelfadjointMatrixVector.h"
+#include "src/Core/products/SelfadjointMatrixMatrix.h"
+#include "src/Core/products/SelfadjointProduct.h"
+#include "src/Core/products/SelfadjointRank2Update.h"
+#include "src/Core/products/TriangularMatrixVector.h"
+#include "src/Core/products/TriangularMatrixMatrix.h"
+#include "src/Core/products/TriangularSolverMatrix.h"
+#include "src/Core/products/TriangularSolverVector.h"
+#include "src/Core/BandMatrix.h"
+
+#include "src/Core/BooleanRedux.h"
+#include "src/Core/Select.h"
+#include "src/Core/VectorwiseOp.h"
+#include "src/Core/Random.h"
+#include "src/Core/Replicate.h"
+#include "src/Core/Reverse.h"
+#include "src/Core/ArrayBase.h"
+#include "src/Core/ArrayWrapper.h"
+
+} // namespace Eigen
+
+#include "src/Core/GlobalFunctions.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#ifdef EIGEN2_SUPPORT
+#include "Eigen2Support"
+#endif
+
+#endif // EIGEN_CORE_H

Eigen/Dense

@@ -0,0 +1,7 @@
+#include "Core"
+#include "LU"
+#include "Cholesky"
+#include "QR"
+#include "SVD"
+#include "Geometry"
+#include "Eigenvalues"

Eigen/Eigen

@@ -0,0 +1,2 @@
+#include "Dense"
+//#include "Sparse"

Eigen/Eigen2Support

@@ -0,0 +1,82 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN2SUPPORT_H
+#define EIGEN2SUPPORT_H
+
+#if (!defined(EIGEN2_SUPPORT)) || (!defined(EIGEN_CORE_H))
+#error Eigen2 support must be enabled by defining EIGEN2_SUPPORT before including any Eigen header
+#endif
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup Eigen2Support_Module Eigen2 support module
+  * 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
+  * \endcode
+  *
+  */
+
+#include "src/Eigen2Support/Macros.h"
+#include "src/Eigen2Support/Memory.h"
+#include "src/Eigen2Support/Meta.h"
+#include "src/Eigen2Support/Lazy.h"
+#include "src/Eigen2Support/Cwise.h"
+#include "src/Eigen2Support/CwiseOperators.h"
+#include "src/Eigen2Support/TriangularSolver.h"
+#include "src/Eigen2Support/Block.h"
+#include "src/Eigen2Support/VectorBlock.h"
+#include "src/Eigen2Support/Minor.h"
+#include "src/Eigen2Support/MathFunctions.h"
+
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+// Eigen2 used to include iostream
+#include<iostream>
+
+#define USING_PART_OF_NAMESPACE_EIGEN \
+EIGEN_USING_MATRIX_TYPEDEFS \
+using Eigen::Matrix; \
+using Eigen::MatrixBase; \
+using Eigen::ei_random; \
+using Eigen::ei_real; \
+using Eigen::ei_imag; \
+using Eigen::ei_conj; \
+using Eigen::ei_abs; \
+using Eigen::ei_abs2; \
+using Eigen::ei_sqrt; \
+using Eigen::ei_exp; \
+using Eigen::ei_log; \
+using Eigen::ei_sin; \
+using Eigen::ei_cos;
+
+#endif // EIGEN2SUPPORT_H

Eigen/Eigenvalues

@@ -0,0 +1,44 @@
+#ifndef EIGEN_EIGENVALUES_MODULE_H
+#define EIGEN_EIGENVALUES_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "Cholesky"
+#include "Jacobi"
+#include "Householder"
+#include "LU"
+
+namespace Eigen {
+
+/** \defgroup Eigenvalues_Module Eigenvalues module
+  *
+  *
+  *
+  * This module mainly provides various eigenvalue solvers.
+  * This module also provides some MatrixBase methods, including:
+  *  - MatrixBase::eigenvalues(),
+  *  - MatrixBase::operatorNorm()
+  *
+  * \code
+  * #include <Eigen/Eigenvalues>
+  * \endcode
+  */
+
+#include "src/Eigenvalues/Tridiagonalization.h"
+#include "src/Eigenvalues/RealSchur.h"
+#include "src/Eigenvalues/EigenSolver.h"
+#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
+#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
+#include "src/Eigenvalues/HessenbergDecomposition.h"
+#include "src/Eigenvalues/ComplexSchur.h"
+#include "src/Eigenvalues/ComplexEigenSolver.h"
+#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_EIGENVALUES_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/Geometry

@@ -0,0 +1,67 @@
+#ifndef EIGEN_GEOMETRY_MODULE_H
+#define EIGEN_GEOMETRY_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "SVD"
+#include "LU"
+#include <limits>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+namespace Eigen {
+
+/** \defgroup Geometry_Module Geometry module
+  *
+  *
+  *
+  * This module provides support for:
+  *  - fixed-size homogeneous transformations
+  *  - translation, scaling, 2D and 3D rotations
+  *  - quaternions
+  *  - \ref MatrixBase::cross() "cross product"
+  *  - \ref MatrixBase::unitOrthogonal() "orthognal vector generation"
+  *  - some linear components: parametrized-lines and hyperplanes
+  *
+  * \code
+  * #include <Eigen/Geometry>
+  * \endcode
+  */
+
+#include "src/Geometry/OrthoMethods.h"
+#include "src/Geometry/EulerAngles.h"
+
+#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+  #include "src/Geometry/Homogeneous.h"
+  #include "src/Geometry/RotationBase.h"
+  #include "src/Geometry/Rotation2D.h"
+  #include "src/Geometry/Quaternion.h"
+  #include "src/Geometry/AngleAxis.h"
+  #include "src/Geometry/Transform.h"
+  #include "src/Geometry/Translation.h"
+  #include "src/Geometry/Scaling.h"
+  #include "src/Geometry/Hyperplane.h"
+  #include "src/Geometry/ParametrizedLine.h"
+  #include "src/Geometry/AlignedBox.h"
+  #include "src/Geometry/Umeyama.h"
+
+  #if defined EIGEN_VECTORIZE_SSE
+    #include "src/Geometry/arch/Geometry_SSE.h"
+  #endif
+#endif
+
+#ifdef EIGEN2_SUPPORT
+#include "src/Eigen2Support/Geometry/All.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_GEOMETRY_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
+

Eigen/Householder

@@ -0,0 +1,27 @@
+#ifndef EIGEN_HOUSEHOLDER_MODULE_H
+#define EIGEN_HOUSEHOLDER_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup Householder_Module Householder module
+  * This module provides Householder transformations.
+  *
+  * \code
+  * #include <Eigen/Householder>
+  * \endcode
+  */
+
+#include "src/Householder/Householder.h"
+#include "src/Householder/HouseholderSequence.h"
+#include "src/Householder/BlockHouseholder.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_HOUSEHOLDER_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/Jacobi

@@ -0,0 +1,30 @@
+#ifndef EIGEN_JACOBI_MODULE_H
+#define EIGEN_JACOBI_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup Jacobi_Module Jacobi module
+  * This module provides Jacobi and Givens rotations.
+  *
+  * \code
+  * #include <Eigen/Jacobi>
+  * \endcode
+  *
+  * In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
+  *  - MatrixBase::applyOnTheLeft()
+  *  - MatrixBase::applyOnTheRight().
+  */
+
+#include "src/Jacobi/Jacobi.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_JACOBI_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
+

Eigen/LU

@@ -0,0 +1,42 @@
+#ifndef EIGEN_LU_MODULE_H
+#define EIGEN_LU_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup LU_Module LU module
+  * This module includes %LU decomposition and related notions such as matrix inversion and determinant.
+  * This module defines the following MatrixBase methods:
+  *  - MatrixBase::inverse()
+  *  - MatrixBase::determinant()
+  *
+  * \code
+  * #include <Eigen/LU>
+  * \endcode
+  */
+
+#include "src/misc/Solve.h"
+#include "src/misc/Kernel.h"
+#include "src/misc/Image.h"
+#include "src/LU/FullPivLU.h"
+#include "src/LU/PartialPivLU.h"
+#include "src/LU/Determinant.h"
+#include "src/LU/Inverse.h"
+
+#if defined EIGEN_VECTORIZE_SSE
+  #include "src/LU/arch/Inverse_SSE.h"
+#endif
+
+#ifdef EIGEN2_SUPPORT
+  #include "src/Eigen2Support/LU.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_LU_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/LeastSquares

@@ -0,0 +1,36 @@
+#ifndef EIGEN_REGRESSION_MODULE_H
+#define EIGEN_REGRESSION_MODULE_H
+
+#ifndef EIGEN2_SUPPORT
+#error LeastSquares is only available in Eigen2 support mode (define EIGEN2_SUPPORT)
+#endif
+
+// exclude from normal eigen3-only documentation
+#ifdef EIGEN2_SUPPORT
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "Eigenvalues"
+#include "Geometry"
+
+namespace Eigen {
+
+/** \defgroup LeastSquares_Module LeastSquares module
+  * This module provides linear regression and related features.
+  *
+  * \code
+  * #include <Eigen/LeastSquares>
+  * \endcode
+  */
+
+#include "src/Eigen2Support/LeastSquares.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN2_SUPPORT
+
+#endif // EIGEN_REGRESSION_MODULE_H

Eigen/QR

@@ -0,0 +1,45 @@
+#ifndef EIGEN_QR_MODULE_H
+#define EIGEN_QR_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "Cholesky"
+#include "Jacobi"
+#include "Householder"
+
+namespace Eigen {
+
+/** \defgroup QR_Module QR module
+  *
+  *
+  *
+  * This module provides various QR decompositions
+  * This module also provides some MatrixBase methods, including:
+  *  - MatrixBase::qr(),
+  *
+  * \code
+  * #include <Eigen/QR>
+  * \endcode
+  */
+
+#include "src/misc/Solve.h"
+#include "src/QR/HouseholderQR.h"
+#include "src/QR/FullPivHouseholderQR.h"
+#include "src/QR/ColPivHouseholderQR.h"
+
+#ifdef EIGEN2_SUPPORT
+#include "src/Eigen2Support/QR.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#ifdef EIGEN2_SUPPORT
+#include "Eigenvalues"
+#endif
+
+#endif // EIGEN_QR_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/QtAlignedMalloc

@@ -0,0 +1,34 @@
+
+#ifndef EIGEN_QTMALLOC_MODULE_H
+#define EIGEN_QTMALLOC_MODULE_H
+
+#include "Core"
+
+#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+void *qMalloc(size_t size)
+{
+  return Eigen::internal::aligned_malloc(size);
+}
+
+void qFree(void *ptr)
+{
+  Eigen::internal::aligned_free(ptr);
+}
+
+void *qRealloc(void *ptr, size_t size)
+{
+  void* newPtr = Eigen::internal::aligned_malloc(size);
+  memcpy(newPtr, ptr, size);
+  Eigen::internal::aligned_free(ptr);
+  return newPtr;
+}
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif
+
+#endif // EIGEN_QTMALLOC_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/SVD

@@ -0,0 +1,38 @@
+#ifndef EIGEN_SVD_MODULE_H
+#define EIGEN_SVD_MODULE_H
+
+#include "QR"
+#include "Householder"
+#include "Jacobi"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup SVD_Module SVD module
+  *
+  *
+  *
+  * This module provides SVD decomposition for matrices (both real and complex).
+  * This decomposition is accessible via the following MatrixBase method:
+  *  - MatrixBase::jacobiSvd()
+  *
+  * \code
+  * #include <Eigen/SVD>
+  * \endcode
+  */
+
+#include "src/misc/Solve.h"
+#include "src/SVD/JacobiSVD.h"
+#include "src/SVD/UpperBidiagonalization.h"
+
+#ifdef EIGEN2_SUPPORT
+#include "src/Eigen2Support/SVD.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SVD_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

Eigen/Sparse

@@ -0,0 +1,69 @@
+#ifndef EIGEN_SPARSE_MODULE_H
+#define EIGEN_SPARSE_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include <vector>
+#include <map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+
+#ifdef EIGEN2_SUPPORT
+#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
+#endif
+
+#ifndef EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
+#error The sparse module API is not stable yet. To use it anyway, please define the EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET preprocessor token.
+#endif
+
+namespace Eigen {
+
+/** \defgroup Sparse_Module Sparse module
+  *
+  *
+  *
+  * See the \ref TutorialSparse "Sparse tutorial"
+  *
+  * \code
+  * #include <Eigen/Sparse>
+  * \endcode
+  */
+
+/** The type used to identify a general sparse storage. */
+struct Sparse {};
+
+#include "src/Sparse/SparseUtil.h"
+#include "src/Sparse/SparseMatrixBase.h"
+#include "src/Sparse/CompressedStorage.h"
+#include "src/Sparse/AmbiVector.h"
+#include "src/Sparse/SparseMatrix.h"
+#include "src/Sparse/DynamicSparseMatrix.h"
+#include "src/Sparse/MappedSparseMatrix.h"
+#include "src/Sparse/SparseVector.h"
+#include "src/Sparse/CoreIterators.h"
+#include "src/Sparse/SparseBlock.h"
+#include "src/Sparse/SparseTranspose.h"
+#include "src/Sparse/SparseCwiseUnaryOp.h"
+#include "src/Sparse/SparseCwiseBinaryOp.h"
+#include "src/Sparse/SparseDot.h"
+#include "src/Sparse/SparseAssign.h"
+#include "src/Sparse/SparseRedux.h"
+#include "src/Sparse/SparseFuzzy.h"
+#include "src/Sparse/SparseProduct.h"
+#include "src/Sparse/SparseSparseProduct.h"
+#include "src/Sparse/SparseDenseProduct.h"
+#include "src/Sparse/SparseDiagonalProduct.h"
+#include "src/Sparse/SparseTriangularView.h"
+#include "src/Sparse/SparseSelfAdjointView.h"
+#include "src/Sparse/TriangularSolver.h"
+#include "src/Sparse/SparseView.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPARSE_MODULE_H
+

Eigen/StdDeque

@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STDDEQUE_MODULE_H
+#define EIGEN_STDDEQUE_MODULE_H
+
+#include "Core"
+#include <deque>
+
+#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */
+
+#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdDeque.h"
+
+#endif
+
+#endif // EIGEN_STDDEQUE_MODULE_H

Eigen/StdList

@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STDLIST_MODULE_H
+#define EIGEN_STDLIST_MODULE_H
+
+#include "Core"
+#include <list>
+
+#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */    
+
+#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdList.h"
+
+#endif
+
+#endif // EIGEN_STDLIST_MODULE_H

Eigen/StdVector

@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STDVECTOR_MODULE_H
+#define EIGEN_STDVECTOR_MODULE_H
+
+#include "Core"
+#include <vector>
+
+#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */
+
+#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdVector.h"
+
+#endif
+
+#endif // EIGEN_STDVECTOR_MODULE_H

Eigen/src/CMakeLists.txt

@@ -0,0 +1,7 @@
+file(GLOB Eigen_src_subdirectories "*")
+escape_string_as_regex(ESCAPED_CMAKE_CURRENT_SOURCE_DIR "${CMAKE_CURRENT_SOURCE_DIR}")
+foreach(f ${Eigen_src_subdirectories})
+  if(NOT f MATCHES "\\.txt" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/[.].+" )
+    add_subdirectory(${f})
+  endif()
+endforeach()

Eigen/src/Cholesky/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Cholesky_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Cholesky_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Cholesky COMPONENT Devel
+  )

Eigen/src/Cholesky/LDLT.h

@@ -0,0 +1,484 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_LDLT_H
+#define EIGEN_LDLT_H
+
+namespace internal {
+template<typename MatrixType, int UpLo> struct LDLT_Traits;
+}
+
+/** \ingroup cholesky_Module
+  *
+  * \class LDLT
+  *
+  * \brief Robust Cholesky decomposition of a matrix with pivoting
+  *
+  * \param MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
+  *
+  * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
+  * matrix \f$ A \f$ such that \f$ A =  P^TLDL^*P \f$, where P is a permutation matrix, L
+  * is lower triangular with a unit diagonal and D is a diagonal matrix.
+  *
+  * The decomposition uses pivoting to ensure stability, so that L will have
+  * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
+  * on D also stabilizes the computation.
+  *
+  * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
+	* decomposition to determine whether a system of equations has a solution.
+  *
+  * \sa MatrixBase::ldlt(), class LLT
+  */
+ /* THIS PART OF THE DOX IS CURRENTLY DISABLED BECAUSE INACCURATE BECAUSE OF BUG IN THE DECOMPOSITION CODE
+  * Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
+  * the strict lower part does not have to store correct values.
+  */
+template<typename _MatrixType, int _UpLo> class LDLT
+{
+  public:
+    typedef _MatrixType MatrixType;
+    enum {
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      Options = MatrixType::Options & ~RowMajorBit, // these are the options for the TmpMatrixType, we need a ColMajor matrix here!
+      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+      UpLo = _UpLo
+    };
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef typename MatrixType::Index Index;
+    typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> TmpMatrixType;
+
+    typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
+    typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
+
+    typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
+
+    /** \brief Default Constructor.
+      *
+      * 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) {}
+
+    /** \brief Default Constructor with memory preallocation
+      *
+      * Like the default constructor but with preallocation of the internal data
+      * according to the specified problem \a size.
+      * \sa LDLT()
+      */
+    LDLT(Index size)
+      : m_matrix(size, size),
+        m_transpositions(size),
+        m_temporary(size),
+        m_isInitialized(false)
+    {}
+
+    LDLT(const MatrixType& matrix)
+      : m_matrix(matrix.rows(), matrix.cols()),
+        m_transpositions(matrix.rows()),
+        m_temporary(matrix.rows()),
+        m_isInitialized(false)
+    {
+      compute(matrix);
+    }
+
+    /** \returns a view of the upper triangular matrix U */
+    inline typename Traits::MatrixU matrixU() const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return Traits::getU(m_matrix);
+    }
+
+    /** \returns a view of the lower triangular matrix L */
+    inline typename Traits::MatrixL matrixL() const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return Traits::getL(m_matrix);
+    }
+
+    /** \returns the permutation matrix P as a transposition sequence.
+      */
+    inline const TranspositionType& transpositionsP() const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return m_transpositions;
+    }
+
+    /** \returns the coefficients of the diagonal matrix D */
+    inline Diagonal<const MatrixType> vectorD(void) const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return m_matrix.diagonal();
+    }
+
+    /** \returns true if the matrix is positive (semidefinite) */
+    inline bool isPositive(void) const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return m_sign == 1;
+    }
+    
+    #ifdef EIGEN2_SUPPORT
+    inline bool isPositiveDefinite() const
+    {
+      return isPositive();
+    }
+    #endif
+
+    /** \returns true if the matrix is negative (semidefinite) */
+    inline bool isNegative(void) const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return m_sign == -1;
+    }
+
+    /** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
+      *
+      * This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
+      *
+      * \note_about_checking_solutions
+      *
+      * More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
+      * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$, 
+      * \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
+      * \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
+      * least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
+      * computes the least-square solution of \f$ A x = b \f$ is \f$ A \f$ is singular.
+      *
+      * \sa MatrixBase::ldlt()
+      */
+    template<typename Rhs>
+    inline const internal::solve_retval<LDLT, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      eigen_assert(m_matrix.rows()==b.rows()
+                && "LDLT::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::solve_retval<LDLT, Rhs>(*this, b.derived());
+    }
+
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived, typename ResultType>
+    bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+    {
+      *result = this->solve(b);
+      return true;
+    }
+    #endif
+
+    template<typename Derived>
+    bool solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+    LDLT& compute(const MatrixType& matrix);
+
+    /** \returns the internal LDLT decomposition matrix
+      *
+      * TODO: document the storage layout
+      */
+    inline const MatrixType& matrixLDLT() const
+    {
+      eigen_assert(m_isInitialized && "LDLT is not initialized.");
+      return m_matrix;
+    }
+
+    MatrixType reconstructedMatrix() const;
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+
+  protected:
+
+    /** \internal
+      * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
+      * The strict upper part is used during the decomposition, the strict lower
+      * part correspond to the coefficients of L (its diagonal is equal to 1 and
+      * is not stored), and the diagonal entries correspond to D.
+      */
+    MatrixType m_matrix;
+    TranspositionType m_transpositions;
+    TmpMatrixType m_temporary;
+    int m_sign;
+    bool m_isInitialized;
+};
+
+namespace internal {
+
+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)
+  {
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::RealScalar RealScalar;
+    typedef typename MatrixType::Index Index;
+    eigen_assert(mat.rows()==mat.cols());
+    const Index size = mat.rows();
+
+    if (size <= 1)
+    {
+      transpositions.setIdentity();
+      if(sign)
+        *sign = real(mat.coeff(0,0))>0 ? 1:-1;
+      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);
+      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;
+      }
+
+      // 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)
+      {
+        // apply the transposition while taking care to consider only
+        // the lower triangular part
+        Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
+        mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
+        mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
+        std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
+        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(index_of_biggest_in_corner,i) = conj(tmp);
+        }
+        if(NumTraits<Scalar>::IsComplex)
+          mat.coeffRef(index_of_biggest_in_corner,k) = conj(mat.coeff(index_of_biggest_in_corner,k));
+      }
+
+      // partition the matrix:
+      //       A00 |  -  |  -
+      // lu  = A10 | A11 |  -
+      //       A20 | A21 | A22
+      Index rs = size - k - 1;
+      Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+      Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
+      Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
+
+      if(k>0)
+      {
+        temp.head(k) = mat.diagonal().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);
+    }
+
+    return true;
+  }
+};
+
+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)
+  {
+    Transpose<MatrixType> matt(mat);
+    return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
+  }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
+{
+  typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
+  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
+  inline static MatrixL getL(const MatrixType& m) { return m; }
+  inline static MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
+{
+  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
+  typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
+  inline static MatrixL getL(const MatrixType& m) { return m.adjoint(); }
+  inline static MatrixU getU(const MatrixType& m) { return m; }
+};
+
+} // end namespace internal
+
+/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
+  */
+template<typename MatrixType, int _UpLo>
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
+{
+  eigen_assert(a.rows()==a.cols());
+  const Index size = a.rows();
+
+  m_matrix = a;
+
+  m_transpositions.resize(size);
+  m_isInitialized = false;
+  m_temporary.resize(size);
+
+  internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, &m_sign);
+
+  m_isInitialized = true;
+  return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int _UpLo, typename Rhs>
+struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
+  : solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs>
+{
+  typedef LDLT<_MatrixType,_UpLo> LDLTType;
+  EIGEN_MAKE_SOLVE_HELPERS(LDLTType,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    eigen_assert(rhs().rows() == dec().matrixLDLT().rows());
+    // dst = P b
+    dst = dec().transpositionsP() * rhs();
+
+    // dst = L^-1 (P b)
+    dec().matrixL().solveInPlace(dst);
+
+    // dst = D^-1 (L^-1 P b)
+    // more precisely, use pseudo-inverse of D (see bug 241)
+    using std::abs;
+    using std::max;
+    typedef typename LDLTType::MatrixType MatrixType;
+    typedef typename LDLTType::Scalar Scalar;
+    typedef typename LDLTType::RealScalar RealScalar;
+    const Diagonal<const MatrixType> vectorD = dec().vectorD();
+    RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
+				 RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
+    for (Index i = 0; i < vectorD.size(); ++i) {
+      if(abs(vectorD(i)) > tolerance)
+	dst.row(i) /= vectorD(i);
+      else
+	dst.row(i).setZero();
+    }
+
+    // dst = L^-T (D^-1 L^-1 P b)
+    dec().matrixU().solveInPlace(dst);
+
+    // dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b
+    dst = dec().transpositionsP().transpose() * dst;
+  }
+};
+}
+
+/** \internal use x = ldlt_object.solve(x);
+  *
+  * This is the \em in-place version of solve().
+  *
+  * \param bAndX represents both the right-hand side matrix b and result x.
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * This version avoids a copy when the right hand side matrix b is not
+  * needed anymore.
+  *
+  * \sa LDLT::solve(), MatrixBase::ldlt()
+  */
+template<typename MatrixType,int _UpLo>
+template<typename Derived>
+bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+  eigen_assert(m_isInitialized && "LDLT is not initialized.");
+  const Index size = m_matrix.rows();
+  eigen_assert(size == bAndX.rows());
+
+  bAndX = this->solve(bAndX);
+
+  return true;
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^T L D L^* P.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int _UpLo>
+MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
+{
+  eigen_assert(m_isInitialized && "LDLT is not initialized.");
+  const Index size = m_matrix.rows();
+  MatrixType res(size,size);
+
+  // P
+  res.setIdentity();
+  res = transpositionsP() * res;
+  // L^* P
+  res = matrixU() * res;
+  // D(L^*P)
+  res = vectorD().asDiagonal() * res;
+  // L(DL^*P)
+  res = matrixL() * res;
+  // P^T (LDL^*P)
+  res = transpositionsP().transpose() * res;
+
+  return res;
+}
+
+/** \cholesky_module
+  * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+  */
+template<typename MatrixType, unsigned int UpLo>
+inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::ldlt() const
+{
+  return LDLT<PlainObject,UpLo>(m_matrix);
+}
+
+/** \cholesky_module
+  * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+  */
+template<typename Derived>
+inline const LDLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::ldlt() const
+{
+  return LDLT<PlainObject>(derived());
+}
+
+#endif // EIGEN_LDLT_H

Eigen/src/Cholesky/LLT.h

@@ -0,0 +1,386 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_LLT_H
+#define EIGEN_LLT_H
+
+namespace internal{
+template<typename MatrixType, int UpLo> struct LLT_Traits;
+}
+
+/** \ingroup cholesky_Module
+  *
+  * \class LLT
+  *
+  * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
+  *
+  * \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
+  *
+  * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
+  * matrix A such that A = LL^* = U^*U, where L is lower triangular.
+  *
+  * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like  D^*D x = b,
+  * for that purpose, we recommend the Cholesky decomposition without square root which is more stable
+  * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
+  * situations like generalised eigen problems with hermitian matrices.
+  *
+  * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
+  * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
+  * has a solution.
+  *
+  * \sa MatrixBase::llt(), class LDLT
+  */
+ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH)
+  * Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
+  * the strict lower part does not have to store correct values.
+  */
+template<typename _MatrixType, int _UpLo> class LLT
+{
+  public:
+    typedef _MatrixType MatrixType;
+    enum {
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      Options = MatrixType::Options,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+    };
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef typename MatrixType::Index Index;
+
+    enum {
+      PacketSize = internal::packet_traits<Scalar>::size,
+      AlignmentMask = int(PacketSize)-1,
+      UpLo = _UpLo
+    };
+
+    typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
+
+    /**
+      * \brief Default Constructor.
+      *
+      * The default constructor is useful in cases in which the user intends to
+      * perform decompositions via LLT::compute(const MatrixType&).
+      */
+    LLT() : m_matrix(), m_isInitialized(false) {}
+
+    /** \brief Default Constructor with memory preallocation
+      *
+      * Like the default constructor but with preallocation of the internal data
+      * according to the specified problem \a size.
+      * \sa LLT()
+      */
+    LLT(Index size) : m_matrix(size, size),
+                    m_isInitialized(false) {}
+
+    LLT(const MatrixType& matrix)
+      : m_matrix(matrix.rows(), matrix.cols()),
+        m_isInitialized(false)
+    {
+      compute(matrix);
+    }
+
+    /** \returns a view of the upper triangular matrix U */
+    inline typename Traits::MatrixU matrixU() const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      return Traits::getU(m_matrix);
+    }
+
+    /** \returns a view of the lower triangular matrix L */
+    inline typename Traits::MatrixL matrixL() const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      return Traits::getL(m_matrix);
+    }
+
+    /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+      *
+      * Since this LLT class assumes anyway that the matrix A is invertible, the solution
+      * theoretically exists and is unique regardless of b.
+      *
+      * Example: \include LLT_solve.cpp
+      * Output: \verbinclude LLT_solve.out
+      *
+      * \sa solveInPlace(), MatrixBase::llt()
+      */
+    template<typename Rhs>
+    inline const internal::solve_retval<LLT, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      eigen_assert(m_matrix.rows()==b.rows()
+                && "LLT::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::solve_retval<LLT, Rhs>(*this, b.derived());
+    }
+
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived, typename ResultType>
+    bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
+    {
+      *result = this->solve(b);
+      return true;
+    }
+    
+    bool isPositiveDefinite() const { return true; }
+    #endif
+
+    template<typename Derived>
+    void solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+    LLT& compute(const MatrixType& matrix);
+
+    /** \returns the LLT decomposition matrix
+      *
+      * TODO: document the storage layout
+      */
+    inline const MatrixType& matrixLLT() const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      return m_matrix;
+    }
+
+    MatrixType reconstructedMatrix() const;
+
+
+    /** \brief Reports whether previous computation was successful.
+      *
+      * \returns \c Success if computation was succesful,
+      *          \c NumericalIssue if the matrix.appears to be negative.
+      */
+    ComputationInfo info() const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      return m_info;
+    }
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+
+  protected:
+    /** \internal
+      * Used to compute and store L
+      * The strict upper part is not used and even not initialized.
+      */
+    MatrixType m_matrix;
+    bool m_isInitialized;
+    ComputationInfo m_info;
+};
+
+namespace internal {
+
+template<int UpLo> struct llt_inplace;
+
+template<> struct llt_inplace<Lower>
+{
+  template<typename MatrixType>
+  static typename MatrixType::Index unblocked(MatrixType& mat)
+  {
+    typedef typename MatrixType::Index Index;
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::RealScalar RealScalar;
+    
+    eigen_assert(mat.rows()==mat.cols());
+    const Index size = mat.rows();
+    for(Index k = 0; k < size; ++k)
+    {
+      Index rs = size-k-1; // remaining size
+
+      Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+      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));
+      if (k>0) x -= A10.squaredNorm();
+      if (x<=RealScalar(0))
+        return k;
+      mat.coeffRef(k,k) = x = sqrt(x);
+      if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
+      if (rs>0) A21 *= RealScalar(1)/x;
+    }
+    return -1;
+  }
+
+  template<typename MatrixType>
+  static typename MatrixType::Index blocked(MatrixType& m)
+  {
+    typedef typename MatrixType::Index Index;
+    eigen_assert(m.rows()==m.cols());
+    Index size = m.rows();
+    if(size<32)
+      return unblocked(m);
+
+    Index blockSize = size/8;
+    blockSize = (blockSize/16)*16;
+    blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
+
+    for (Index k=0; k<size; k+=blockSize)
+    {
+      // partition the matrix:
+      //       A00 |  -  |  -
+      // lu  = A10 | A11 |  -
+      //       A20 | A21 | A22
+      Index bs = (std::min)(blockSize, size-k);
+      Index rs = size - k - bs;
+      Block<MatrixType,Dynamic,Dynamic> A11(m,k,   k,   bs,bs);
+      Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k,   rs,bs);
+      Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
+
+      Index ret;
+      if((ret=unblocked(A11))>=0) return k+ret;
+      if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
+      if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,-1); // bottleneck
+    }
+    return -1;
+  }
+};
+
+template<> struct llt_inplace<Upper>
+{
+  template<typename MatrixType>
+  static EIGEN_STRONG_INLINE typename MatrixType::Index unblocked(MatrixType& mat)
+  {
+    Transpose<MatrixType> matt(mat);
+    return llt_inplace<Lower>::unblocked(matt);
+  }
+  template<typename MatrixType>
+  static EIGEN_STRONG_INLINE typename MatrixType::Index blocked(MatrixType& mat)
+  {
+    Transpose<MatrixType> matt(mat);
+    return llt_inplace<Lower>::blocked(matt);
+  }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
+{
+  typedef const TriangularView<const MatrixType, Lower> MatrixL;
+  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
+  inline static MatrixL getL(const MatrixType& m) { return m; }
+  inline static MatrixU getU(const MatrixType& m) { return m.adjoint(); }
+  static bool inplace_decomposition(MatrixType& m)
+  { return llt_inplace<Lower>::blocked(m)==-1; }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
+{
+  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
+  typedef const TriangularView<const MatrixType, Upper> MatrixU;
+  inline static MatrixL getL(const MatrixType& m) { return m.adjoint(); }
+  inline static MatrixU getU(const MatrixType& m) { return m; }
+  static bool inplace_decomposition(MatrixType& m)
+  { return llt_inplace<Upper>::blocked(m)==-1; }
+};
+
+} // end namespace internal
+
+/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
+  *
+  *
+  * \returns a reference to *this
+  */
+template<typename MatrixType, int _UpLo>
+LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a)
+{
+  assert(a.rows()==a.cols());
+  const Index size = a.rows();
+  m_matrix.resize(size, size);
+  m_matrix = a;
+
+  m_isInitialized = true;
+  bool ok = Traits::inplace_decomposition(m_matrix);
+  m_info = ok ? Success : NumericalIssue;
+
+  return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int UpLo, typename Rhs>
+struct solve_retval<LLT<_MatrixType, UpLo>, Rhs>
+  : solve_retval_base<LLT<_MatrixType, UpLo>, Rhs>
+{
+  typedef LLT<_MatrixType,UpLo> LLTType;
+  EIGEN_MAKE_SOLVE_HELPERS(LLTType,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    dst = rhs();
+    dec().solveInPlace(dst);
+  }
+};
+}
+
+/** \internal use x = llt_object.solve(x);
+  * 
+  * This is the \em in-place version of solve().
+  *
+  * \param bAndX represents both the right-hand side matrix b and result x.
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * This version avoids a copy when the right hand side matrix b is not
+  * needed anymore.
+  *
+  * \sa LLT::solve(), MatrixBase::llt()
+  */
+template<typename MatrixType, int _UpLo>
+template<typename Derived>
+void LLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+  eigen_assert(m_isInitialized && "LLT is not initialized.");
+  eigen_assert(m_matrix.rows()==bAndX.rows());
+  matrixL().solveInPlace(bAndX);
+  matrixU().solveInPlace(bAndX);
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: L L^*.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int _UpLo>
+MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
+{
+  eigen_assert(m_isInitialized && "LLT is not initialized.");
+  return matrixL() * matrixL().adjoint().toDenseMatrix();
+}
+
+/** \cholesky_module
+  * \returns the LLT decomposition of \c *this
+  */
+template<typename Derived>
+inline const LLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::llt() const
+{
+  return LLT<PlainObject>(derived());
+}
+
+/** \cholesky_module
+  * \returns the LLT decomposition of \c *this
+  */
+template<typename MatrixType, unsigned int UpLo>
+inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::llt() const
+{
+  return LLT<PlainObject,UpLo>(m_matrix);
+}
+
+#endif // EIGEN_LLT_H

Eigen/src/Core/Array.h

@@ -0,0 +1,320 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAY_H
+#define EIGEN_ARRAY_H
+
+/** \class Array 
+  * \ingroup Core_Module
+  *
+  * \brief General-purpose arrays with easy API for coefficient-wise operations
+  *
+  * The %Array class is very similar to the Matrix class. It provides
+  * general-purpose one- and two-dimensional arrays. The difference between the
+  * %Array and the %Matrix class is primarily in the API: the API for the
+  * %Array class provides easy access to coefficient-wise operations, while the
+  * API for the %Matrix class provides easy access to linear-algebra
+  * operations.
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
+  *
+  * \sa \ref TutorialArrayClass, \ref TopicClassHierarchy
+  */
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  typedef ArrayXpr XprKind;
+  typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
+};
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+class Array
+  : public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  public:
+
+    typedef PlainObjectBase<Array> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Array)
+
+    enum { Options = _Options };
+    typedef typename Base::PlainObject PlainObject;
+
+  protected:
+    template <typename Derived, typename OtherDerived, bool IsVector>
+    friend struct internal::conservative_resize_like_impl;
+
+    using Base::m_storage;
+
+  public:
+
+    using Base::base;
+    using Base::coeff;
+    using Base::coeffRef;
+
+    /**
+      * The usage of
+      *   using Base::operator=;
+      * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
+      * the usage of 'using'. This should be done only for operator=.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
+    {
+      return Base::operator=(other);
+    }
+
+    /** Copies the value of the expression \a other into \c *this with automatic resizing.
+      *
+      * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+      * it will be initialized.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Array& operator=(const ArrayBase<OtherDerived>& other)
+    {
+      return Base::_set(other);
+    }
+
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    EIGEN_STRONG_INLINE Array& operator=(const Array& other)
+    {
+      return Base::_set(other);
+    }
+
+    /** Default constructor.
+      *
+      * For fixed-size matrices, does nothing.
+      *
+      * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+      * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+      * a matrix to 0 is not supported.
+      *
+      * \sa resize(Index,Index)
+      */
+    EIGEN_STRONG_INLINE explicit Array() : Base()
+    {
+      Base::_check_template_params();
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    // FIXME is it still needed ??
+    /** \internal */
+    Array(internal::constructor_without_unaligned_array_assert)
+      : Base(internal::constructor_without_unaligned_array_assert())
+    {
+      Base::_check_template_params();
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+#endif
+
+    /** Constructs a vector or row-vector with given dimension. \only_for_vectors
+      *
+      * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+      * it is redundant to pass the dimension here, so it makes more sense to use the default
+      * constructor Matrix() instead.
+      */
+    EIGEN_STRONG_INLINE explicit Array(Index dim)
+      : Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Array)
+      eigen_assert(dim >= 0);
+      eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE Array(const T0& x, const T1& y)
+    {
+      Base::_check_template_params();
+      this->template _init2<T0,T1>(x, y);
+    }
+    #else
+    /** constructs an uninitialized matrix with \a rows rows and \a cols columns.
+      *
+      * This is useful for dynamic-size matrices. For fixed-size matrices,
+      * it is redundant to pass these parameters, so one should use the default constructor
+      * Matrix() instead. */
+    Array(Index rows, Index cols);
+    /** constructs an initialized 2D vector with given coefficients */
+    Array(const Scalar& x, const Scalar& y);
+    #endif
+
+    /** constructs an initialized 3D vector with given coefficients */
+    EIGEN_STRONG_INLINE Array(const Scalar& x, const Scalar& y, const Scalar& z)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+    }
+    /** constructs an initialized 4D vector with given coefficients */
+    EIGEN_STRONG_INLINE Array(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+      m_storage.data()[3] = w;
+    }
+
+    explicit Array(const Scalar *data);
+
+    /** Constructor copying the value of the expression \a other */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Array(const ArrayBase<OtherDerived>& other)
+             : Base(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      Base::_check_template_params();
+      Base::_set_noalias(other);
+    }
+    /** Copy constructor */
+    EIGEN_STRONG_INLINE Array(const Array& other)
+            : Base(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      Base::_check_template_params();
+      Base::_set_noalias(other);
+    }
+    /** Copy constructor with in-place evaluation */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Array(const ReturnByValue<OtherDerived>& other)
+    {
+      Base::_check_template_params();
+      Base::resize(other.rows(), other.cols());
+      other.evalTo(*this);
+    }
+
+    /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other)
+      : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+    {
+      Base::_check_template_params();
+      Base::resize(other.rows(), other.cols());
+      *this = other;
+    }
+
+    /** Override MatrixBase::swap() since for dynamic-sized matrices of same type it is enough to swap the
+      * data pointers.
+      */
+    template<typename OtherDerived>
+    void swap(ArrayBase<OtherDerived> const & other)
+    { this->_swap(other.derived()); }
+
+    inline Index innerStride() const { return 1; }
+    inline Index outerStride() const { return this->innerSize(); }
+
+    #ifdef EIGEN_ARRAY_PLUGIN
+    #include EIGEN_ARRAY_PLUGIN
+    #endif
+
+  private:
+
+    template<typename MatrixType, typename OtherDerived, bool SwapPointers>
+    friend struct internal::matrix_swap_impl;
+};
+
+/** \defgroup arraytypedefs Global array typedefs
+  * \ingroup Core_Module
+  *
+  * Eigen defines several typedef shortcuts for most common 1D and 2D array types.
+  *
+  * The general patterns are the following:
+  *
+  * \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+  * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+  * for complex double.
+  *
+  * For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
+  *
+  * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
+  * a fixed-size 1D array of 4 complex floats.
+  *
+  * \sa class Array
+  */
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \
+/** \ingroup arraytypedefs */                                    \
+typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix;  \
+/** \ingroup arraytypedefs */                                    \
+typedef Array<Type, Size, 1>    Array##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \
+/** \ingroup arraytypedefs */                                    \
+typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix;  \
+/** \ingroup arraytypedefs */                                    \
+typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int,                  i)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float,                f)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double,               d)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_LARGE
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
+using Eigen::Matrix##SizeSuffix##TypeSuffix; \
+using Eigen::Vector##SizeSuffix##TypeSuffix; \
+using Eigen::RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
+
+#define EIGEN_USING_ARRAY_TYPEDEFS \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
+
+
+#endif // EIGEN_ARRAY_H

Eigen/src/Core/ArrayBase.h

@@ -0,0 +1,239 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAYBASE_H
+#define EIGEN_ARRAYBASE_H
+
+template<typename ExpressionType> class MatrixWrapper;
+
+/** \class ArrayBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for all 1D and 2D array, and related expressions
+  *
+  * An array is similar to a dense vector or matrix. While matrices are mathematical
+  * objects with well defined linear algebra operators, an array is just a collection
+  * of scalar values arranged in a one or two dimensionnal fashion. As the main consequence,
+  * all operations applied to an array are performed coefficient wise. Furthermore,
+  * arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
+  * constructors allowing to easily write generic code working for both scalar values
+  * and arrays.
+  *
+  * This class is the base that is inherited by all array expression types.
+  *
+  * \tparam Derived is the derived type, e.g., an array or an expression type.
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
+  *
+  * \sa class MatrixBase, \ref TopicClassHierarchy
+  */
+template<typename Derived> class ArrayBase
+  : public DenseBase<Derived>
+{
+  public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** The base class for a given storage type. */
+    typedef ArrayBase StorageBaseType;
+
+    typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
+
+    using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+                typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
+
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    typedef DenseBase<Derived> Base;
+    using Base::RowsAtCompileTime;
+    using Base::ColsAtCompileTime;
+    using Base::SizeAtCompileTime;
+    using Base::MaxRowsAtCompileTime;
+    using Base::MaxColsAtCompileTime;
+    using Base::MaxSizeAtCompileTime;
+    using Base::IsVectorAtCompileTime;
+    using Base::Flags;
+    using Base::CoeffReadCost;
+
+    using Base::derived;
+    using Base::const_cast_derived;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::coeff;
+    using Base::coeffRef;
+    using Base::lazyAssign;
+    using Base::operator=;
+    using Base::operator+=;
+    using Base::operator-=;
+    using Base::operator*=;
+    using Base::operator/=;
+
+    typedef typename Base::CoeffReturnType CoeffReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
+      * exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
+      * reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either
+      * PlainObject or const PlainObject&.
+      */
+    typedef Array<typename internal::traits<Derived>::Scalar,
+                internal::traits<Derived>::RowsAtCompileTime,
+                internal::traits<Derived>::ColsAtCompileTime,
+                AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                internal::traits<Derived>::MaxRowsAtCompileTime,
+                internal::traits<Derived>::MaxColsAtCompileTime
+          > PlainObject;
+
+
+    /** \internal Represents a matrix with all coefficients equal to one another*/
+    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
+#   include "../plugins/CommonCwiseUnaryOps.h"
+#   include "../plugins/MatrixCwiseUnaryOps.h"
+#   include "../plugins/ArrayCwiseUnaryOps.h"
+#   include "../plugins/CommonCwiseBinaryOps.h"
+#   include "../plugins/MatrixCwiseBinaryOps.h"
+#   include "../plugins/ArrayCwiseBinaryOps.h"
+#   ifdef EIGEN_ARRAYBASE_PLUGIN
+#     include EIGEN_ARRAYBASE_PLUGIN
+#   endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+    /** Special case of the template operator=, in order to prevent the compiler
+      * from generating a default operator= (issue hit with g++ 4.1)
+      */
+    Derived& operator=(const ArrayBase& other)
+    {
+      return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+    }
+
+    Derived& operator+=(const Scalar& scalar)
+    { return *this = derived() + scalar; }
+    Derived& operator-=(const Scalar& scalar)
+    { return *this = derived() - scalar; }
+
+    template<typename OtherDerived>
+    Derived& operator+=(const ArrayBase<OtherDerived>& other);
+    template<typename OtherDerived>
+    Derived& operator-=(const ArrayBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    Derived& operator*=(const ArrayBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    Derived& operator/=(const ArrayBase<OtherDerived>& other);
+
+  public:
+    ArrayBase<Derived>& array() { return *this; }
+    const ArrayBase<Derived>& array() const { return *this; }
+
+    /** \returns an \link MatrixBase Matrix \endlink expression of this array
+      * \sa MatrixBase::array() */
+    MatrixWrapper<Derived> matrix() { return derived(); }
+    const MatrixWrapper<Derived> matrix() const { return derived(); }
+
+//     template<typename Dest>
+//     inline void evalTo(Dest& dst) const { dst = matrix(); }
+
+  protected:
+    ArrayBase() : Base() {}
+
+  private:
+    explicit ArrayBase(Index);
+    ArrayBase(Index,Index);
+    template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
+  protected:
+    // mixing arrays and matrices is not legal
+    template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
+    {EIGEN_STATIC_ASSERT(sizeof(typename OtherDerived::Scalar)==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);}
+    // mixing arrays and matrices is not legal
+    template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
+    {EIGEN_STATIC_ASSERT(sizeof(typename OtherDerived::Scalar)==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);}
+};
+
+/** replaces \c *this by \c *this - \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
+{
+  SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
+{
+  SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+/** replaces \c *this by \c *this * \a other coefficient wise.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
+{
+  SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+/** replaces \c *this by \c *this / \a other coefficient wise.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
+{
+  SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+#endif // EIGEN_ARRAYBASE_H

Eigen/src/Core/ArrayWrapper.h

@@ -0,0 +1,239 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAYWRAPPER_H
+#define EIGEN_ARRAYWRAPPER_H
+
+/** \class ArrayWrapper
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a mathematical vector or matrix as an array object
+  *
+  * This class is the return type of MatrixBase::array(), and most of the time
+  * this is the only way it is use.
+  *
+  * \sa MatrixBase::array(), class MatrixWrapper
+  */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ArrayWrapper<ExpressionType> >
+  : public traits<typename remove_all<typename ExpressionType::Nested>::type >
+{
+  typedef ArrayXpr XprKind;
+};
+}
+
+template<typename ExpressionType>
+class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
+{
+  public:
+    typedef ArrayBase<ArrayWrapper> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
+
+    typedef typename internal::conditional<
+                       internal::is_lvalue<ExpressionType>::value,
+                       Scalar,
+                       const Scalar
+                     >::type ScalarWithConstIfNotLvalue;
+
+    typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
+
+    inline ArrayWrapper(const ExpressionType& matrix) : m_expression(matrix) {}
+
+    inline Index rows() const { return m_expression.rows(); }
+    inline Index cols() const { return m_expression.cols(); }
+    inline Index outerStride() const { return m_expression.outerStride(); }
+    inline Index innerStride() const { return m_expression.innerStride(); }
+
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    inline const Scalar* data() const { return m_expression.data(); }
+
+    inline const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_expression.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return m_expression.coeff(index);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return m_expression.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return m_expression.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const { dst = m_expression; }
+
+  protected:
+    const NestedExpressionType m_expression;
+};
+
+/** \class MatrixWrapper
+  * \ingroup Core_Module
+  *
+  * \brief Expression of an array as a mathematical vector or matrix
+  *
+  * This class is the return type of ArrayBase::matrix(), and most of the time
+  * this is the only way it is use.
+  *
+  * \sa MatrixBase::matrix(), class ArrayWrapper
+  */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<MatrixWrapper<ExpressionType> >
+ : public traits<typename remove_all<typename ExpressionType::Nested>::type >
+{
+  typedef MatrixXpr XprKind;
+};
+}
+
+template<typename ExpressionType>
+class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
+{
+  public:
+    typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
+
+    typedef typename internal::conditional<
+                       internal::is_lvalue<ExpressionType>::value,
+                       Scalar,
+                       const Scalar
+                     >::type ScalarWithConstIfNotLvalue;
+
+    typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
+
+    inline MatrixWrapper(const ExpressionType& matrix) : m_expression(matrix) {}
+
+    inline Index rows() const { return m_expression.rows(); }
+    inline Index cols() const { return m_expression.cols(); }
+    inline Index outerStride() const { return m_expression.outerStride(); }
+    inline Index innerStride() const { return m_expression.innerStride(); }
+
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    inline const Scalar* data() const { return m_expression.data(); }
+
+    inline const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_expression.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_expression.derived().coeffRef(row, col);
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return m_expression.coeff(index);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return m_expression.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return m_expression.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+  protected:
+    const NestedExpressionType m_expression;
+};
+
+#endif // EIGEN_ARRAYWRAPPER_H

Eigen/src/Core/Assign.h

@@ -0,0 +1,593 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ASSIGN_H
+#define EIGEN_ASSIGN_H
+
+namespace internal {
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for traversal and unrolling       *
+***************************************************************************/
+
+template <typename Derived, typename OtherDerived>
+struct assign_traits
+{
+public:
+  enum {
+    DstIsAligned = Derived::Flags & AlignedBit,
+    DstHasDirectAccess = Derived::Flags & DirectAccessBit,
+    SrcIsAligned = OtherDerived::Flags & AlignedBit,
+    JointAlignment = bool(DstIsAligned) && bool(SrcIsAligned) ? Aligned : Unaligned
+  };
+
+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(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 Derived1, typename Derived2, int Index, int Stop>
+struct assign_DefaultTraversal_CompleteUnrolling
+{
+  enum {
+    outer = Index / Derived1::InnerSizeAtCompileTime,
+    inner = Index % Derived1::InnerSizeAtCompileTime
+  };
+
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    dst.copyCoeffByOuterInner(outer, inner, src);
+    assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_DefaultTraversal_InnerUnrolling
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src, int outer)
+  {
+    dst.copyCoeffByOuterInner(outer, Index, src);
+    assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src, outer);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &, int) {}
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_LinearTraversal_CompleteUnrolling
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    dst.copyCoeff(Index, src);
+    assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &) {}
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_innervec_CompleteUnrolling
+{
+  enum {
+    outer = Index / Derived1::InnerSizeAtCompileTime,
+    inner = Index % Derived1::InnerSizeAtCompileTime,
+    JointAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+  };
+
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    dst.template copyPacketByOuterInner<Derived2, Aligned, JointAlignment>(outer, inner, src);
+    assign_innervec_CompleteUnrolling<Derived1, Derived2,
+      Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_innervec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct assign_innervec_InnerUnrolling
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src, int outer)
+  {
+    dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, Index, src);
+    assign_innervec_InnerUnrolling<Derived1, Derived2,
+      Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src, outer);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct assign_innervec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &, int) {}
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Derived1, typename Derived2,
+         int Traversal = assign_traits<Derived1, Derived2>::Traversal,
+         int Unrolling = assign_traits<Derived1, Derived2>::Unrolling>
+struct assign_impl;
+
+/************************
+*** Default traversal ***
+************************/
+
+template<typename Derived1, typename Derived2, int Unrolling>
+struct assign_impl<Derived1, Derived2, InvalidTraversal, Unrolling>
+{
+  inline static void run(Derived1 &, const Derived2 &) { }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, NoUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index innerSize = dst.innerSize();
+    const Index outerSize = dst.outerSize();
+    for(Index outer = 0; outer < outerSize; ++outer)
+      for(Index inner = 0; inner < innerSize; ++inner)
+        dst.copyCoeffByOuterInner(outer, inner, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+      ::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, DefaultTraversal, InnerUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index outerSize = dst.outerSize();
+    for(Index outer = 0; outer < outerSize; ++outer)
+      assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
+        ::run(dst, src, outer);
+  }
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, LinearTraversal, NoUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index size = dst.size();
+    for(Index i = 0; i < size; ++i)
+      dst.copyCoeff(i, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, LinearTraversal, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+      ::run(dst, src);
+  }
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, NoUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index innerSize = dst.innerSize();
+    const Index outerSize = dst.outerSize();
+    const Index packetSize = packet_traits<typename Derived1::Scalar>::size;
+    for(Index outer = 0; outer < outerSize; ++outer)
+      for(Index inner = 0; inner < innerSize; inner+=packetSize)
+        dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, inner, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+      ::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, InnerUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index outerSize = dst.outerSize();
+    for(Index outer = 0; outer < outerSize; ++outer)
+      assign_innervec_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
+        ::run(dst, src, outer);
+  }
+};
+
+/***************************
+*** Linear vectorization ***
+***************************/
+
+template <bool IsAligned = false>
+struct unaligned_assign_impl
+{
+  template <typename Derived, typename OtherDerived>
+  static EIGEN_STRONG_INLINE void run(const Derived&, OtherDerived&, typename Derived::Index, typename Derived::Index) {}
+};
+
+template <>
+struct unaligned_assign_impl<false>
+{
+  // MSVC must not inline this functions. If it does, it fails to optimize the
+  // packet access path.
+#ifdef _MSC_VER
+  template <typename Derived, typename OtherDerived>
+  static EIGEN_DONT_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
+#else
+  template <typename Derived, typename OtherDerived>
+  static EIGEN_STRONG_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
+#endif
+  {
+    for (typename Derived::Index index = start; index < end; ++index)
+      dst.copyCoeff(index, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, NoUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const Index size = dst.size();
+    typedef packet_traits<typename Derived1::Scalar> PacketTraits;
+    enum {
+      packetSize = PacketTraits::size,
+      dstAlignment = PacketTraits::AlignedOnScalar ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
+      srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+    };
+    const Index alignedStart = assign_traits<Derived1,Derived2>::DstIsAligned ? 0
+                             : first_aligned(&dst.coeffRef(0), size);
+    const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
+
+    unaligned_assign_impl<assign_traits<Derived1,Derived2>::DstIsAligned!=0>::run(src,dst,0,alignedStart);
+
+    for(Index index = alignedStart; index < alignedEnd; index += packetSize)
+    {
+      dst.template copyPacket<Derived2, dstAlignment, srcAlignment>(index, src);
+    }
+
+    unaligned_assign_impl<>::run(src,dst,alignedEnd,size);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, CompleteUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    enum { size = Derived1::SizeAtCompileTime,
+           packetSize = packet_traits<typename Derived1::Scalar>::size,
+           alignedSize = (size/packetSize)*packetSize };
+
+    assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, alignedSize>::run(dst, src);
+    assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, alignedSize, size>::run(dst, src);
+  }
+};
+
+/**************************
+*** Slice vectorization ***
+***************************/
+
+template<typename Derived1, typename Derived2>
+struct assign_impl<Derived1, Derived2, SliceVectorizedTraversal, NoUnrolling>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    typedef packet_traits<typename Derived1::Scalar> PacketTraits;
+    enum {
+      packetSize = PacketTraits::size,
+      alignable = PacketTraits::AlignedOnScalar,
+      dstAlignment = alignable ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
+      srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
+    };
+    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
+                       : first_aligned(&dst.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)
+        dst.copyCoeffByOuterInner(outer, inner, src);
+
+      // do the vectorizable part of the assignment
+      for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize)
+        dst.template copyPacketByOuterInner<Derived2, dstAlignment, Unaligned>(outer, inner, src);
+
+      // do the non-vectorizable part of the assignment
+      for(Index inner = alignedEnd; inner<innerSize ; ++inner)
+        dst.copyCoeffByOuterInner(outer, inner, src);
+
+      alignedStart = std::min<Index>((alignedStart+alignedStep)%packetSize, innerSize);
+    }
+  }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Part 4 : implementation of DenseBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
+  ::lazyAssign(const DenseBase<OtherDerived>& other)
+{
+  enum{
+    SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
+  };
+
+  EIGEN_STATIC_ASSERT_LVALUE(Derived)
+  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+  EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+#ifdef EIGEN_DEBUG_ASSIGN
+  internal::assign_traits<Derived, OtherDerived>::debug();
+#endif
+  eigen_assert(rows() == other.rows() && cols() == other.cols());
+  internal::assign_impl<Derived, OtherDerived, int(SameType) ? int(internal::assign_traits<Derived, OtherDerived>::Traversal)
+                                                       : int(InvalidTraversal)>::run(derived(),other.derived());
+#ifndef EIGEN_NO_DEBUG
+  checkTransposeAliasing(other.derived());
+#endif
+  return derived();
+}
+
+namespace internal {
+
+template<typename Derived, typename OtherDerived,
+         bool EvalBeforeAssigning = (int(OtherDerived::Flags) & EvalBeforeAssigningBit) != 0,
+         bool NeedToTranspose = Derived::IsVectorAtCompileTime
+                && OtherDerived::IsVectorAtCompileTime
+                && ((int(Derived::RowsAtCompileTime) == 1 && int(OtherDerived::ColsAtCompileTime) == 1)
+                      |  // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
+                         // revert to || as soon as not needed anymore.
+                    (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> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,true,false> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.eval()); }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,false,true> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose()); }
+};
+template<typename Derived, typename OtherDerived>
+struct assign_selector<Derived,OtherDerived,true,true> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose().eval()); }
+};
+
+} // end namespace internal
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+  return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
+{
+  return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
+{
+  return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+  return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
+{
+  other.derived().evalTo(derived());
+  return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+  other.evalTo(derived());
+  return derived();
+}
+
+#endif // EIGEN_ASSIGN_H

Eigen/src/Core/BandMatrix.h

@@ -0,0 +1,346 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_BANDMATRIX_H
+#define EIGEN_BANDMATRIX_H
+
+namespace internal {
+
+
+template<typename Derived>
+class BandMatrixBase : public EigenBase<Derived>
+{
+  public:
+
+    enum {
+      Flags = internal::traits<Derived>::Flags,
+      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+      Supers = internal::traits<Derived>::Supers,
+      Subs   = internal::traits<Derived>::Subs,
+      Options = internal::traits<Derived>::Options
+    };
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
+    typedef typename DenseMatrixType::Index Index;
+    typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
+    typedef EigenBase<Derived> Base;
+
+  protected:
+    enum {
+      DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
+                            ? 1 + Supers + Subs
+                            : Dynamic,
+      SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
+    };
+
+  public:
+    
+    using Base::derived;
+    using Base::rows;
+    using Base::cols;
+
+    /** \returns the number of super diagonals */
+    inline Index supers() const { return derived().supers(); }
+
+    /** \returns the number of sub diagonals */
+    inline Index subs() const { return derived().subs(); }
+    
+    /** \returns an expression of the underlying coefficient matrix */
+    inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
+    
+    /** \returns an expression of the underlying coefficient matrix */
+    inline CoefficientsType& coeffs() { return derived().coeffs(); }
+
+    /** \returns a vector expression of the \a i -th column,
+      * only the meaningful part is returned.
+      * \warning the internal storage must be column major. */
+    inline Block<CoefficientsType,Dynamic,1> col(Index i)
+    {
+      EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+      Index start = 0;
+      Index len = coeffs().rows();
+      if (i<=supers())
+      {
+        start = supers()-i;
+        len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
+      }
+      else if (i>=rows()-subs())
+        len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
+      return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
+    }
+
+    /** \returns a vector expression of the main diagonal */
+    inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
+    { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+    /** \returns a vector expression of the main diagonal (const version) */
+    inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
+    { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+    template<int Index> struct DiagonalIntReturnType {
+      enum {
+        ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),
+        Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
+        ActualIndex = ReturnOpposite ? -Index : Index,
+        DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
+                     ? Dynamic
+                     : (ActualIndex<0
+                     ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
+                     : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
+      };
+      typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
+      typedef typename internal::conditional<Conjugate,
+                 CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
+                 BuildType>::type Type;
+    };
+
+    /** \returns a vector expression of the \a N -th sub or super diagonal */
+    template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
+    {
+      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+    }
+
+    /** \returns a vector expression of the \a N -th sub or super diagonal */
+    template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
+    {
+      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+    }
+
+    /** \returns a vector expression of the \a i -th sub or super diagonal */
+    inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
+    {
+      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+      return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+    }
+
+    /** \returns a vector expression of the \a i -th sub or super diagonal */
+    inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
+    {
+      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+      return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+    }
+    
+    template<typename Dest> inline void evalTo(Dest& dst) const
+    {
+      dst.resize(rows(),cols());
+      dst.setZero();
+      dst.diagonal() = diagonal();
+      for (Index i=1; i<=supers();++i)
+        dst.diagonal(i) = diagonal(i);
+      for (Index i=1; i<=subs();++i)
+        dst.diagonal(-i) = diagonal(-i);
+    }
+
+    DenseMatrixType toDenseMatrix() const
+    {
+      DenseMatrixType res(rows(),cols());
+      evalTo(res);
+      return res;
+    }
+
+  protected:
+
+    inline Index diagonalLength(Index i) const
+    { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
+};
+
+/**
+  * \class BandMatrix
+  * \ingroup Core_Module
+  *
+  * \brief Represents a rectangular matrix with a banded storage
+  *
+  * \param _Scalar Numeric type, i.e. float, double, int
+  * \param Rows Number of rows, or \b Dynamic
+  * \param Cols Number of columns, or \b Dynamic
+  * \param Supers Number of super diagonal
+  * \param Subs Number of sub diagonal
+  * \param _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
+  *                 The former controls \ref TopicStorageOrders "storage order", and defaults to
+  *                 column-major. The latter controls whether the matrix represents a selfadjoint 
+  *                 matrix in which case either Supers of Subs have to be null.
+  *
+  * \sa class TridiagonalMatrix
+  */
+
+template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
+struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+  typedef _Scalar Scalar;
+  typedef Dense StorageKind;
+  typedef DenseIndex Index;
+  enum {
+    CoeffReadCost = NumTraits<Scalar>::ReadCost,
+    RowsAtCompileTime = _Rows,
+    ColsAtCompileTime = _Cols,
+    MaxRowsAtCompileTime = _Rows,
+    MaxColsAtCompileTime = _Cols,
+    Flags = LvalueBit,
+    Supers = _Supers,
+    Subs = _Subs,
+    Options = _Options,
+    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+  };
+  typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;
+};
+
+template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
+class BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >
+{
+  public:
+
+    typedef typename internal::traits<BandMatrix>::Scalar Scalar;
+    typedef typename internal::traits<BandMatrix>::Index Index;
+    typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
+
+    inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
+      : m_coeffs(1+supers+subs,cols),
+        m_rows(rows), m_supers(supers), m_subs(subs)
+    {
+    }
+
+    /** \returns the number of columns */
+    inline Index rows() const { return m_rows.value(); }
+
+    /** \returns the number of rows */
+    inline Index cols() const { return m_coeffs.cols(); }
+
+    /** \returns the number of super diagonals */
+    inline Index supers() const { return m_supers.value(); }
+
+    /** \returns the number of sub diagonals */
+    inline Index subs() const { return m_subs.value(); }
+
+    inline const CoefficientsType& coeffs() const { return m_coeffs; }
+    inline CoefficientsType& coeffs() { return m_coeffs; }
+
+  protected:
+
+    CoefficientsType m_coeffs;
+    internal::variable_if_dynamic<Index, Rows>   m_rows;
+    internal::variable_if_dynamic<Index, Supers> m_supers;
+    internal::variable_if_dynamic<Index, Subs>   m_subs;
+};
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+class BandMatrixWrapper;
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+  typedef typename _CoefficientsType::Scalar Scalar;
+  typedef typename _CoefficientsType::StorageKind StorageKind;
+  typedef typename _CoefficientsType::Index Index;
+  enum {
+    CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
+    RowsAtCompileTime = _Rows,
+    ColsAtCompileTime = _Cols,
+    MaxRowsAtCompileTime = _Rows,
+    MaxColsAtCompileTime = _Cols,
+    Flags = LvalueBit,
+    Supers = _Supers,
+    Subs = _Subs,
+    Options = _Options,
+    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+  };
+  typedef _CoefficientsType CoefficientsType;
+};
+
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
+class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
+{
+  public:
+
+    typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
+    typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
+    typedef typename internal::traits<BandMatrixWrapper>::Index Index;
+
+    inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
+      : m_coeffs(coeffs),
+        m_rows(rows), m_supers(supers), m_subs(subs)
+    {
+      EIGEN_UNUSED_VARIABLE(cols);
+      //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
+    }
+
+    /** \returns the number of columns */
+    inline Index rows() const { return m_rows.value(); }
+
+    /** \returns the number of rows */
+    inline Index cols() const { return m_coeffs.cols(); }
+
+    /** \returns the number of super diagonals */
+    inline Index supers() const { return m_supers.value(); }
+
+    /** \returns the number of sub diagonals */
+    inline Index subs() const { return m_subs.value(); }
+
+    inline const CoefficientsType& coeffs() const { return m_coeffs; }
+
+  protected:
+
+    const CoefficientsType& m_coeffs;
+    internal::variable_if_dynamic<Index, _Rows>   m_rows;
+    internal::variable_if_dynamic<Index, _Supers> m_supers;
+    internal::variable_if_dynamic<Index, _Subs>   m_subs;
+};
+
+/**
+  * \class TridiagonalMatrix
+  * \ingroup Core_Module
+  *
+  * \brief Represents a tridiagonal matrix with a compact banded storage
+  *
+  * \param _Scalar Numeric type, i.e. float, double, int
+  * \param Size Number of rows and cols, or \b Dynamic
+  * \param _Options Can be 0 or \b SelfAdjoint
+  *
+  * \sa class BandMatrix
+  */
+template<typename Scalar, int Size, int Options>
+class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
+{
+    typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
+    typedef typename Base::Index Index;
+  public:
+    TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
+
+    inline typename Base::template DiagonalIntReturnType<1>::Type super()
+    { return Base::template diagonal<1>(); }
+    inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
+    { return Base::template diagonal<1>(); }
+    inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
+    { return Base::template diagonal<-1>(); }
+    inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
+    { return Base::template diagonal<-1>(); }
+  protected:
+};
+
+} // end namespace internal
+
+#endif // EIGEN_BANDMATRIX_H

Eigen/src/Core/Block.h

@@ -0,0 +1,349 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_BLOCK_H
+#define EIGEN_BLOCK_H
+
+/** \class Block
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a fixed-size or dynamic-size block
+  *
+  * \param XprType the type of the expression in which we are taking a block
+  * \param BlockRows the number of rows of the block we are taking at compile time (optional)
+  * \param BlockCols the number of columns of the block we are taking at compile time (optional)
+  * \param _DirectAccessStatus \internal used for partial specialization
+  *
+  * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
+  * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
+  * most of the time this is the only way it is used.
+  *
+  * However, if you want to directly maniputate block expressions,
+  * for instance if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * Here is an example illustrating the dynamic case:
+  * \include class_Block.cpp
+  * Output: \verbinclude class_Block.out
+  *
+  * \note Even though this expression has dynamic size, in the case where \a XprType
+  * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+  * it does not cause a dynamic memory allocation.
+  *
+  * Here is an example illustrating the fixed-size case:
+  * \include class_FixedBlock.cpp
+  * Output: \verbinclude class_FixedBlock.out
+  *
+  * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
+  */
+
+namespace internal {
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess>
+struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel, HasDirectAccess> > : traits<XprType>
+{
+  typedef typename traits<XprType>::Scalar Scalar;
+  typedef typename traits<XprType>::StorageKind StorageKind;
+  typedef typename traits<XprType>::XprKind XprKind;
+  typedef typename nested<XprType>::type XprTypeNested;
+  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
+  enum{
+    MatrixRows = traits<XprType>::RowsAtCompileTime,
+    MatrixCols = traits<XprType>::ColsAtCompileTime,
+    RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
+    ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
+    MaxRowsAtCompileTime = BlockRows==0 ? 0
+                         : RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
+                         : int(traits<XprType>::MaxRowsAtCompileTime),
+    MaxColsAtCompileTime = BlockCols==0 ? 0
+                         : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
+                         : int(traits<XprType>::MaxColsAtCompileTime),
+    XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
+    IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+               : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+               : XprTypeIsRowMajor,
+    HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
+    InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+    InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
+                             ? int(inner_stride_at_compile_time<XprType>::ret)
+                             : int(outer_stride_at_compile_time<XprType>::ret),
+    OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
+                             ? int(outer_stride_at_compile_time<XprType>::ret)
+                             : int(inner_stride_at_compile_time<XprType>::ret),
+    MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits<Scalar>::size) == 0)
+                       && (InnerStrideAtCompileTime == 1)
+                        ? PacketAccessBit : 0,
+    MaskAlignedBit = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
+    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+    FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
+    FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
+    Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) |
+                                        DirectAccessBit |
+                                        MaskPacketAccessBit |
+                                        MaskAlignedBit),
+    Flags = Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit
+  };
+};
+}
+
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class Block
+  : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel, HasDirectAccess> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<Block>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Block)
+
+    class InnerIterator;
+
+    /** Column or Row constructor
+      */
+    inline Block(XprType& xpr, Index i)
+      : m_xpr(xpr),
+        // It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
+        // and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
+        // all other cases are invalid.
+        // The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
+        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+        m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+        m_blockCols(BlockCols==1 ? 1 : xpr.cols())
+    {
+      eigen_assert( (i>=0) && (
+          ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
+        ||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
+    }
+
+    /** Fixed-size constructor
+      */
+    inline Block(XprType& xpr, Index startRow, Index startCol)
+      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
+        m_blockRows(BlockRows), m_blockCols(BlockCols)
+    {
+      EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+      eigen_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= xpr.rows()
+             && startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= xpr.cols());
+    }
+
+    /** Dynamic-size constructor
+      */
+    inline Block(XprType& xpr,
+          Index startRow, Index startCol,
+          Index blockRows, Index blockCols)
+      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
+                          m_blockRows(blockRows), m_blockCols(blockCols)
+    {
+      eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+          && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+      eigen_assert(startRow >= 0 && blockRows >= 0 && startRow + blockRows <= xpr.rows()
+          && startCol >= 0 && blockCols >= 0 && startCol + blockCols <= xpr.cols());
+    }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+    inline Index rows() const { return m_blockRows.value(); }
+    inline Index cols() const { return m_blockCols.value(); }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(XprType)
+      return m_xpr.const_cast_derived()
+               .coeffRef(row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_xpr.derived()
+               .coeffRef(row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_xpr.coeff(row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(XprType)
+      return m_xpr.const_cast_derived()
+             .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                       m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_xpr.const_cast_derived()
+             .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                       m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return m_xpr
+             .coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                    m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(Index row, Index col) const
+    {
+      return m_xpr.template packet<Unaligned>
+              (row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_xpr.const_cast_derived().template writePacket<Unaligned>
+              (row + m_startRow.value(), col + m_startCol.value(), x);
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(Index index) const
+    {
+      return m_xpr.template packet<Unaligned>
+              (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+               m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_xpr.const_cast_derived().template writePacket<Unaligned>
+         (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+          m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), x);
+    }
+
+    #ifdef EIGEN_PARSED_BY_DOXYGEN
+    /** \sa MapBase::data() */
+    inline const Scalar* data() const;
+    inline Index innerStride() const;
+    inline Index outerStride() const;
+    #endif
+
+  protected:
+
+    const typename XprType::Nested m_xpr;
+    const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+    const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;
+    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;
+};
+
+/** \internal */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class Block<XprType,BlockRows,BlockCols, InnerPanel,true>
+  : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel, true> >
+{
+  public:
+
+    typedef MapBase<Block> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Block)
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+    /** Column or Row constructor
+      */
+    inline Block(XprType& xpr, Index i)
+      : Base(internal::const_cast_ptr(&xpr.coeffRef(
+              (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0,
+              (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)),
+             BlockRows==1 ? 1 : xpr.rows(),
+             BlockCols==1 ? 1 : xpr.cols()),
+        m_xpr(xpr)
+    {
+      eigen_assert( (i>=0) && (
+          ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
+        ||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
+      init();
+    }
+
+    /** Fixed-size constructor
+      */
+    inline Block(XprType& xpr, Index startRow, Index startCol)
+      : Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol))), m_xpr(xpr)
+    {
+      eigen_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= xpr.rows()
+             && startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= xpr.cols());
+      init();
+    }
+
+    /** Dynamic-size constructor
+      */
+    inline Block(XprType& xpr,
+          Index startRow, Index startCol,
+          Index blockRows, Index blockCols)
+      : Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol)), blockRows, blockCols),
+        m_xpr(xpr)
+    {
+      eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+             && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+      eigen_assert(startRow >= 0 && blockRows >= 0 && startRow + blockRows <= xpr.rows()
+             && startCol >= 0 && blockCols >= 0 && startCol + blockCols <= xpr.cols());
+      init();
+    }
+
+    /** \sa MapBase::innerStride() */
+    inline Index innerStride() const
+    {
+      return internal::traits<Block>::HasSameStorageOrderAsXprType
+             ? m_xpr.innerStride()
+             : m_xpr.outerStride();
+    }
+
+    /** \sa MapBase::outerStride() */
+    inline Index outerStride() const
+    {
+      return m_outerStride;
+    }
+
+  #ifndef __SUNPRO_CC
+  // FIXME sunstudio is not friendly with the above friend...
+  // META-FIXME there is no 'friend' keyword around here. Is this obsolete?
+  protected:
+  #endif
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal used by allowAligned() */
+    inline Block(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
+      : Base(data, blockRows, blockCols), m_xpr(xpr)
+    {
+      init();
+    }
+    #endif
+
+  protected:
+    void init()
+    {
+      m_outerStride = internal::traits<Block>::HasSameStorageOrderAsXprType
+                    ? m_xpr.outerStride()
+                    : m_xpr.innerStride();
+    }
+
+    const typename XprType::Nested m_xpr;
+    Index m_outerStride;
+};
+
+
+#endif // EIGEN_BLOCK_H

Eigen/src/Core/BooleanRedux.h

@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ALLANDANY_H
+#define EIGEN_ALLANDANY_H
+
+namespace internal {
+
+template<typename Derived, int UnrollCount>
+struct all_unroller
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static bool run(const Derived &mat)
+  {
+    return all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
+  }
+};
+
+template<typename Derived>
+struct all_unroller<Derived, 1>
+{
+  inline static bool run(const Derived &mat) { return mat.coeff(0, 0); }
+};
+
+template<typename Derived>
+struct all_unroller<Derived, Dynamic>
+{
+  inline static bool run(const Derived &) { return false; }
+};
+
+template<typename Derived, int UnrollCount>
+struct any_unroller
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static bool run(const Derived &mat)
+  {
+    return any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
+  }
+};
+
+template<typename Derived>
+struct any_unroller<Derived, 1>
+{
+  inline static bool run(const Derived &mat) { return mat.coeff(0, 0); }
+};
+
+template<typename Derived>
+struct any_unroller<Derived, Dynamic>
+{
+  inline static bool run(const Derived &) { return false; }
+};
+
+} // end namespace internal
+
+/** \returns true if all coefficients are true
+  *
+  * Example: \include MatrixBase_all.cpp
+  * Output: \verbinclude MatrixBase_all.out
+  *
+  * \sa any(), Cwise::operator<()
+  */
+template<typename Derived>
+inline bool DenseBase<Derived>::all() const
+{
+  enum {
+    unroll = SizeAtCompileTime != Dynamic
+          && CoeffReadCost != Dynamic
+          && NumTraits<Scalar>::AddCost != Dynamic
+          && SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
+  };
+  if(unroll)
+    return internal::all_unroller<Derived,
+                           unroll ? int(SizeAtCompileTime) : Dynamic
+     >::run(derived());
+  else
+  {
+    for(Index j = 0; j < cols(); ++j)
+      for(Index i = 0; i < rows(); ++i)
+        if (!coeff(i, j)) return false;
+    return true;
+  }
+}
+
+/** \returns true if at least one coefficient is true
+  *
+  * \sa all()
+  */
+template<typename Derived>
+inline bool DenseBase<Derived>::any() const
+{
+  enum {
+    unroll = SizeAtCompileTime != Dynamic
+          && CoeffReadCost != Dynamic
+          && NumTraits<Scalar>::AddCost != Dynamic
+          && SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
+  };
+  if(unroll)
+    return internal::any_unroller<Derived,
+                           unroll ? int(SizeAtCompileTime) : Dynamic
+           >::run(derived());
+  else
+  {
+    for(Index j = 0; j < cols(); ++j)
+      for(Index i = 0; i < rows(); ++i)
+        if (coeff(i, j)) return true;
+    return false;
+  }
+}
+
+/** \returns the number of coefficients which evaluate to true
+  *
+  * \sa all(), any()
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::Index DenseBase<Derived>::count() const
+{
+  return derived().template cast<bool>().template cast<Index>().sum();
+}
+
+#endif // EIGEN_ALLANDANY_H

Eigen/src/Core/CMakeLists.txt

@@ -0,0 +1,10 @@
+FILE(GLOB Eigen_Core_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core COMPONENT Devel
+  )
+
+ADD_SUBDIRECTORY(products)
+ADD_SUBDIRECTORY(util)
+ADD_SUBDIRECTORY(arch)

Eigen/src/Core/CommaInitializer.h

@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COMMAINITIALIZER_H
+#define EIGEN_COMMAINITIALIZER_H
+
+/** \class CommaInitializer
+  * \ingroup Core_Module
+  *
+  * \brief Helper class used by the comma initializer operator
+  *
+  * This class is internally used to implement the comma initializer feature. It is
+  * the return type of MatrixBase::operator<<, and most of the time this is the only
+  * way it is used.
+  *
+  * \sa \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
+  */
+template<typename XprType>
+struct CommaInitializer
+{
+  typedef typename XprType::Scalar Scalar;
+  typedef typename XprType::Index Index;
+
+  inline CommaInitializer(XprType& xpr, const Scalar& s)
+    : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
+  {
+    m_xpr.coeffRef(0,0) = s;
+  }
+
+  template<typename OtherDerived>
+  inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
+    : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
+  {
+    m_xpr.block(0, 0, other.rows(), other.cols()) = other;
+  }
+
+  /* inserts a scalar value in the target matrix */
+  CommaInitializer& operator,(const Scalar& s)
+  {
+    if (m_col==m_xpr.cols())
+    {
+      m_row+=m_currentBlockRows;
+      m_col = 0;
+      m_currentBlockRows = 1;
+      eigen_assert(m_row<m_xpr.rows()
+        && "Too many rows passed to comma initializer (operator<<)");
+    }
+    eigen_assert(m_col<m_xpr.cols()
+      && "Too many coefficients passed to comma initializer (operator<<)");
+    eigen_assert(m_currentBlockRows==1);
+    m_xpr.coeffRef(m_row, m_col++) = s;
+    return *this;
+  }
+
+  /* inserts a matrix expression in the target matrix */
+  template<typename OtherDerived>
+  CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
+  {
+    if (m_col==m_xpr.cols())
+    {
+      m_row+=m_currentBlockRows;
+      m_col = 0;
+      m_currentBlockRows = other.rows();
+      eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
+        && "Too many rows passed to comma initializer (operator<<)");
+    }
+    eigen_assert(m_col<m_xpr.cols()
+      && "Too many coefficients passed to comma initializer (operator<<)");
+    eigen_assert(m_currentBlockRows==other.rows());
+    if (OtherDerived::SizeAtCompileTime != Dynamic)
+      m_xpr.template block<OtherDerived::RowsAtCompileTime != Dynamic ? OtherDerived::RowsAtCompileTime : 1,
+                              OtherDerived::ColsAtCompileTime != Dynamic ? OtherDerived::ColsAtCompileTime : 1>
+                    (m_row, m_col) = other;
+    else
+      m_xpr.block(m_row, m_col, other.rows(), other.cols()) = other;
+    m_col += other.cols();
+    return *this;
+  }
+
+  inline ~CommaInitializer()
+  {
+    eigen_assert((m_row+m_currentBlockRows) == m_xpr.rows()
+         && m_col == m_xpr.cols()
+         && "Too few coefficients passed to comma initializer (operator<<)");
+  }
+
+  /** \returns the built matrix once all its coefficients have been set.
+    * Calling finished is 100% optional. Its purpose is to write expressions
+    * like this:
+    * \code
+    * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
+    * \endcode
+    */
+  inline XprType& finished() { return m_xpr; }
+
+  XprType& m_xpr;   // target expression
+  Index m_row;              // current row id
+  Index m_col;              // current col id
+  Index m_currentBlockRows; // current block height
+};
+
+/** \anchor MatrixBaseCommaInitRef
+  * Convenient operator to set the coefficients of a matrix.
+  *
+  * The coefficients must be provided in a row major order and exactly match
+  * the size of the matrix. Otherwise an assertion is raised.
+  *
+  * Example: \include MatrixBase_set.cpp
+  * Output: \verbinclude MatrixBase_set.out
+  *
+  * \sa CommaInitializer::finished(), class CommaInitializer
+  */
+template<typename Derived>
+inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)
+{
+  return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
+}
+
+/** \sa operator<<(const Scalar&) */
+template<typename Derived>
+template<typename OtherDerived>
+inline CommaInitializer<Derived>
+DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
+{
+  return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
+}
+
+#endif // EIGEN_COMMAINITIALIZER_H

Eigen/src/Core/CwiseBinaryOp.h

@@ -0,0 +1,240 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_BINARY_OP_H
+#define EIGEN_CWISE_BINARY_OP_H
+
+/** \class CwiseBinaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
+  *
+  * \param BinaryOp template functor implementing the operator
+  * \param Lhs the type of the left-hand side
+  * \param Rhs the type of the right-hand side
+  *
+  * This class represents an expression  where a coefficient-wise binary operator is applied to two expressions.
+  * It is the return type of binary operators, by which we mean only those binary operators where
+  * both the left-hand side and the right-hand side are Eigen expressions.
+  * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
+  *
+  * Most of the time, this is the only way that it is used, so you typically don't have to name
+  * CwiseBinaryOp types explicitly.
+  *
+  * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
+  */
+
+namespace internal {
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+  // we must not inherit from traits<Lhs> since it has
+  // the potential to cause problems with MSVC
+  typedef typename remove_all<Lhs>::type Ancestor;
+  typedef typename traits<Ancestor>::XprKind XprKind;
+  enum {
+    RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
+    ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
+    MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
+  };
+
+  // even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
+  // we still want to handle the case when the result type is different.
+  typedef typename result_of<
+                     BinaryOp(
+                       typename Lhs::Scalar,
+                       typename Rhs::Scalar
+                     )
+                   >::type Scalar;
+  typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
+                                           typename traits<Rhs>::StorageKind>::ret StorageKind;
+  typedef typename promote_index_type<typename traits<Lhs>::Index,
+                                         typename traits<Rhs>::Index>::type Index;
+  typedef typename Lhs::Nested LhsNested;
+  typedef typename Rhs::Nested RhsNested;
+  typedef typename remove_reference<LhsNested>::type _LhsNested;
+  typedef typename remove_reference<RhsNested>::type _RhsNested;
+  enum {
+    LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+    RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+    SameType = is_same<typename _LhsNested::Scalar,typename _RhsNested::Scalar>::value,
+    StorageOrdersAgree = (int(Lhs::Flags)&RowMajorBit)==(int(Rhs::Flags)&RowMajorBit),
+    Flags0 = (int(LhsFlags) | int(RhsFlags)) & (
+        HereditaryBits
+      | (int(LhsFlags) & int(RhsFlags) &
+           ( AlignedBit
+           | (StorageOrdersAgree ? LinearAccessBit : 0)
+           | (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)
+           )
+        )
+     ),
+    Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
+    CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + functor_traits<BinaryOp>::Cost
+  };
+};
+} // end namespace internal
+
+// we require Lhs and Rhs to have the same scalar type. Currently there is no example of a binary functor
+// that would take two operands of different types. If there were such an example, then this check should be
+// moved to the BinaryOp functors, on a per-case basis. This would however require a change in the BinaryOp functors, as
+// currently they take only one typename Scalar template parameter.
+// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
+// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
+// add together a float matrix and a double matrix.
+#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
+  EIGEN_STATIC_ASSERT((internal::functor_allows_mixing_real_and_complex<BINOP>::ret \
+                        ? int(internal::is_same<typename NumTraits<LHS>::Real, typename NumTraits<RHS>::Real>::value) \
+                        : 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)
+
+template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
+class CwiseBinaryOpImpl;
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOp : internal::no_assignment_operator,
+  public CwiseBinaryOpImpl<
+          BinaryOp, Lhs, Rhs,
+          typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
+                                           typename internal::traits<Rhs>::StorageKind>::ret>
+{
+  public:
+
+    typedef typename CwiseBinaryOpImpl<
+        BinaryOp, Lhs, Rhs,
+        typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
+                                         typename internal::traits<Rhs>::StorageKind>::ret>::Base Base;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
+
+    typedef typename internal::nested<Lhs>::type LhsNested;
+    typedef typename internal::nested<Rhs>::type RhsNested;
+    typedef typename internal::remove_reference<LhsNested>::type _LhsNested;
+    typedef typename internal::remove_reference<RhsNested>::type _RhsNested;
+
+    EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& lhs, const Rhs& rhs, const BinaryOp& func = BinaryOp())
+      : m_lhs(lhs), m_rhs(rhs), m_functor(func)
+    {
+      EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);
+      // require the sizes to match
+      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
+      eigen_assert(lhs.rows() == rhs.rows() && lhs.cols() == rhs.cols());
+    }
+
+    EIGEN_STRONG_INLINE Index rows() const {
+      // return the fixed size type if available to enable compile time optimizations
+      if (internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic)
+        return m_rhs.rows();
+      else
+        return m_lhs.rows();
+    }
+    EIGEN_STRONG_INLINE Index cols() const {
+      // return the fixed size type if available to enable compile time optimizations
+      if (internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic)
+        return m_rhs.cols();
+      else
+        return m_lhs.cols();
+    }
+
+    /** \returns the left hand side nested expression */
+    const _LhsNested& lhs() const { return m_lhs; }
+    /** \returns the right hand side nested expression */
+    const _RhsNested& rhs() const { return m_rhs; }
+    /** \returns the functor representing the binary operation */
+    const BinaryOp& functor() const { return m_functor; }
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+    const BinaryOp m_functor;
+};
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Dense>
+  : public internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
+{
+    typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;
+  public:
+
+    typedef typename internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE( Derived )
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+    {
+      return derived().functor()(derived().lhs().coeff(row, col),
+                                 derived().rhs().coeff(row, col));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+    {
+      return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(row, col),
+                                          derived().rhs().template packet<LoadMode>(row, col));
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+    {
+      return derived().functor()(derived().lhs().coeff(index),
+                                 derived().rhs().coeff(index));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+    {
+      return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(index),
+                                          derived().rhs().template packet<LoadMode>(index));
+    }
+};
+
+/** replaces \c *this by \c *this - \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
+{
+  SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
+{
+  SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
+  tmp = other.derived();
+  return derived();
+}
+
+#endif // EIGEN_CWISE_BINARY_OP_H

Eigen/src/Core/CwiseNullaryOp.h

@@ -0,0 +1,851 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_NULLARY_OP_H
+#define EIGEN_CWISE_NULLARY_OP_H
+
+/** \class CwiseNullaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression of a matrix where all coefficients are defined by a functor
+  *
+  * \param NullaryOp template functor implementing the operator
+  * \param PlainObjectType the underlying plain matrix/array type
+  *
+  * This class represents an expression of a generic nullary operator.
+  * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
+  * and most of the time this is the only way it is used.
+  *
+  * However, if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
+  */
+
+namespace internal {
+template<typename NullaryOp, typename PlainObjectType>
+struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
+{
+  enum {
+    Flags = (traits<PlainObjectType>::Flags
+      & (  HereditaryBits
+         | (functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
+         | (functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
+      | (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
+    CoeffReadCost = functor_traits<NullaryOp>::Cost
+  };
+};
+}
+
+template<typename NullaryOp, typename PlainObjectType>
+class CwiseNullaryOp : internal::no_assignment_operator,
+  public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
+
+    CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
+      : m_rows(rows), m_cols(cols), m_functor(func)
+    {
+      eigen_assert(rows >= 0
+            && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+            &&  cols >= 0
+            && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+    }
+
+    EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index rows, Index cols) const
+    {
+      return m_functor(rows, cols);
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+    {
+      return m_functor.packetOp(row, col);
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+    {
+      return m_functor(index);
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+    {
+      return m_functor.packetOp(index);
+    }
+
+  protected:
+    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+    const NullaryOp m_functor;
+};
+
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(rows, cols, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, Derived>(1, size, func);
+  else return CwiseNullaryOp<CustomNullaryOp, Derived>(size, 1, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(RowsAtCompileTime, ColsAtCompileTime, func);
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this DenseBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
+{
+  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this DenseBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index size, const Scalar& value)
+{
+  return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(const Scalar& value)
+{
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
+}
+
+/**
+  * \brief Sets a linearly space vector.
+  *
+  * The function generates 'size' equally spaced values in the closed interval [low,high].
+  * This particular version of LinSpaced() uses sequential access, i.e. vector access is
+  * assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization
+  * and yields faster code than the random access version.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include DenseBase_LinSpaced_seq.cpp
+  * Output: \verbinclude DenseBase_LinSpaced_seq.out
+  *
+  * \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,false>(low,high,size));
+}
+
+/**
+  * \copydoc DenseBase::LinSpaced(Sequential_t, Index, const Scalar&, const Scalar&)
+  * Special version for fixed size types which does not require the size parameter.
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,false>(low,high,Derived::SizeAtCompileTime));
+}
+
+/**
+  * \brief Sets a linearly space vector.
+  *
+  * The function generates 'size' equally spaced values in the closed interval [low,high].
+  *
+  * \only_for_vectors
+  *
+  * Example: \include DenseBase_LinSpaced.cpp
+  * Output: \verbinclude DenseBase_LinSpaced.out
+  *
+  * \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,true>(low,high,size));
+}
+
+/**
+  * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
+  * Special version for fixed size types which does not require the size parameter.
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,true>(low,high,Derived::SizeAtCompileTime));
+}
+
+/** \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+bool DenseBase<Derived>::isApproxToConstant
+(const Scalar& value, RealScalar prec) const
+{
+  for(Index j = 0; j < cols(); ++j)
+    for(Index i = 0; i < rows(); ++i)
+      if(!internal::isApprox(this->coeff(i, j), value, prec))
+        return false;
+  return true;
+}
+
+/** This is just an alias for isApproxToConstant().
+  *
+  * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+bool DenseBase<Derived>::isConstant
+(const Scalar& value, RealScalar prec) const
+{
+  return isApproxToConstant(value, prec);
+}
+
+/** Alias for setConstant(): sets all coefficients in this expression to \a value.
+  *
+  * \sa setConstant(), Constant(), class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& value)
+{
+  setConstant(value);
+}
+
+/** Sets all coefficients in this expression to \a value.
+  *
+  * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& value)
+{
+  return derived() = Constant(rows(), cols(), value);
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to the given \a value.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setConstant_int.cpp
+  * Output: \verbinclude Matrix_setConstant_int.out
+  *
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index size, const Scalar& value)
+{
+  resize(size);
+  return setConstant(value);
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to the given \a value.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  * \param value the value to which all coefficients are set
+  *
+  * Example: \include Matrix_setConstant_int_int.cpp
+  * Output: \verbinclude Matrix_setConstant_int_int.out
+  *
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& value)
+{
+  resize(rows, cols);
+  return setConstant(value);
+}
+
+/**
+  * \brief Sets a linearly space vector.
+  *
+  * The function generates 'size' equally spaced values in the closed interval [low,high].
+  *
+  * \only_for_vectors
+  *
+  * Example: \include DenseBase_setLinSpaced.cpp
+  * Output: \verbinclude DenseBase_setLinSpaced.out
+  *
+  * \sa CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index size, const Scalar& low, const Scalar& high)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return derived() = Derived::NullaryExpr(size, internal::linspaced_op<Scalar,false>(low,high,size));
+}
+
+// zero:
+
+/** \returns an expression of a zero matrix.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_zero_int_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int_int.out
+  *
+  * \sa Zero(), Zero(Index)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index rows, Index cols)
+{
+  return Constant(rows, cols, Scalar(0));
+}
+
+/** \returns an expression of a zero vector.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_zero_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int.out
+  *
+  * \sa Zero(), Zero(Index,Index)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index size)
+{
+  return Constant(size, Scalar(0));
+}
+
+/** \returns an expression of a fixed-size zero matrix or vector.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_zero.cpp
+  * Output: \verbinclude MatrixBase_zero.out
+  *
+  * \sa Zero(Index), Zero(Index,Index)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero()
+{
+  return Constant(Scalar(0));
+}
+
+/** \returns true if *this is approximately equal to the zero matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isZero.cpp
+  * Output: \verbinclude MatrixBase_isZero.out
+  *
+  * \sa class CwiseNullaryOp, Zero()
+  */
+template<typename Derived>
+bool DenseBase<Derived>::isZero(RealScalar prec) const
+{
+  for(Index j = 0; j < cols(); ++j)
+    for(Index i = 0; i < rows(); ++i)
+      if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<Scalar>(1), prec))
+        return false;
+  return true;
+}
+
+/** Sets all coefficients in this expression to zero.
+  *
+  * Example: \include MatrixBase_setZero.cpp
+  * Output: \verbinclude MatrixBase_setZero.out
+  *
+  * \sa class CwiseNullaryOp, Zero()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
+{
+  return setConstant(Scalar(0));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setZero_int.cpp
+  * Output: \verbinclude Matrix_setZero_int.out
+  *
+  * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index size)
+{
+  resize(size);
+  return setConstant(Scalar(0));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to zero.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setZero_int_int.cpp
+  * Output: \verbinclude Matrix_setZero_int_int.out
+  *
+  * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index rows, Index cols)
+{
+  resize(rows, cols);
+  return setConstant(Scalar(0));
+}
+
+// ones:
+
+/** \returns an expression of a matrix where all coefficients equal one.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_ones_int_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int_int.out
+  *
+  * \sa Ones(), Ones(Index), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index rows, Index cols)
+{
+  return Constant(rows, cols, Scalar(1));
+}
+
+/** \returns an expression of a vector where all coefficients equal one.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Ones() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_ones_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int.out
+  *
+  * \sa Ones(), Ones(Index,Index), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index size)
+{
+  return Constant(size, Scalar(1));
+}
+
+/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_ones.cpp
+  * Output: \verbinclude MatrixBase_ones.out
+  *
+  * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones()
+{
+  return Constant(Scalar(1));
+}
+
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+  *          are equal to 1, within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOnes.cpp
+  * Output: \verbinclude MatrixBase_isOnes.out
+  *
+  * \sa class CwiseNullaryOp, Ones()
+  */
+template<typename Derived>
+bool DenseBase<Derived>::isOnes
+(RealScalar prec) const
+{
+  return isApproxToConstant(Scalar(1), prec);
+}
+
+/** Sets all coefficients in this expression to one.
+  *
+  * Example: \include MatrixBase_setOnes.cpp
+  * Output: \verbinclude MatrixBase_setOnes.out
+  *
+  * \sa class CwiseNullaryOp, Ones()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
+{
+  return setConstant(Scalar(1));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to one.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setOnes_int.cpp
+  * Output: \verbinclude Matrix_setOnes_int.out
+  *
+  * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index size)
+{
+  resize(size);
+  return setConstant(Scalar(1));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to one.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setOnes_int_int.cpp
+  * Output: \verbinclude Matrix_setOnes_int_int.out
+  *
+  * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index rows, Index cols)
+{
+  resize(rows, cols);
+  return setConstant(Scalar(1));
+}
+
+// Identity:
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_identity_int_int.cpp
+  * Output: \verbinclude MatrixBase_identity_int_int.out
+  *
+  * \sa Identity(), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity(Index rows, Index cols)
+{
+  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variant taking size arguments.
+  *
+  * Example: \include MatrixBase_identity.cpp
+  * Output: \verbinclude MatrixBase_identity.out
+  *
+  * \sa Identity(Index,Index), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity()
+{
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns true if *this is approximately equal to the identity matrix
+  *          (not necessarily square),
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isIdentity.cpp
+  * Output: \verbinclude MatrixBase_isIdentity.out
+  *
+  * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isIdentity
+(RealScalar prec) const
+{
+  for(Index j = 0; j < cols(); ++j)
+  {
+    for(Index i = 0; i < rows(); ++i)
+    {
+      if(i == j)
+      {
+        if(!internal::isApprox(this->coeff(i, j), static_cast<Scalar>(1), prec))
+          return false;
+      }
+      else
+      {
+        if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<RealScalar>(1), prec))
+          return false;
+      }
+    }
+  }
+  return true;
+}
+
+namespace internal {
+
+template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
+struct setIdentity_impl
+{
+  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+  {
+    return m = Derived::Identity(m.rows(), m.cols());
+  }
+};
+
+template<typename Derived>
+struct setIdentity_impl<Derived, true>
+{
+  typedef typename Derived::Index Index;
+  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+  {
+    m.setZero();
+    const Index size = (std::min)(m.rows(), m.cols());
+    for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
+    return m;
+  }
+};
+
+} // end namespace internal
+
+/** Writes the identity expression (not necessarily square) into *this.
+  *
+  * Example: \include MatrixBase_setIdentity.cpp
+  * Output: \verbinclude MatrixBase_setIdentity.out
+  *
+  * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
+{
+  return internal::setIdentity_impl<Derived>::run(derived());
+}
+
+/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setIdentity_int_int.cpp
+  * Output: \verbinclude Matrix_setIdentity_int_int.out
+  *
+  * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)
+{
+  derived().resize(rows, cols);
+  return setIdentity();
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index size, Index i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return BasisReturnType(SquareMatrixType::Identity(size,size), i);
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * This variant is for fixed-size vector only.
+  *
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return BasisReturnType(SquareMatrixType::Identity(),i);
+}
+
+/** \returns an expression of the X axis unit vector (1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
+{ return Derived::Unit(0); }
+
+/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
+{ return Derived::Unit(1); }
+
+/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
+{ return Derived::Unit(2); }
+
+/** \returns an expression of the W axis unit vector (0,0,0,1)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
+{ return Derived::Unit(3); }
+
+#endif // EIGEN_CWISE_NULLARY_OP_H

Eigen/src/Core/CwiseUnaryOp.h

@@ -0,0 +1,137 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_UNARY_OP_H
+#define EIGEN_CWISE_UNARY_OP_H
+
+/** \class CwiseUnaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression where a coefficient-wise unary operator is applied to an expression
+  *
+  * \param UnaryOp template functor implementing the operator
+  * \param XprType the type of the expression to which we are applying the unary operator
+  *
+  * This class represents an expression where a unary operator is applied to an expression.
+  * It is the return type of all operations taking exactly 1 input expression, regardless of the
+  * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
+  * is considered unary, because only the right-hand side is an expression, and its
+  * return type is a specialization of CwiseUnaryOp.
+  *
+  * Most of the time, this is the only way that it is used, so you typically don't have to name
+  * CwiseUnaryOp types explicitly.
+  *
+  * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
+  */
+
+namespace internal {
+template<typename UnaryOp, typename XprType>
+struct traits<CwiseUnaryOp<UnaryOp, XprType> >
+ : traits<XprType>
+{
+  typedef typename result_of<
+                     UnaryOp(typename XprType::Scalar)
+                   >::type Scalar;
+  typedef typename XprType::Nested XprTypeNested;
+  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
+  enum {
+    Flags = _XprTypeNested::Flags & (
+      HereditaryBits | LinearAccessBit | AlignedBit
+      | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
+    CoeffReadCost = _XprTypeNested::CoeffReadCost + functor_traits<UnaryOp>::Cost
+  };
+};
+}
+
+template<typename UnaryOp, typename XprType, typename StorageKind>
+class CwiseUnaryOpImpl;
+
+template<typename UnaryOp, typename XprType>
+class CwiseUnaryOp : internal::no_assignment_operator,
+  public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>
+{
+  public:
+
+    typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
+
+    inline CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+      : m_xpr(xpr), m_functor(func) {}
+
+    EIGEN_STRONG_INLINE Index rows() const { return m_xpr.rows(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_xpr.cols(); }
+
+    /** \returns the functor representing the unary operation */
+    const UnaryOp& functor() const { return m_functor; }
+
+    /** \returns the nested expression */
+    const typename internal::remove_all<typename XprType::Nested>::type&
+    nestedExpression() const { return m_xpr; }
+
+    /** \returns the nested expression */
+    typename internal::remove_all<typename XprType::Nested>::type&
+    nestedExpression() { return m_xpr.const_cast_derived(); }
+
+  protected:
+    const typename XprType::Nested m_xpr;
+    const UnaryOp m_functor;
+};
+
+// This is the generic implementation for dense storage.
+// It can be used for any expression types implementing the dense concept.
+template<typename UnaryOp, typename XprType>
+class CwiseUnaryOpImpl<UnaryOp,XprType,Dense>
+  : public internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
+{
+  public:
+
+    typedef CwiseUnaryOp<UnaryOp, XprType> Derived;
+    typedef typename internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+    {
+      return derived().functor()(derived().nestedExpression().coeff(row, col));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+    {
+      return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(row, col));
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+    {
+      return derived().functor()(derived().nestedExpression().coeff(index));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+    {
+      return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(index));
+    }
+};
+
+#endif // EIGEN_CWISE_UNARY_OP_H

Eigen/src/Core/CwiseUnaryView.h

@@ -0,0 +1,148 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_UNARY_VIEW_H
+#define EIGEN_CWISE_UNARY_VIEW_H
+
+/** \class CwiseUnaryView
+  * \ingroup Core_Module
+  *
+  * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
+  *
+  * \param ViewOp template functor implementing the view
+  * \param MatrixType the type of the matrix we are applying the unary operator
+  *
+  * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
+  * It is the return type of real() and imag(), and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
+  */
+
+namespace internal {
+template<typename ViewOp, typename MatrixType>
+struct traits<CwiseUnaryView<ViewOp, MatrixType> >
+ : traits<MatrixType>
+{
+  typedef typename result_of<
+                     ViewOp(typename traits<MatrixType>::Scalar)
+                   >::type Scalar;
+  typedef typename MatrixType::Nested MatrixTypeNested;
+  typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    Flags = (traits<_MatrixTypeNested>::Flags & (HereditaryBits | LvalueBit | LinearAccessBit | DirectAccessBit)),
+    CoeffReadCost = traits<_MatrixTypeNested>::CoeffReadCost + functor_traits<ViewOp>::Cost,
+    MatrixTypeInnerStride =  inner_stride_at_compile_time<MatrixType>::ret,
+    // need to cast the sizeof's from size_t to int explicitly, otherwise:
+    // "error: no integral type can represent all of the enumerator values
+    InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic
+                             ? int(Dynamic)
+                             : int(MatrixTypeInnerStride)
+                               * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),
+    OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret
+  };
+};
+}
+
+template<typename ViewOp, typename MatrixType, typename StorageKind>
+class CwiseUnaryViewImpl;
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryView : internal::no_assignment_operator,
+  public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
+{
+  public:
+
+    typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
+
+    inline CwiseUnaryView(const MatrixType& mat, const ViewOp& func = ViewOp())
+      : m_matrix(mat), m_functor(func) {}
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
+
+    EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
+
+    /** \returns the functor representing unary operation */
+    const ViewOp& functor() const { return m_functor; }
+
+    /** \returns the nested expression */
+    const typename internal::remove_all<typename MatrixType::Nested>::type&
+    nestedExpression() const { return m_matrix; }
+
+    /** \returns the nested expression */
+    typename internal::remove_all<typename MatrixType::Nested>::type&
+    nestedExpression() { return m_matrix.const_cast_derived(); }
+
+  protected:
+    // FIXME changed from MatrixType::Nested because of a weird compilation error with sun CC
+    const typename internal::nested<MatrixType>::type m_matrix;
+    ViewOp m_functor;
+};
+
+template<typename ViewOp, typename MatrixType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
+  : public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type
+{
+  public:
+
+    typedef CwiseUnaryView<ViewOp, MatrixType> Derived;
+    typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
+
+    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+
+    inline Index innerStride() const
+    {
+      return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
+    }
+
+    inline Index outerStride() const
+    {
+      return derived().nestedExpression().outerStride();
+    }
+
+    EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
+    {
+      return derived().functor()(derived().nestedExpression().coeff(row, col));
+    }
+
+    EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+    {
+      return derived().functor()(derived().nestedExpression().coeff(index));
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+    {
+      return derived().functor()(const_cast_derived().nestedExpression().coeffRef(row, col));
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+    {
+      return derived().functor()(const_cast_derived().nestedExpression().coeffRef(index));
+    }
+};
+
+
+
+#endif // EIGEN_CWISE_UNARY_VIEW_H

Eigen/src/Core/DenseBase.h

@@ -0,0 +1,543 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DENSEBASE_H
+#define EIGEN_DENSEBASE_H
+
+/** \class DenseBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for all dense matrices, vectors, and arrays
+  *
+  * This class is the base that is inherited by all dense objects (matrix, vector, arrays,
+  * and related expression types). The common Eigen API for dense objects is contained in this class.
+  *
+  * \tparam Derived is the derived type, e.g., a matrix type or an expression.
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived> class DenseBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  : public internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+                                     typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>
+#else
+  : public DenseCoeffsBase<Derived>
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+{
+  public:
+    using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
+                typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
+
+    class InnerIterator;
+
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+
+    /** \brief The type of indices 
+      * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+      * \sa \ref TopicPreprocessorDirectives.
+      */
+    typedef typename internal::traits<Derived>::Index Index; 
+
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    typedef DenseCoeffsBase<Derived> Base;
+    using Base::derived;
+    using Base::const_cast_derived;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::rowIndexByOuterInner;
+    using Base::colIndexByOuterInner;
+    using Base::coeff;
+    using Base::coeffByOuterInner;
+    using Base::packet;
+    using Base::packetByOuterInner;
+    using Base::writePacket;
+    using Base::writePacketByOuterInner;
+    using Base::coeffRef;
+    using Base::coeffRefByOuterInner;
+    using Base::copyCoeff;
+    using Base::copyCoeffByOuterInner;
+    using Base::copyPacket;
+    using Base::copyPacketByOuterInner;
+    using Base::operator();
+    using Base::operator[];
+    using Base::x;
+    using Base::y;
+    using Base::z;
+    using Base::w;
+    using Base::stride;
+    using Base::innerStride;
+    using Base::outerStride;
+    using Base::rowStride;
+    using Base::colStride;
+    typedef typename Base::CoeffReturnType CoeffReturnType;
+
+    enum {
+
+      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+        /**< The number of rows at compile-time. This is just a copy of the value provided
+          * by the \a Derived type. If a value is not known at compile-time,
+          * it is set to the \a Dynamic constant.
+          * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+        /**< The number of columns at compile-time. This is just a copy of the value provided
+          * by the \a Derived type. If a value is not known at compile-time,
+          * it is set to the \a Dynamic constant.
+          * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
+                                                   internal::traits<Derived>::ColsAtCompileTime>::ret),
+        /**< This is equal to the number of coefficients, i.e. the number of
+          * rows times the number of columns, or to \a Dynamic if this is not
+          * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+        /**< This value is equal to the maximum possible number of rows that this expression
+          * might have. If this expression might have an arbitrarily high number of rows,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
+          */
+
+      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+        /**< This value is equal to the maximum possible number of columns that this expression
+          * might have. If this expression might have an arbitrarily high number of columns,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
+          */
+
+      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
+                                                      internal::traits<Derived>::MaxColsAtCompileTime>::ret),
+        /**< This value is equal to the maximum possible number of coefficients that this expression
+          * might have. If this expression might have an arbitrarily high number of coefficients,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
+          */
+
+      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
+                           || internal::traits<Derived>::MaxColsAtCompileTime == 1,
+        /**< This is set to true if either the number of rows or the number of
+          * columns is known at compile-time to be equal to 1. Indeed, in that case,
+          * we are dealing with a column-vector (if there is only one column) or with
+          * a row-vector (if there is only one row). */
+
+      Flags = internal::traits<Derived>::Flags,
+        /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+          * constructed from this one. See the \ref flags "list of flags".
+          */
+
+      IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
+
+      InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
+                             : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+
+      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+        /**< This is a rough measure of how expensive it is to read one coefficient from
+          * this expression.
+          */
+
+      InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
+      OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
+    };
+
+    enum { ThisConstantIsPrivateInPlainObjectBase };
+
+    /** \returns the number of nonzero coefficients which is in practice the number
+      * of stored coefficients. */
+    inline Index nonZeros() const { return size(); }
+    /** \returns true if either the number of rows or the number of columns is equal to 1.
+      * In other words, this function returns
+      * \code rows()==1 || cols()==1 \endcode
+      * \sa rows(), cols(), IsVectorAtCompileTime. */
+
+    /** \returns the outer size.
+      *
+      * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
+      * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
+      * column-major matrix, and the number of rows for a row-major matrix. */
+    Index outerSize() const
+    {
+      return IsVectorAtCompileTime ? 1
+           : int(IsRowMajor) ? this->rows() : this->cols();
+    }
+
+    /** \returns the inner size.
+      *
+      * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
+      * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a 
+      * column-major matrix, and the number of columns for a row-major matrix. */
+    Index innerSize() const
+    {
+      return IsVectorAtCompileTime ? this->size()
+           : int(IsRowMajor) ? this->cols() : this->rows();
+    }
+
+    /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+      * nothing else.
+      */
+    void resize(Index size)
+    {
+      EIGEN_ONLY_USED_FOR_DEBUG(size);
+      eigen_assert(size == this->size()
+                && "DenseBase::resize() does not actually allow to resize.");
+    }
+    /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+      * nothing else.
+      */
+    void resize(Index rows, Index cols)
+    {
+      EIGEN_ONLY_USED_FOR_DEBUG(rows);
+      EIGEN_ONLY_USED_FOR_DEBUG(cols);
+      eigen_assert(rows == this->rows() && cols == this->cols()
+                && "DenseBase::resize() does not actually allow to resize.");
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+    /** \internal Represents a matrix with all coefficients equal to one another*/
+    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+    /** \internal Represents a vector with linearly spaced coefficients that allows sequential access only. */
+    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,false>,Derived> SequentialLinSpacedReturnType;
+    /** \internal Represents a vector with linearly spaced coefficients that allows random access. */
+    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,true>,Derived> RandomAccessLinSpacedReturnType;
+    /** \internal the return type of MatrixBase::eigenvalues() */
+    typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** Copies \a other into *this. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& operator=(const DenseBase<OtherDerived>& other);
+
+    /** Special case of the template operator=, in order to prevent the compiler
+      * from generating a default operator= (issue hit with g++ 4.1)
+      */
+    Derived& operator=(const DenseBase& other);
+
+    template<typename OtherDerived>
+    Derived& operator=(const EigenBase<OtherDerived> &other);
+
+    template<typename OtherDerived>
+    Derived& operator+=(const EigenBase<OtherDerived> &other);
+
+    template<typename OtherDerived>
+    Derived& operator-=(const EigenBase<OtherDerived> &other);
+
+    template<typename OtherDerived>
+    Derived& operator=(const ReturnByValue<OtherDerived>& func);
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** Copies \a other into *this without evaluating other. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const DenseBase<OtherDerived>& other);
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    CommaInitializer<Derived> operator<< (const Scalar& s);
+
+    template<unsigned int Added,unsigned int Removed>
+    const Flagged<Derived, Added, Removed> flagged() const;
+
+    template<typename OtherDerived>
+    CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
+
+    Eigen::Transpose<Derived> transpose();
+    typedef const Transpose<const Derived> ConstTransposeReturnType;
+    ConstTransposeReturnType transpose() const;
+    void transposeInPlace();
+#ifndef EIGEN_NO_DEBUG
+  protected:
+    template<typename OtherDerived>
+    void checkTransposeAliasing(const OtherDerived& other) const;
+  public:
+#endif
+
+    typedef VectorBlock<Derived> SegmentReturnType;
+    typedef const VectorBlock<const Derived> ConstSegmentReturnType;
+    template<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };
+    template<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };
+    
+    // Note: The "DenseBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
+    SegmentReturnType segment(Index start, Index size);
+    typename DenseBase::ConstSegmentReturnType segment(Index start, Index size) const;
+
+    SegmentReturnType head(Index size);
+    typename DenseBase::ConstSegmentReturnType head(Index size) const;
+
+    SegmentReturnType tail(Index size);
+    typename DenseBase::ConstSegmentReturnType tail(Index size) const;
+
+    template<int Size> typename FixedSegmentReturnType<Size>::Type head();
+    template<int Size> typename ConstFixedSegmentReturnType<Size>::Type head() const;
+
+    template<int Size> typename FixedSegmentReturnType<Size>::Type tail();
+    template<int Size> typename ConstFixedSegmentReturnType<Size>::Type tail() const;
+
+    template<int Size> typename FixedSegmentReturnType<Size>::Type segment(Index start);
+    template<int Size> typename ConstFixedSegmentReturnType<Size>::Type segment(Index start) const;
+
+    static const ConstantReturnType
+    Constant(Index rows, Index cols, const Scalar& value);
+    static const ConstantReturnType
+    Constant(Index size, const Scalar& value);
+    static const ConstantReturnType
+    Constant(const Scalar& value);
+
+    static const SequentialLinSpacedReturnType
+    LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
+    static const RandomAccessLinSpacedReturnType
+    LinSpaced(Index size, const Scalar& low, const Scalar& high);
+    static const SequentialLinSpacedReturnType
+    LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
+    static const RandomAccessLinSpacedReturnType
+    LinSpaced(const Scalar& low, const Scalar& high);
+
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(Index size, const CustomNullaryOp& func);
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(const CustomNullaryOp& func);
+
+    static const ConstantReturnType Zero(Index rows, Index cols);
+    static const ConstantReturnType Zero(Index size);
+    static const ConstantReturnType Zero();
+    static const ConstantReturnType Ones(Index rows, Index cols);
+    static const ConstantReturnType Ones(Index size);
+    static const ConstantReturnType Ones();
+
+    void fill(const Scalar& value);
+    Derived& setConstant(const Scalar& value);
+    Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
+    Derived& setLinSpaced(const Scalar& low, const Scalar& high);
+    Derived& setZero();
+    Derived& setOnes();
+    Derived& setRandom();
+
+    template<typename OtherDerived>
+    bool isApprox(const DenseBase<OtherDerived>& other,
+                  RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isMuchSmallerThan(const RealScalar& other,
+                           RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    template<typename OtherDerived>
+    bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
+                           RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+
+    bool isApproxToConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isZero(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isOnes(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+
+    inline Derived& operator*=(const Scalar& other);
+    inline Derived& operator/=(const Scalar& other);
+
+    /** \returns the matrix or vector obtained by evaluating this expression.
+      *
+      * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+      * a const reference, in order to avoid a useless copy.
+      */
+    EIGEN_STRONG_INLINE const typename internal::eval<Derived>::type eval() const
+    {
+      // Even though MSVC does not honor strong inlining when the return type
+      // is a dynamic matrix, we desperately need strong inlining for fixed
+      // size types on MSVC.
+      return typename internal::eval<Derived>::type(derived());
+    }
+
+    /** swaps *this with the expression \a other.
+      *
+      */
+    template<typename OtherDerived>
+    void swap(const DenseBase<OtherDerived>& other,
+              int = OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
+    {
+      SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
+    }
+
+    /** swaps *this with the matrix or array \a other.
+      *
+      */
+    template<typename OtherDerived>
+    void swap(PlainObjectBase<OtherDerived>& other)
+    {
+      SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
+    }
+
+
+    inline const NestByValue<Derived> nestByValue() const;
+    inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
+    inline ForceAlignedAccess<Derived> forceAlignedAccess();
+    template<bool Enable> inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;
+    template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
+
+    Scalar sum() const;
+    Scalar mean() const;
+    Scalar trace() const;
+
+    Scalar prod() const;
+
+    typename internal::traits<Derived>::Scalar minCoeff() const;
+    typename internal::traits<Derived>::Scalar maxCoeff() const;
+
+    template<typename IndexType>
+    typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
+    template<typename IndexType>
+    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
+    template<typename IndexType>
+    typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
+    template<typename IndexType>
+    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
+
+    template<typename BinaryOp>
+    typename internal::result_of<BinaryOp(typename internal::traits<Derived>::Scalar)>::type
+    redux(const BinaryOp& func) const;
+
+    template<typename Visitor>
+    void visit(Visitor& func) const;
+
+    inline const WithFormat<Derived> format(const IOFormat& fmt) const;
+
+    /** \returns the unique coefficient of a 1x1 expression */
+    CoeffReturnType value() const
+    {
+      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+      eigen_assert(this->rows() == 1 && this->cols() == 1);
+      return derived().coeff(0,0);
+    }
+
+/////////// Array module ///////////
+
+    bool all(void) const;
+    bool any(void) const;
+    Index count() const;
+
+    typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
+    typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
+    typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
+    typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
+
+    ConstRowwiseReturnType rowwise() const;
+    RowwiseReturnType rowwise();
+    ConstColwiseReturnType colwise() const;
+    ColwiseReturnType colwise();
+
+    static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index rows, Index cols);
+    static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index size);
+    static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random();
+
+    template<typename ThenDerived,typename ElseDerived>
+    const Select<Derived,ThenDerived,ElseDerived>
+    select(const DenseBase<ThenDerived>& thenMatrix,
+           const DenseBase<ElseDerived>& elseMatrix) const;
+
+    template<typename ThenDerived>
+    inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
+    select(const DenseBase<ThenDerived>& thenMatrix, 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;
+
+    template<int p> RealScalar lpNorm() const;
+
+    template<int RowFactor, int ColFactor>
+    const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+    const Replicate<Derived,Dynamic,Dynamic> replicate(Index rowFacor,Index colFactor) const;
+
+    typedef Reverse<Derived, BothDirections> ReverseReturnType;
+    typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
+    ReverseReturnType reverse();
+    ConstReverseReturnType reverse() const;
+    void reverseInPlace();
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
+#   include "../plugins/BlockMethods.h"
+#   ifdef EIGEN_DENSEBASE_PLUGIN
+#     include EIGEN_DENSEBASE_PLUGIN
+#   endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+#ifdef EIGEN2_SUPPORT
+
+    Block<Derived> corner(CornerType type, Index cRows, Index cCols);
+    const Block<Derived> corner(CornerType type, Index cRows, Index cCols) const;
+    template<int CRows, int CCols>
+    Block<Derived, CRows, CCols> corner(CornerType type);
+    template<int CRows, int CCols>
+    const Block<Derived, CRows, CCols> corner(CornerType type) const;
+
+#endif // EIGEN2_SUPPORT
+
+
+    // disable the use of evalTo for dense objects with a nice compilation error
+    template<typename Dest> inline void evalTo(Dest& ) const
+    {
+      EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
+    }
+
+  protected:
+    /** Default constructor. Do nothing. */
+    DenseBase()
+    {
+      /* Just checks for self-consistency of the flags.
+       * Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down
+       */
+#ifdef EIGEN_INTERNAL_DEBUGGING
+      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
+                        && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
+                          INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
+#endif
+    }
+
+  private:
+    explicit DenseBase(int);
+    DenseBase(int,int);
+    template<typename OtherDerived> explicit DenseBase(const DenseBase<OtherDerived>&);
+};
+
+#endif // EIGEN_DENSEBASE_H

Eigen/src/Core/DenseCoeffsBase.h

@@ -0,0 +1,765 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DENSECOEFFSBASE_H
+#define EIGEN_DENSECOEFFSBASE_H
+
+namespace internal {
+template<typename T> struct add_const_on_value_type_if_arithmetic
+{
+  typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
+};
+}
+
+/** \brief Base class providing read-only coefficient access to matrices and arrays.
+  * \ingroup Core_Module
+  * \tparam Derived Type of the derived class
+  * \tparam #ReadOnlyAccessors Constant indicating read-only access
+  *
+  * This class defines the \c operator() \c const function and friends, which can be used to read specific
+  * entries of a matrix or array.
+  * 
+  * \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
+  *     \ref TopicClassHierarchy
+  */
+template<typename Derived>
+class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
+{
+  public:
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+
+    // Explanation for this CoeffReturnType typedef.
+    // - This is the return type of the coeff() method.
+    // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
+    // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
+    // - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
+    // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
+    // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
+    typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
+                         const Scalar&,
+                         typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type
+                     >::type CoeffReturnType;
+
+    typedef typename internal::add_const_on_value_type_if_arithmetic<
+                         typename internal::packet_traits<Scalar>::type
+                     >::type PacketReturnType;
+
+    typedef EigenBase<Derived> Base;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::derived;
+
+    EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
+    {
+      return int(Derived::RowsAtCompileTime) == 1 ? 0
+          : int(Derived::ColsAtCompileTime) == 1 ? inner
+          : int(Derived::Flags)&RowMajorBit ? outer
+          : inner;
+    }
+
+    EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
+    {
+      return int(Derived::ColsAtCompileTime) == 1 ? 0
+          : int(Derived::RowsAtCompileTime) == 1 ? inner
+          : int(Derived::Flags)&RowMajorBit ? inner
+          : outer;
+    }
+
+    /** Short version: don't use this function, use
+      * \link operator()(Index,Index) const \endlink instead.
+      *
+      * Long version: this function is similar to
+      * \link operator()(Index,Index) const \endlink, but without the assertion.
+      * Use this for limiting the performance cost of debugging code when doing
+      * repeated coefficient access. Only use this when it is guaranteed that the
+      * parameters \a row and \a col are in range.
+      *
+      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+      * function equivalent to \link operator()(Index,Index) const \endlink.
+      *
+      * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
+      */
+    EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      return derived().coeff(row, col);
+    }
+
+    EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
+    {
+      return coeff(rowIndexByOuterInner(outer, inner),
+                   colIndexByOuterInner(outer, inner));
+    }
+
+    /** \returns the coefficient at given the given row and column.
+      *
+      * \sa operator()(Index,Index), operator[](Index)
+      */
+    EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
+    {
+      eigen_assert(row >= 0 && row < rows()
+          && col >= 0 && col < cols());
+      return derived().coeff(row, col);
+    }
+
+    /** Short version: don't use this function, use
+      * \link operator[](Index) const \endlink instead.
+      *
+      * Long version: this function is similar to
+      * \link operator[](Index) const \endlink, but without the assertion.
+      * Use this for limiting the performance cost of debugging code when doing
+      * repeated coefficient access. Only use this when it is guaranteed that the
+      * parameter \a index is in range.
+      *
+      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+      * function equivalent to \link operator[](Index) const \endlink.
+      *
+      * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
+      */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    coeff(Index index) const
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      return derived().coeff(index);
+    }
+
+
+    /** \returns the coefficient at given index.
+      *
+      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+      *
+      * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+      * z() const, w() const
+      */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    operator[](Index index) const
+    {
+      #ifndef EIGEN2_SUPPORT
+      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+      #endif
+      eigen_assert(index >= 0 && index < size());
+      return derived().coeff(index);
+    }
+
+    /** \returns the coefficient at given index.
+      *
+      * This is synonymous to operator[](Index) const.
+      *
+      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+      *
+      * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+      * z() const, w() const
+      */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    operator()(Index index) const
+    {
+      eigen_assert(index >= 0 && index < size());
+      return derived().coeff(index);
+    }
+
+    /** equivalent to operator[](0).  */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    x() const { return (*this)[0]; }
+
+    /** equivalent to operator[](1).  */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    y() const { return (*this)[1]; }
+
+    /** equivalent to operator[](2).  */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    z() const { return (*this)[2]; }
+
+    /** equivalent to operator[](3).  */
+
+    EIGEN_STRONG_INLINE CoeffReturnType
+    w() const { return (*this)[3]; }
+
+    /** \internal
+      * \returns the packet of coefficients starting at the given row and column. It is your responsibility
+      * to ensure that a packet really starts there. This method is only available on expressions having the
+      * PacketAccessBit.
+      *
+      * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+      * starting at an address which is a multiple of the packet size.
+      */
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                      && col >= 0 && col < cols());
+      return derived().template packet<LoadMode>(row,col);
+    }
+
+
+    /** \internal */
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
+    {
+      return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
+                              colIndexByOuterInner(outer, inner));
+    }
+
+    /** \internal
+      * \returns the packet of coefficients starting at the given index. It is your responsibility
+      * to ensure that a packet really starts there. This method is only available on expressions having the
+      * PacketAccessBit and the LinearAccessBit.
+      *
+      * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+      * starting at an address which is a multiple of the packet size.
+      */
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      return derived().template packet<LoadMode>(index);
+    }
+
+  protected:
+    // explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
+    // But some methods are only available in the DirectAccess case.
+    // So we add dummy methods here with these names, so that "using... " doesn't fail.
+    // It's not private so that the child class DenseBase can access them, and it's not public
+    // either since it's an implementation detail, so has to be protected.
+    void coeffRef();
+    void coeffRefByOuterInner();
+    void writePacket();
+    void writePacketByOuterInner();
+    void copyCoeff();
+    void copyCoeffByOuterInner();
+    void copyPacket();
+    void copyPacketByOuterInner();
+    void stride();
+    void innerStride();
+    void outerStride();
+    void rowStride();
+    void colStride();
+};
+
+/** \brief Base class providing read/write coefficient access to matrices and arrays.
+  * \ingroup Core_Module
+  * \tparam Derived Type of the derived class
+  * \tparam #WriteAccessors Constant indicating read/write access
+  *
+  * This class defines the non-const \c operator() function and friends, which can be used to write specific
+  * entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
+  * defines the const variant for reading specific entries.
+  * 
+  * \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
+  */
+template<typename Derived>
+class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+  public:
+
+    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    using Base::coeff;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::derived;
+    using Base::rowIndexByOuterInner;
+    using Base::colIndexByOuterInner;
+    using Base::operator[];
+    using Base::operator();
+    using Base::x;
+    using Base::y;
+    using Base::z;
+    using Base::w;
+
+    /** Short version: don't use this function, use
+      * \link operator()(Index,Index) \endlink instead.
+      *
+      * Long version: this function is similar to
+      * \link operator()(Index,Index) \endlink, but without the assertion.
+      * Use this for limiting the performance cost of debugging code when doing
+      * repeated coefficient access. Only use this when it is guaranteed that the
+      * parameters \a row and \a col are in range.
+      *
+      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+      * function equivalent to \link operator()(Index,Index) \endlink.
+      *
+      * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
+      */
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      return derived().coeffRef(row, col);
+    }
+
+    EIGEN_STRONG_INLINE Scalar&
+    coeffRefByOuterInner(Index outer, Index inner)
+    {
+      return coeffRef(rowIndexByOuterInner(outer, inner),
+                      colIndexByOuterInner(outer, inner));
+    }
+
+    /** \returns a reference to the coefficient at given the given row and column.
+      *
+      * \sa operator[](Index)
+      */
+
+    EIGEN_STRONG_INLINE Scalar&
+    operator()(Index row, Index col)
+    {
+      eigen_assert(row >= 0 && row < rows()
+          && col >= 0 && col < cols());
+      return derived().coeffRef(row, col);
+    }
+
+
+    /** Short version: don't use this function, use
+      * \link operator[](Index) \endlink instead.
+      *
+      * Long version: this function is similar to
+      * \link operator[](Index) \endlink, but without the assertion.
+      * Use this for limiting the performance cost of debugging code when doing
+      * repeated coefficient access. Only use this when it is guaranteed that the
+      * parameters \a row and \a col are in range.
+      *
+      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+      * function equivalent to \link operator[](Index) \endlink.
+      *
+      * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
+      */
+
+    EIGEN_STRONG_INLINE Scalar&
+    coeffRef(Index index)
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      return derived().coeffRef(index);
+    }
+
+    /** \returns a reference to the coefficient at given index.
+      *
+      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+      *
+      * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+      */
+
+    EIGEN_STRONG_INLINE Scalar&
+    operator[](Index index)
+    {
+      #ifndef EIGEN2_SUPPORT
+      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+      #endif
+      eigen_assert(index >= 0 && index < size());
+      return derived().coeffRef(index);
+    }
+
+    /** \returns a reference to the coefficient at given index.
+      *
+      * This is synonymous to operator[](Index).
+      *
+      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+      *
+      * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+      */
+
+    EIGEN_STRONG_INLINE Scalar&
+    operator()(Index index)
+    {
+      eigen_assert(index >= 0 && index < size());
+      return derived().coeffRef(index);
+    }
+
+    /** equivalent to operator[](0).  */
+
+    EIGEN_STRONG_INLINE Scalar&
+    x() { return (*this)[0]; }
+
+    /** equivalent to operator[](1).  */
+
+    EIGEN_STRONG_INLINE Scalar&
+    y() { return (*this)[1]; }
+
+    /** equivalent to operator[](2).  */
+
+    EIGEN_STRONG_INLINE Scalar&
+    z() { return (*this)[2]; }
+
+    /** equivalent to operator[](3).  */
+
+    EIGEN_STRONG_INLINE Scalar&
+    w() { return (*this)[3]; }
+
+    /** \internal
+      * Stores the given packet of coefficients, at the given row and column of this expression. It is your responsibility
+      * to ensure that a packet really starts there. This method is only available on expressions having the
+      * PacketAccessBit.
+      *
+      * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+      * starting at an address which is a multiple of the packet size.
+      */
+
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket
+    (Index row, Index col, const typename internal::packet_traits<Scalar>::type& x)
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      derived().template writePacket<StoreMode>(row,col,x);
+    }
+
+
+    /** \internal */
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacketByOuterInner
+    (Index outer, Index inner, const typename internal::packet_traits<Scalar>::type& x)
+    {
+      writePacket<StoreMode>(rowIndexByOuterInner(outer, inner),
+                            colIndexByOuterInner(outer, inner),
+                            x);
+    }
+
+    /** \internal
+      * Stores the given packet of coefficients, at the given index in this expression. It is your responsibility
+      * to ensure that a packet really starts there. This method is only available on expressions having the
+      * PacketAccessBit and the LinearAccessBit.
+      *
+      * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+      * starting at an address which is a multiple of the packet size.
+      */
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket
+    (Index index, const typename internal::packet_traits<Scalar>::type& x)
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      derived().template writePacket<StoreMode>(index,x);
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+    /** \internal Copies the coefficient at position (row,col) of other into *this.
+      *
+      * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+      * with usual assignments.
+      *
+      * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+      */
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      derived().coeffRef(row, col) = other.derived().coeff(row, col);
+    }
+
+    /** \internal Copies the coefficient at the given index of other into *this.
+      *
+      * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+      * with usual assignments.
+      *
+      * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+      */
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      derived().coeffRef(index) = other.derived().coeff(index);
+    }
+
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void copyCoeffByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
+    {
+      const Index row = rowIndexByOuterInner(outer,inner);
+      const Index col = colIndexByOuterInner(outer,inner);
+      // derived() is important here: copyCoeff() may be reimplemented in Derived!
+      derived().copyCoeff(row, col, other);
+    }
+
+    /** \internal Copies the packet at position (row,col) of other into *this.
+      *
+      * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+      * with usual assignments.
+      *
+      * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+      */
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    EIGEN_STRONG_INLINE void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      derived().template writePacket<StoreMode>(row, col,
+        other.derived().template packet<LoadMode>(row, col));
+    }
+
+    /** \internal Copies the packet at the given index of other into *this.
+      *
+      * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+      * with usual assignments.
+      *
+      * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+      */
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    EIGEN_STRONG_INLINE void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+    {
+      eigen_internal_assert(index >= 0 && index < size());
+      derived().template writePacket<StoreMode>(index,
+        other.derived().template packet<LoadMode>(index));
+    }
+
+    /** \internal */
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    EIGEN_STRONG_INLINE void copyPacketByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
+    {
+      const Index row = rowIndexByOuterInner(outer,inner);
+      const Index col = colIndexByOuterInner(outer,inner);
+      // derived() is important here: copyCoeff() may be reimplemented in Derived!
+      derived().template copyPacket< OtherDerived, StoreMode, LoadMode>(row, col, other);
+    }
+#endif
+
+};
+
+/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
+  * \ingroup Core_Module
+  * \tparam Derived Type of the derived class
+  * \tparam #DirectAccessors Constant indicating direct access
+  *
+  * This class defines functions to work with strides which can be used to access entries directly. This class
+  * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
+  * \c operator() .
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+  public:
+
+    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::derived;
+
+    /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+      *
+      * \sa outerStride(), rowStride(), colStride()
+      */
+    inline Index innerStride() const
+    {
+      return derived().innerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+      *          in a column-major matrix).
+      *
+      * \sa innerStride(), rowStride(), colStride()
+      */
+    inline Index outerStride() const
+    {
+      return derived().outerStride();
+    }
+
+    // FIXME shall we remove it ?
+    inline Index stride() const
+    {
+      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive rows.
+      *
+      * \sa innerStride(), outerStride(), colStride()
+      */
+    inline Index rowStride() const
+    {
+      return Derived::IsRowMajor ? outerStride() : innerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive columns.
+      *
+      * \sa innerStride(), outerStride(), rowStride()
+      */
+    inline Index colStride() const
+    {
+      return Derived::IsRowMajor ? innerStride() : outerStride();
+    }
+};
+
+/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
+  * \ingroup Core_Module
+  * \tparam Derived Type of the derived class
+  * \tparam #DirectWriteAccessors Constant indicating direct access
+  *
+  * This class defines functions to work with strides which can be used to access entries directly. This class
+  * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
+  * \c operator().
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectWriteAccessors>
+  : public DenseCoeffsBase<Derived, WriteAccessors>
+{
+  public:
+
+    typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::derived;
+
+    /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+      *
+      * \sa outerStride(), rowStride(), colStride()
+      */
+    inline Index innerStride() const
+    {
+      return derived().innerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+      *          in a column-major matrix).
+      *
+      * \sa innerStride(), rowStride(), colStride()
+      */
+    inline Index outerStride() const
+    {
+      return derived().outerStride();
+    }
+
+    // FIXME shall we remove it ?
+    inline Index stride() const
+    {
+      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive rows.
+      *
+      * \sa innerStride(), outerStride(), colStride()
+      */
+    inline Index rowStride() const
+    {
+      return Derived::IsRowMajor ? outerStride() : innerStride();
+    }
+
+    /** \returns the pointer increment between two consecutive columns.
+      *
+      * \sa innerStride(), outerStride(), rowStride()
+      */
+    inline Index colStride() const
+    {
+      return Derived::IsRowMajor ? innerStride() : outerStride();
+    }
+};
+
+namespace internal {
+
+template<typename Derived, bool JustReturnZero>
+struct first_aligned_impl
+{
+  inline static typename Derived::Index run(const Derived&)
+  { return 0; }
+};
+
+template<typename Derived>
+struct first_aligned_impl<Derived, false>
+{
+  inline static typename Derived::Index run(const Derived& m)
+  {
+    return first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
+  }
+};
+
+/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
+  *
+  * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
+  * documentation.
+  */
+template<typename Derived>
+inline static typename Derived::Index first_aligned(const Derived& m)
+{
+  return first_aligned_impl
+          <Derived, (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
+          ::run(m);
+}
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct inner_stride_at_compile_time
+{
+  enum { ret = traits<Derived>::InnerStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct inner_stride_at_compile_time<Derived, false>
+{
+  enum { ret = 0 };
+};
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct outer_stride_at_compile_time
+{
+  enum { ret = traits<Derived>::OuterStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct outer_stride_at_compile_time<Derived, false>
+{
+  enum { ret = 0 };
+};
+
+} // end namespace internal
+
+#endif // EIGEN_DENSECOEFFSBASE_H

Eigen/src/Core/DenseStorage.h

@@ -0,0 +1,304 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIXSTORAGE_H
+#define EIGEN_MATRIXSTORAGE_H
+
+#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+  #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
+#else
+  #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+#endif
+
+namespace internal {
+
+struct constructor_without_unaligned_array_assert {};
+
+/** \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.
+  */
+template <typename T, int Size, int MatrixOrArrayOptions,
+          int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0
+                        : (((Size*sizeof(T))%16)==0) ? 16
+                        : 0 >
+struct plain_array
+{
+  T array[Size];
+  plain_array() {}
+  plain_array(constructor_without_unaligned_array_assert) {}
+};
+
+#ifdef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+  #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)
+#else
+  #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
+    eigen_assert((reinterpret_cast<size_t>(array) & sizemask) == 0 \
+              && "this assertion is explained here: " \
+              "http://eigen.tuxfamily.org/dox-devel/TopicUnalignedArrayAssert.html" \
+              " **** READ THIS WEB PAGE !!! ****");
+#endif
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 16>
+{
+  EIGEN_USER_ALIGN16 T array[Size];
+  plain_array() { EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(0xf) }
+  plain_array(constructor_without_unaligned_array_assert) {}
+};
+
+template <typename T, int MatrixOrArrayOptions, int Alignment>
+struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
+{
+  EIGEN_USER_ALIGN16 T array[1];
+  plain_array() {}
+  plain_array(constructor_without_unaligned_array_assert) {}
+};
+
+} // end namespace internal
+
+/** \internal
+  *
+  * \class DenseStorage
+  * \ingroup Core_Module
+  *
+  * \brief Stores the data of a matrix
+  *
+  * This class stores the data of fixed-size, dynamic-size or mixed matrices
+  * in a way as compact as possible.
+  *
+  * \sa Matrix
+  */
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage;
+
+// purely fixed-size matrix
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage
+{
+    internal::plain_array<T,Size,_Options> m_data;
+  public:
+    inline explicit DenseStorage() {}
+    inline DenseStorage(internal::constructor_without_unaligned_array_assert)
+      : m_data(internal::constructor_without_unaligned_array_assert()) {}
+    inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }
+    inline static DenseIndex rows(void) {return _Rows;}
+    inline static DenseIndex cols(void) {return _Cols;}
+    inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+    inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// null matrix
+template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
+{
+  public:
+    inline explicit DenseStorage() {}
+    inline DenseStorage(internal::constructor_without_unaligned_array_assert) {}
+    inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
+    inline void swap(DenseStorage& ) {}
+    inline static DenseIndex rows(void) {return _Rows;}
+    inline static DenseIndex cols(void) {return _Cols;}
+    inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
+    inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
+    inline const T *data() const { return 0; }
+    inline T *data() { return 0; }
+};
+
+// dynamic-size matrix with fixed-size storage
+template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic, Dynamic, _Options>
+{
+    internal::plain_array<T,Size,_Options> m_data;
+    DenseIndex m_rows;
+    DenseIndex m_cols;
+  public:
+    inline explicit 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 rows, DenseIndex cols) : m_rows(rows), m_cols(cols) {}
+    inline void swap(DenseStorage& other)
+    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+    inline DenseIndex rows(void) const {return m_rows;}
+    inline DenseIndex cols(void) const {return m_cols;}
+    inline void conservativeResize(DenseIndex, DenseIndex rows, DenseIndex cols) { m_rows = rows; m_cols = cols; }
+    inline void resize(DenseIndex, DenseIndex rows, DenseIndex cols) { m_rows = rows; m_cols = cols; }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed width
+template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Size, Dynamic, _Cols, _Options>
+{
+    internal::plain_array<T,Size,_Options> m_data;
+    DenseIndex m_rows;
+  public:
+    inline explicit 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 rows, DenseIndex) : m_rows(rows) {}
+    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    inline DenseIndex rows(void) const {return m_rows;}
+    inline DenseIndex cols(void) const {return _Cols;}
+    inline void conservativeResize(DenseIndex, DenseIndex rows, DenseIndex) { m_rows = rows; }
+    inline void resize(DenseIndex, DenseIndex rows, DenseIndex) { m_rows = rows; }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed height
+template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Size, _Rows, Dynamic, _Options>
+{
+    internal::plain_array<T,Size,_Options> m_data;
+    DenseIndex m_cols;
+  public:
+    inline explicit 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 cols) : m_cols(cols) {}
+    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    inline DenseIndex rows(void) const {return _Rows;}
+    inline DenseIndex cols(void) const {return m_cols;}
+    inline void conservativeResize(DenseIndex, DenseIndex, DenseIndex cols) { m_cols = cols; }
+    inline void resize(DenseIndex, DenseIndex, DenseIndex cols) { m_cols = cols; }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// purely dynamic matrix.
+template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynamic, _Options>
+{
+    T *m_data;
+    DenseIndex m_rows;
+    DenseIndex m_cols;
+  public:
+    inline explicit 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 rows, DenseIndex cols)
+      : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows), m_cols(cols) 
+    { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
+    inline void swap(DenseStorage& other)
+    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+    inline DenseIndex rows(void) const {return m_rows;}
+    inline DenseIndex cols(void) const {return m_cols;}
+    inline void conservativeResize(DenseIndex size, DenseIndex rows, DenseIndex cols)
+    {
+      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);
+      m_rows = rows;
+      m_cols = cols;
+    }
+    void resize(DenseIndex size, DenseIndex rows, DenseIndex cols)
+    {
+      if(size != m_rows*m_cols)
+      {
+        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols);
+        if (size)
+          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+        else
+          m_data = 0;
+        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+      }
+      m_rows = rows;
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+// matrix with dynamic width and fixed height (so that matrix has dynamic size).
+template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Rows, Dynamic, _Options>
+{
+    T *m_data;
+    DenseIndex m_cols;
+  public:
+    inline explicit 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 cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(cols)
+    { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
+    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    inline static DenseIndex rows(void) {return _Rows;}
+    inline DenseIndex cols(void) const {return m_cols;}
+    inline void conservativeResize(DenseIndex size, DenseIndex, DenseIndex cols)
+    {
+      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);
+      m_cols = cols;
+    }
+    EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex, DenseIndex cols)
+    {
+      if(size != _Rows*m_cols)
+      {
+        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols);
+        if (size)
+          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+        else
+          m_data = 0;
+        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+      }
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+// matrix with dynamic height and fixed width (so that matrix has dynamic size).
+template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dynamic, _Cols, _Options>
+{
+    T *m_data;
+    DenseIndex m_rows;
+  public:
+    inline explicit 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 rows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows)
+    { EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
+    inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
+    inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    inline DenseIndex rows(void) const {return m_rows;}
+    inline static DenseIndex cols(void) {return _Cols;}
+    inline void conservativeResize(DenseIndex size, DenseIndex rows, DenseIndex)
+    {
+      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);
+      m_rows = rows;
+    }
+    EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex rows, DenseIndex)
+    {
+      if(size != m_rows*_Cols)
+      {
+        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows);
+        if (size)
+          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
+        else
+          m_data = 0;
+        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
+      }
+      m_rows = rows;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+#endif // EIGEN_MATRIX_H

Eigen/src/Core/Diagonal.h

@@ -0,0 +1,227 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONAL_H
+#define EIGEN_DIAGONAL_H
+
+/** \class Diagonal
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
+  *
+  * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
+  * \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
+  *              A positive value means a superdiagonal, a negative value means a subdiagonal.
+  *              You can also use Dynamic so the index can be set at runtime.
+  *
+  * The matrix is not required to be square.
+  *
+  * This class represents an expression of the main diagonal, or any sub/super diagonal
+  * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
+  * time this is the only way it is used.
+  *
+  * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
+  */
+
+namespace internal {
+template<typename MatrixType, int DiagIndex>
+struct traits<Diagonal<MatrixType,DiagIndex> >
+ : traits<MatrixType>
+{
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+  typedef typename MatrixType::StorageKind StorageKind;
+  enum {
+    AbsDiagIndex = DiagIndex<0 ? -DiagIndex : DiagIndex, // only used if DiagIndex != Dynamic
+    // FIXME these computations are broken in the case where the matrix is rectangular and DiagIndex!=0
+    RowsAtCompileTime = (int(DiagIndex) == Dynamic || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
+                      : (EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime,
+                                        MatrixType::ColsAtCompileTime) - AbsDiagIndex),
+    ColsAtCompileTime = 1,
+    MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
+                         : DiagIndex == Dynamic ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
+                                                                    MatrixType::MaxColsAtCompileTime)
+                         : (EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime) - AbsDiagIndex),
+    MaxColsAtCompileTime = 1,
+    MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+    Flags = (unsigned int)_MatrixTypeNested::Flags & (HereditaryBits | LinearAccessBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit,
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost,
+    MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
+    InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
+    OuterStrideAtCompileTime = 0
+  };
+};
+}
+
+template<typename MatrixType, int DiagIndex> class Diagonal
+   : public internal::dense_xpr_base< Diagonal<MatrixType,DiagIndex> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<Diagonal>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
+
+    inline Diagonal(MatrixType& matrix, Index index = DiagIndex) : m_matrix(matrix), m_index(index) {}
+
+    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()); }
+
+    inline Index cols() const { return 1; }
+
+    inline Index innerStride() const
+    {
+      return m_matrix.outerStride() + 1;
+    }
+
+    inline Index outerStride() const
+    {
+      return 0;
+    }
+
+    inline Scalar& coeffRef(Index row, Index)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+      return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+    }
+
+    inline const Scalar& coeffRef(Index row, Index) const
+    {
+      return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+    }
+
+    inline CoeffReturnType coeff(Index row, Index) const
+    {
+      return m_matrix.coeff(row+rowOffset(), row+colOffset());
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+      return m_matrix.const_cast_derived().coeffRef(index+rowOffset(), index+colOffset());
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_matrix.const_cast_derived().coeffRef(index+rowOffset(), index+colOffset());
+    }
+
+    inline CoeffReturnType coeff(Index index) const
+    {
+      return m_matrix.coeff(index+rowOffset(), index+colOffset());
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+    const internal::variable_if_dynamic<Index, DiagIndex> m_index;
+
+  private:
+    // some compilers may fail to optimize std::max etc in case of compile-time constants...
+    EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
+    EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
+    EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
+    // triger a compile time error is someone try to call packet
+    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
+    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
+};
+
+/** \returns an expression of the main diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * Example: \include MatrixBase_diagonal.cpp
+  * Output: \verbinclude MatrixBase_diagonal.out
+  *
+  * \sa class Diagonal */
+template<typename Derived>
+inline typename MatrixBase<Derived>::DiagonalReturnType
+MatrixBase<Derived>::diagonal()
+{
+  return derived();
+}
+
+/** This is the const version of diagonal(). */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::ConstDiagonalReturnType
+MatrixBase<Derived>::diagonal() const
+{
+  return ConstDiagonalReturnType(derived());
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+  * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+  *
+  * Example: \include MatrixBase_diagonal_int.cpp
+  * Output: \verbinclude MatrixBase_diagonal_int.out
+  *
+  * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Dynamic>::Type
+MatrixBase<Derived>::diagonal(Index index)
+{
+  return typename DiagonalIndexReturnType<Dynamic>::Type(derived(), index);
+}
+
+/** This is the const version of diagonal(Index). */
+template<typename Derived>
+inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Dynamic>::Type
+MatrixBase<Derived>::diagonal(Index index) const
+{
+  return typename ConstDiagonalIndexReturnType<Dynamic>::Type(derived(), index);
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+  * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+  *
+  * Example: \include MatrixBase_diagonal_template_int.cpp
+  * Output: \verbinclude MatrixBase_diagonal_template_int.out
+  *
+  * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+template<int Index>
+inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index>::Type
+MatrixBase<Derived>::diagonal()
+{
+  return derived();
+}
+
+/** This is the const version of diagonal<int>(). */
+template<typename Derived>
+template<int Index>
+inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index>::Type
+MatrixBase<Derived>::diagonal() const
+{
+  return derived();
+}
+
+#endif // EIGEN_DIAGONAL_H

Eigen/src/Core/DiagonalMatrix.h

@@ -0,0 +1,306 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONALMATRIX_H
+#define EIGEN_DIAGONALMATRIX_H
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename Derived>
+class DiagonalBase : public EigenBase<Derived>
+{
+  public:
+    typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
+    typedef typename DiagonalVectorType::Scalar Scalar;
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+
+    enum {
+      RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+      ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+      MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+      MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+      IsVectorAtCompileTime = 0,
+      Flags = 0
+    };
+
+    typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
+    typedef DenseMatrixType DenseType;
+    typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
+
+    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+    inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+    DenseMatrixType toDenseMatrix() const { return derived(); }
+    template<typename DenseDerived>
+    void evalTo(MatrixBase<DenseDerived> &other) const;
+    template<typename DenseDerived>
+    void addTo(MatrixBase<DenseDerived> &other) const
+    { other.diagonal() += diagonal(); }
+    template<typename DenseDerived>
+    void subTo(MatrixBase<DenseDerived> &other) const
+    { other.diagonal() -= diagonal(); }
+
+    inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
+    inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
+
+    inline Index rows() const { return diagonal().size(); }
+    inline Index cols() const { return diagonal().size(); }
+
+    template<typename MatrixDerived>
+    const DiagonalProduct<MatrixDerived, Derived, OnTheLeft>
+    operator*(const MatrixBase<MatrixDerived> &matrix) const;
+
+    inline const DiagonalWrapper<CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> >
+    inverse() const
+    {
+      return diagonal().cwiseInverse();
+    }
+    
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived>
+    bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+    {
+      return diagonal().isApprox(other.diagonal(), precision);
+    }
+    template<typename OtherDerived>
+    bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+    {
+      return toDenseMatrix().isApprox(other, precision);
+    }
+    #endif
+};
+
+template<typename Derived>
+template<typename DenseDerived>
+void DiagonalBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
+{
+  other.setZero();
+  other.diagonal() = diagonal();
+}
+#endif
+
+/** \class DiagonalMatrix
+  * \ingroup Core_Module
+  *
+  * \brief Represents a diagonal matrix with its storage
+  *
+  * \param _Scalar the type of coefficients
+  * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
+  * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
+  *        to SizeAtCompileTime. Most of the time, you do not need to specify it.
+  *
+  * \sa class DiagonalWrapper
+  */
+
+namespace internal {
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
+ : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+  typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
+  typedef Dense StorageKind;
+  typedef DenseIndex Index;
+  enum {
+    Flags = LvalueBit
+  };
+};
+}
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+class DiagonalMatrix
+  : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+  public:
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
+    typedef const DiagonalMatrix& Nested;
+    typedef _Scalar Scalar;
+    typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
+    typedef typename internal::traits<DiagonalMatrix>::Index Index;
+    #endif
+
+  protected:
+
+    DiagonalVectorType m_diagonal;
+
+  public:
+
+    /** const version of diagonal(). */
+    inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
+    /** \returns a reference to the stored vector of diagonal coefficients. */
+    inline DiagonalVectorType& diagonal() { return m_diagonal; }
+
+    /** Default constructor without initialization */
+    inline DiagonalMatrix() {}
+
+    /** Constructs a diagonal matrix with given dimension  */
+    inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
+
+    /** 2D constructor. */
+    inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
+
+    /** 3D constructor. */
+    inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
+
+    /** Copy constructor. */
+    template<typename OtherDerived>
+    inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
+    inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
+    #endif
+
+    /** generic constructor from expression of the diagonal coefficients */
+    template<typename OtherDerived>
+    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
+    {}
+
+    /** Copy operator. */
+    template<typename OtherDerived>
+    DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
+    {
+      m_diagonal = other.diagonal();
+      return *this;
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    DiagonalMatrix& operator=(const DiagonalMatrix& other)
+    {
+      m_diagonal = other.diagonal();
+      return *this;
+    }
+    #endif
+
+    /** Resizes to given size. */
+    inline void resize(Index size) { m_diagonal.resize(size); }
+    /** Sets all coefficients to zero. */
+    inline void setZero() { m_diagonal.setZero(); }
+    /** Resizes and sets all coefficients to zero. */
+    inline void setZero(Index size) { m_diagonal.setZero(size); }
+    /** Sets this matrix to be the identity matrix of the current size. */
+    inline void setIdentity() { m_diagonal.setOnes(); }
+    /** Sets this matrix to be the identity matrix of the given size. */
+    inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
+};
+
+/** \class DiagonalWrapper
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a diagonal matrix
+  *
+  * \param _DiagonalVectorType the type of the vector of diagonal coefficients
+  *
+  * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
+  * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
+  * and most of the time this is the only way that it is used.
+  *
+  * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
+  */
+
+namespace internal {
+template<typename _DiagonalVectorType>
+struct traits<DiagonalWrapper<_DiagonalVectorType> >
+{
+  typedef _DiagonalVectorType DiagonalVectorType;
+  typedef typename DiagonalVectorType::Scalar Scalar;
+  typedef typename DiagonalVectorType::Index Index;
+  typedef typename DiagonalVectorType::StorageKind StorageKind;
+  enum {
+    RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+    ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+    MaxRowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+    MaxColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+    Flags =  traits<DiagonalVectorType>::Flags & LvalueBit
+  };
+};
+}
+
+template<typename _DiagonalVectorType>
+class DiagonalWrapper
+  : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
+{
+  public:
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef _DiagonalVectorType DiagonalVectorType;
+    typedef DiagonalWrapper Nested;
+    #endif
+
+    /** Constructor from expression of diagonal coefficients to wrap. */
+    inline DiagonalWrapper(const DiagonalVectorType& diagonal) : m_diagonal(diagonal) {}
+
+    /** \returns a const reference to the wrapped expression of diagonal coefficients. */
+    const DiagonalVectorType& diagonal() const { return m_diagonal; }
+
+  protected:
+    const typename DiagonalVectorType::Nested m_diagonal;
+};
+
+/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
+  *
+  * \only_for_vectors
+  *
+  * Example: \include MatrixBase_asDiagonal.cpp
+  * Output: \verbinclude MatrixBase_asDiagonal.out
+  *
+  * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
+  **/
+template<typename Derived>
+inline const DiagonalWrapper<const Derived>
+MatrixBase<Derived>::asDiagonal() const
+{
+  return derived();
+}
+
+/** \returns true if *this is approximately equal to a diagonal matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isDiagonal.cpp
+  * Output: \verbinclude MatrixBase_isDiagonal.out
+  *
+  * \sa asDiagonal()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isDiagonal(RealScalar prec) const
+{
+  if(cols() != rows()) return false;
+  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
+  for(Index j = 0; j < cols(); ++j)
+  {
+    RealScalar absOnDiagonal = internal::abs(coeff(j,j));
+    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
+  }
+  for(Index j = 0; j < cols(); ++j)
+    for(Index i = 0; i < j; ++i)
+    {
+      if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+      if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+    }
+  return true;
+}
+
+#endif // EIGEN_DIAGONALMATRIX_H

Eigen/src/Core/DiagonalProduct.h

@@ -0,0 +1,135 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONALPRODUCT_H
+#define EIGEN_DIAGONALPRODUCT_H
+
+namespace internal {
+template<typename MatrixType, typename DiagonalType, int ProductOrder>
+struct traits<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
+ : traits<MatrixType>
+{
+  typedef typename scalar_product_traits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+
+    _StorageOrder = MatrixType::Flags & RowMajorBit ? RowMajor : ColMajor,
+    _PacketOnDiag = !((int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
+                    ||(int(_StorageOrder) == ColMajor && 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) && _SameTypes && ((!_PacketOnDiag) || (bool(int(DiagonalType::Flags)&PacketAccessBit))),
+
+    Flags = (HereditaryBits & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0),
+    CoeffReadCost = NumTraits<Scalar>::MulCost + MatrixType::CoeffReadCost + DiagonalType::DiagonalVectorType::CoeffReadCost
+  };
+};
+}
+
+template<typename MatrixType, typename DiagonalType, int ProductOrder>
+class DiagonalProduct : internal::no_assignment_operator,
+                        public MatrixBase<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
+{
+  public:
+
+    typedef MatrixBase<DiagonalProduct> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(DiagonalProduct)
+
+    inline DiagonalProduct(const MatrixType& matrix, const DiagonalType& diagonal)
+      : m_matrix(matrix), m_diagonal(diagonal)
+    {
+      eigen_assert(diagonal.diagonal().size() == (ProductOrder == OnTheLeft ? matrix.rows() : matrix.cols()));
+    }
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+
+    const Scalar coeff(Index row, Index col) const
+    {
+      return m_diagonal.diagonal().coeff(ProductOrder == OnTheLeft ? row : col) * m_matrix.coeff(row, col);
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+    {
+      enum {
+        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());
+    }
+
+  protected:
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::true_type) const
+    {
+      return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
+                     internal::pset1<PacketScalar>(m_diagonal.diagonal().coeff(id)));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::false_type) const
+    {
+      enum {
+        InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
+        DiagonalVectorPacketLoadMode = (LoadMode == Aligned && ((InnerSize%16) == 0)) ? Aligned : Unaligned
+      };
+      return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
+                     m_diagonal.diagonal().template packet<DiagonalVectorPacketLoadMode>(id));
+    }
+
+    const typename MatrixType::Nested m_matrix;
+    const typename DiagonalType::Nested m_diagonal;
+};
+
+/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
+  */
+template<typename Derived>
+template<typename DiagonalDerived>
+inline const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
+MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &diagonal) const
+{
+  return DiagonalProduct<Derived, DiagonalDerived, OnTheRight>(derived(), diagonal.derived());
+}
+
+/** \returns the diagonal matrix product of \c *this by the matrix \a matrix.
+  */
+template<typename DiagonalDerived>
+template<typename MatrixDerived>
+inline const DiagonalProduct<MatrixDerived, DiagonalDerived, OnTheLeft>
+DiagonalBase<DiagonalDerived>::operator*(const MatrixBase<MatrixDerived> &matrix) const
+{
+  return DiagonalProduct<MatrixDerived, DiagonalDerived, OnTheLeft>(matrix.derived(), derived());
+}
+
+
+#endif // EIGEN_DIAGONALPRODUCT_H

Eigen/src/Core/Dot.h

@@ -0,0 +1,272 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DOT_H
+#define EIGEN_DOT_H
+
+namespace internal {
+
+// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
+// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
+// looking at the static assertions. Thus this is a trick to get better compile errors.
+template<typename T, typename U,
+// the NeedToTranspose condition here is taken straight from Assign.h
+         bool NeedToTranspose = T::IsVectorAtCompileTime
+                && U::IsVectorAtCompileTime
+                && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
+                      |  // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
+                         // revert to || as soon as not needed anymore.
+                    (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
+>
+struct dot_nocheck
+{
+  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+  static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+  {
+    return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+  }
+};
+
+template<typename T, typename U>
+struct dot_nocheck<T, U, true>
+{
+  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+  static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+  {
+    return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+  }
+};
+
+} // end namespace internal
+
+/** \returns the dot product of *this with other.
+  *
+  * \only_for_vectors
+  *
+  * \note If the scalar type is complex numbers, then this function returns the hermitian
+  * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
+  * second variable.
+  *
+  * \sa squaredNorm(), norm()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+  typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
+  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
+
+  eigen_assert(size() == other.size());
+
+  return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
+}
+
+#ifdef EIGEN2_SUPPORT
+/** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable
+  * (conjugating the second variable). Of course this only makes a difference in the complex case.
+  *
+  * This method is only available in EIGEN2_SUPPORT mode.
+  *
+  * \only_for_vectors
+  *
+  * \sa dot()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+  eigen_assert(size() == other.size());
+
+  return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
+}
+#endif
+
+
+//---------- implementation of L2 norm and related functions ----------
+
+/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm.
+  * In both cases, it consists in the sum of the square of all the matrix entries.
+  * For vectors, this is also equals to the dot product of \c *this with itself.
+  *
+  * \sa dot(), norm()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
+{
+  return internal::real((*this).cwiseAbs2().sum());
+}
+
+/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
+  * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
+  * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
+  *
+  * \sa dot(), squaredNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
+{
+  return internal::sqrt(squaredNorm());
+}
+
+/** \returns an expression of the quotient of *this by its own norm.
+  *
+  * \only_for_vectors
+  *
+  * \sa norm(), normalize()
+  */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::normalized() const
+{
+  typedef typename internal::nested<Derived>::type Nested;
+  typedef typename internal::remove_reference<Nested>::type _Nested;
+  _Nested n(derived());
+  return n / n.norm();
+}
+
+/** Normalizes the vector, i.e. divides it by its own norm.
+  *
+  * \only_for_vectors
+  *
+  * \sa norm(), normalized()
+  */
+template<typename Derived>
+inline void MatrixBase<Derived>::normalize()
+{
+  *this /= norm();
+}
+
+//---------- implementation of other norms ----------
+
+namespace internal {
+
+template<typename Derived, int p>
+struct lpNorm_selector
+{
+  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
+  inline static RealScalar run(const MatrixBase<Derived>& m)
+  {
+    return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
+  }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 1>
+{
+  inline static typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.cwiseAbs().sum();
+  }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 2>
+{
+  inline static typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.norm();
+  }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, Infinity>
+{
+  inline static typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.cwiseAbs().maxCoeff();
+  }
+};
+
+} // end namespace internal
+
+/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
+  *          of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
+  *          norm, that is the maximum of the absolute values of the coefficients of *this.
+  *
+  * \sa norm()
+  */
+template<typename Derived>
+template<int p>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::lpNorm() const
+{
+  return internal::lpNorm_selector<Derived, p>::run(*this);
+}
+
+//---------- implementation of isOrthogonal / isUnitary ----------
+
+/** \returns true if *this is approximately orthogonal to \a other,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOrthogonal.cpp
+  * Output: \verbinclude MatrixBase_isOrthogonal.out
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isOrthogonal
+(const MatrixBase<OtherDerived>& other, RealScalar prec) const
+{
+  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();
+}
+
+/** \returns true if *this is approximately an unitary matrix,
+  *          within the precision given by \a prec. In the case where the \a Scalar
+  *          type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
+  *
+  * \note This can be used to check whether a family of vectors forms an orthonormal basis.
+  *       Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
+  *       orthonormal basis.
+  *
+  * Example: \include MatrixBase_isUnitary.cpp
+  * Output: \verbinclude MatrixBase_isUnitary.out
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isUnitary(RealScalar prec) const
+{
+  typename Derived::Nested nested(derived());
+  for(Index i = 0; i < cols(); ++i)
+  {
+    if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
+      return false;
+    for(Index j = 0; j < i; ++j)
+      if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
+        return false;
+  }
+  return true;
+}
+
+#endif // EIGEN_DOT_H

Eigen/src/Core/EigenBase.h

@@ -0,0 +1,172 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_EIGENBASE_H
+#define EIGEN_EIGENBASE_H
+
+
+/** Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
+  *
+  * In other words, an EigenBase object is an object that can be copied into a MatrixBase.
+  *
+  * Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
+  *
+  * Notice that this class is trivial, it is only used to disambiguate overloaded functions.
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived> struct EigenBase
+{
+//   typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
+
+  typedef typename internal::traits<Derived>::StorageKind StorageKind;
+  typedef typename internal::traits<Derived>::Index Index;
+
+  /** \returns a reference to the derived object */
+  Derived& derived() { return *static_cast<Derived*>(this); }
+  /** \returns a const reference to the derived object */
+  const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+  inline Derived& const_cast_derived() const
+  { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
+  inline const Derived& const_derived() const
+  { return *static_cast<const Derived*>(this); }
+
+  /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+  inline Index rows() const { return derived().rows(); }
+  /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+  inline Index cols() const { return derived().cols(); }
+  /** \returns the number of coefficients, which is rows()*cols().
+    * \sa rows(), cols(), SizeAtCompileTime. */
+  inline Index size() const { return rows() * cols(); }
+
+  /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
+  template<typename Dest> inline void evalTo(Dest& dst) const
+  { derived().evalTo(dst); }
+
+  /** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
+  template<typename Dest> inline void addTo(Dest& dst) const
+  {
+    // This is the default implementation,
+    // derived class can reimplement it in a more optimized way.
+    typename Dest::PlainObject res(rows(),cols());
+    evalTo(res);
+    dst += res;
+  }
+
+  /** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
+  template<typename Dest> inline void subTo(Dest& dst) const
+  {
+    // This is the default implementation,
+    // derived class can reimplement it in a more optimized way.
+    typename Dest::PlainObject res(rows(),cols());
+    evalTo(res);
+    dst -= res;
+  }
+
+  /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
+  template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
+  {
+    // This is the default implementation,
+    // derived class can reimplement it in a more optimized way.
+    dst = dst * this->derived();
+  }
+
+  /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
+  template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
+  {
+    // This is the default implementation,
+    // derived class can reimplement it in a more optimized way.
+    dst = this->derived() * dst;
+  }
+
+};
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \brief Copies the generic expression \a other into *this.
+  *
+  * \details The expression must provide a (templated) evalTo(Derived& dst) const
+  * function which does the actual job. In practice, this allows any user to write
+  * its own special matrix without having to modify MatrixBase
+  *
+  * \returns a reference to *this.
+  */
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
+{
+  other.derived().evalTo(derived());
+  return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
+{
+  other.derived().addTo(derived());
+  return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
+{
+  other.derived().subTo(derived());
+  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());
+}
+
+#endif // EIGEN_EIGENBASE_H

Eigen/src/Core/Flagged.h

@@ -0,0 +1,151 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FLAGGED_H
+#define EIGEN_FLAGGED_H
+
+/** \class Flagged
+  * \ingroup Core_Module
+  *
+  * \brief Expression with modified flags
+  *
+  * \param ExpressionType the type of the object of which we are modifying the flags
+  * \param Added the flags added to the expression
+  * \param Removed the flags removed from the expression (has priority over Added).
+  *
+  * This class represents an expression whose flags have been modified.
+  * It is the return type of MatrixBase::flagged()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::flagged()
+  */
+
+namespace internal {
+template<typename ExpressionType, unsigned int Added, unsigned int Removed>
+struct traits<Flagged<ExpressionType, Added, Removed> > : traits<ExpressionType>
+{
+  enum { Flags = (ExpressionType::Flags | Added) & ~Removed };
+};
+}
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged
+  : public MatrixBase<Flagged<ExpressionType, Added, Removed> >
+{
+  public:
+
+    typedef MatrixBase<Flagged> Base;
+    
+    EIGEN_DENSE_PUBLIC_INTERFACE(Flagged)
+    typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, const ExpressionType&>::type ExpressionTypeNested;
+    typedef typename ExpressionType::InnerIterator InnerIterator;
+
+    inline Flagged(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+    inline Index outerStride() const { return m_matrix.outerStride(); }
+    inline Index innerStride() const { return m_matrix.innerStride(); }
+
+    inline CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_matrix.coeff(row, col);
+    }
+
+    inline CoeffReturnType coeff(Index index) const
+    {
+      return m_matrix.coeff(index);
+    }
+    
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return m_matrix.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return m_matrix.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+    const ExpressionType& _expression() const { return m_matrix; }
+
+    template<typename OtherDerived>
+    typename ExpressionType::PlainObject solveTriangular(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived>
+    void solveTriangularInPlace(const MatrixBase<OtherDerived>& other) const;
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \returns an expression of *this with added and removed flags
+  *
+  * This is mostly for internal use.
+  *
+  * \sa class Flagged
+  */
+template<typename Derived>
+template<unsigned int Added,unsigned int Removed>
+inline const Flagged<Derived, Added, Removed>
+DenseBase<Derived>::flagged() const
+{
+  return derived();
+}
+
+#endif // EIGEN_FLAGGED_H

Eigen/src/Core/ForceAlignedAccess.h

@@ -0,0 +1,157 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FORCEALIGNEDACCESS_H
+#define EIGEN_FORCEALIGNEDACCESS_H
+
+/** \class ForceAlignedAccess
+  * \ingroup Core_Module
+  *
+  * \brief Enforce aligned packet loads and stores regardless of what is requested
+  *
+  * \param ExpressionType the type of the object of which we are forcing aligned packet access
+  *
+  * This class is the return type of MatrixBase::forceAlignedAccess()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::forceAlignedAccess()
+  */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
+{};
+}
+
+template<typename ExpressionType> class ForceAlignedAccess
+  : public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
+
+    inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
+
+    inline Index rows() const { return m_expression.rows(); }
+    inline Index cols() const { return m_expression.cols(); }
+    inline Index outerStride() const { return m_expression.outerStride(); }
+    inline Index innerStride() const { return m_expression.innerStride(); }
+
+    inline const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_expression.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return m_expression.coeff(index);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return m_expression.template packet<Aligned>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return m_expression.template packet<Aligned>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
+    }
+
+    operator const ExpressionType&() const { return m_expression; }
+
+  protected:
+    const ExpressionType& m_expression;
+
+  private:
+    ForceAlignedAccess& operator=(const ForceAlignedAccess&);
+};
+
+/** \returns an expression of *this with forced aligned access
+  * \sa forceAlignedAccessIf(),class ForceAlignedAccess
+  */
+template<typename Derived>
+inline const ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess() const
+{
+  return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access
+  * \sa forceAlignedAccessIf(), class ForceAlignedAccess
+  */
+template<typename Derived>
+inline ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess()
+{
+  return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+  * \sa forceAlignedAccess(), class ForceAlignedAccess
+  */
+template<typename Derived>
+template<bool Enable>
+inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type
+MatrixBase<Derived>::forceAlignedAccessIf() const
+{
+  return derived();
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+  * \sa forceAlignedAccess(), class ForceAlignedAccess
+  */
+template<typename Derived>
+template<bool Enable>
+inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type
+MatrixBase<Derived>::forceAlignedAccessIf()
+{
+  return derived();
+}
+
+#endif // EIGEN_FORCEALIGNEDACCESS_H

Eigen/src/Core/Functors.h

@@ -0,0 +1,942 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FUNCTORS_H
+#define EIGEN_FUNCTORS_H
+
+namespace internal {
+
+// associative functors:
+
+/** \internal
+  * \brief Template functor to compute the sum of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, MatrixBase::sum()
+  */
+template<typename Scalar> struct scalar_sum_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::padd(a,b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  { return internal::predux(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sum_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasAdd
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the product of two scalars
+  *
+  * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
+  */
+template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
+  enum {
+    // TODO vectorize mixed product
+    Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
+  };
+  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
+  EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pmul(a,b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
+  { return internal::predux_mul(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
+  enum {
+    Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
+    PacketAccess = scalar_product_op<LhsScalar,RhsScalar>::Vectorizable
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the conjugate product of two scalars
+  *
+  * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
+  */
+template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
+
+  enum {
+    Conj = NumTraits<LhsScalar>::IsComplex
+  };
+  
+  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+  
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
+  EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
+  { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
+  
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
+  enum {
+    Cost = NumTraits<LhsScalar>::MulCost,
+    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the min of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
+  */
+template<typename Scalar> struct scalar_min_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::min; return (min)(a, b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pmin(a,b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  { return internal::predux_min(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_min_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasMin
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the max of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
+  */
+template<typename Scalar> struct scalar_max_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::max; return (max)(a, b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pmax(a,b); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  { return internal::predux_max(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_max_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasMax
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the hypot of two scalars
+  *
+  * \sa MatrixBase::stableNorm(), class Redux
+  */
+template<typename Scalar> struct scalar_hypot_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
+//   typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
+  {
+    using std::max;
+    using std::min;
+    Scalar p = (max)(_x, _y);
+    Scalar q = (min)(_x, _y);
+    Scalar qp = q/p;
+    return p * sqrt(Scalar(1) + qp*qp);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_hypot_op<Scalar> > {
+  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
+};
+
+// other binary functors:
+
+/** \internal
+  * \brief Template functor to compute the difference of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator-
+  */
+template<typename Scalar> struct scalar_difference_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::psub(a,b); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_difference_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasSub
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the quotient of two scalars
+  *
+  * \sa class CwiseBinaryOp, Cwise::operator/()
+  */
+template<typename Scalar> struct scalar_quotient_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a / b; }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+  { return internal::pdiv(a,b); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_quotient_op<Scalar> > {
+  enum {
+    Cost = 2 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasDiv
+  };
+};
+
+// unary functors:
+
+/** \internal
+  * \brief Template functor to compute the opposite of a scalar
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator-
+  */
+template<typename Scalar> struct scalar_opposite_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return internal::pnegate(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_opposite_op<Scalar> >
+{ enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasNegate };
+};
+
+/** \internal
+  * \brief Template functor to compute the absolute value of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::abs
+  */
+template<typename Scalar> struct scalar_abs_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
+  typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs(a); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return internal::pabs(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs_op<Scalar> >
+{
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasAbs
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the squared absolute value of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::abs2
+  */
+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); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs2_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
+
+/** \internal
+  * \brief Template functor to compute the conjugate of a complex value
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::conjugate()
+  */
+template<typename Scalar> struct scalar_conjugate_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return internal::conj(a); }
+  template<typename Packet>
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_conjugate_op<Scalar> >
+{
+  enum {
+    Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
+    PacketAccess = packet_traits<Scalar>::HasConj
+  };
+};
+
+/** \internal
+  * \brief Template functor to cast a scalar to another type
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::cast()
+  */
+template<typename Scalar, typename NewType>
+struct scalar_cast_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
+  typedef NewType result_type;
+  EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
+};
+template<typename Scalar, typename NewType>
+struct functor_traits<scalar_cast_op<Scalar,NewType> >
+{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the real part of a complex
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::real()
+  */
+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); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the imaginary part of a complex
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::imag()
+  */
+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); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the real part of a complex as a reference
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::real()
+  */
+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)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the imaginary part of a complex as a reference
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::imag()
+  */
+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)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  *
+  * \brief Template functor to compute the exponential of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::exp()
+  */
+template<typename Scalar> struct scalar_exp_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::exp(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_exp_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasExp }; };
+
+/** \internal
+  *
+  * \brief Template functor to compute the logarithm of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::log()
+  */
+template<typename Scalar> struct scalar_log_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::log(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_log_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
+
+/** \internal
+  * \brief Template functor to multiply a scalar by a fixed other one
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator*, MatrixBase::operator/
+  */
+/* NOTE why doing the pset1() in packetOp *is* an optimization ?
+ * indeed it seems better to declare m_other as a Packet and do the pset1() once
+ * in the constructor. However, in practice:
+ *  - GCC does not like m_other as a Packet and generate a load every time it needs it
+ *  - on the other hand GCC is able to moves the pset1() away the loop :)
+ *  - simpler code ;)
+ * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
+ */
+template<typename Scalar>
+struct scalar_multiple_op {
+  typedef typename packet_traits<Scalar>::type Packet;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE scalar_multiple_op(const scalar_multiple_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE scalar_multiple_op(const Scalar& other) : m_other(other) { }
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return internal::pmul(a, pset1<Packet>(m_other)); }
+  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_multiple_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+template<typename Scalar1, typename Scalar2>
+struct scalar_multiple2_op {
+  typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
+  EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
+  typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
+};
+template<typename Scalar1,typename Scalar2>
+struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
+{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
+
+template<typename Scalar, bool IsInteger>
+struct scalar_quotient1_impl {
+  typedef typename packet_traits<Scalar>::type Packet;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE scalar_quotient1_impl(const scalar_quotient1_impl& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE scalar_quotient1_impl(const Scalar& other) : m_other(static_cast<Scalar>(1) / other) {}
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
+  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return internal::pmul(a, pset1<Packet>(m_other)); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_quotient1_impl<Scalar,false> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+template<typename Scalar>
+struct scalar_quotient1_impl<Scalar,true> {
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE scalar_quotient1_impl(const scalar_quotient1_impl& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE scalar_quotient1_impl(const Scalar& other) : m_other(other) {}
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
+  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_quotient1_impl<Scalar,true> >
+{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to divide a scalar by a fixed other one
+  *
+  * This functor is used to implement the quotient of a matrix by
+  * a scalar where the scalar type is not necessarily a floating point type.
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator/
+  */
+template<typename Scalar>
+struct scalar_quotient1_op : scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger > {
+  EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other)
+    : scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger >(other) {}
+};
+template<typename Scalar>
+struct functor_traits<scalar_quotient1_op<Scalar> >
+: functor_traits<scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger> >
+{};
+
+// nullary functors
+
+template<typename Scalar>
+struct scalar_constant_op {
+  typedef typename packet_traits<Scalar>::type Packet;
+  EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index, Index = 0) const { return m_other; }
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Packet packetOp(Index, Index = 0) const { return internal::pset1<Packet>(m_other); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_constant_op<Scalar> >
+// FIXME replace this packet test by a safe one
+{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
+
+template<typename Scalar> struct scalar_identity_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const { return row==col ? Scalar(1) : Scalar(0); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_identity_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
+
+template <typename Scalar, bool RandomAccess> struct linspaced_op_impl;
+
+// linear access for packet ops:
+// 1) initialization
+//   base = [low, ..., low] + ([step, ..., step] * [-size, ..., 0])
+// 2) each step
+//   base += [size*step, ..., size*step]
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,false>
+{
+  typedef typename packet_traits<Scalar>::type Packet;
+
+  linspaced_op_impl(Scalar low, Scalar step) :
+  m_low(low), m_step(step),
+  m_packetStep(pset1<Packet>(packet_traits<Scalar>::size*step)),
+  m_base(padd(pset1<Packet>(low),pmul(pset1<Packet>(step),plset<Scalar>(-packet_traits<Scalar>::size)))) {}
+
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Packet packetOp(Index) const { return m_base = padd(m_base,m_packetStep); }
+
+  const Scalar m_low;
+  const Scalar m_step;
+  const Packet m_packetStep;
+  mutable Packet m_base;
+};
+
+// random access for packet ops:
+// 1) each step
+//   [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,true>
+{
+  typedef typename packet_traits<Scalar>::type Packet;
+
+  linspaced_op_impl(Scalar low, Scalar step) :
+  m_low(low), m_step(step),
+  m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Scalar>(0)) {}
+
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
+
+  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))); }
+
+  const Scalar m_low;
+  const Scalar m_step;
+  const Packet m_lowPacket;
+  const Packet m_stepPacket;
+  const Packet m_interPacket;
+};
+
+// ----- Linspace functor ----------------------------------------------------------------
+
+// Forward declaration (we default to random access which does not really give
+// us a speed gain when using packet access but it allows to use the functor in
+// nested expressions).
+template <typename Scalar, bool RandomAccess = true> struct linspaced_op;
+template <typename Scalar, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,RandomAccess> >
+{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
+template <typename Scalar, bool RandomAccess> struct linspaced_op
+{
+  typedef typename packet_traits<Scalar>::type Packet;
+  linspaced_op(Scalar low, Scalar high, int num_steps) : impl(low, (high-low)/(num_steps-1)) {}
+
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
+
+  // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
+  // there row==0 and col is used for the actual iteration.
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const 
+  {
+    eigen_assert(col==0 || row==0);
+    return impl(col + row);
+  }
+
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Packet packetOp(Index i) const { return impl.packetOp(i); }
+
+  // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
+  // there row==0 and col is used for the actual iteration.
+  template<typename Index>
+  EIGEN_STRONG_INLINE const Packet packetOp(Index row, Index col) const
+  {
+    eigen_assert(col==0 || row==0);
+    return impl.packetOp(col + row);
+  }
+
+  // This proxy object handles the actual required temporaries, the different
+  // implementations (random vs. sequential access) as well as the
+  // correct piping to size 2/4 packet operations.
+  const linspaced_op_impl<Scalar,RandomAccess> impl;
+};
+
+// all functors allow linear access, except scalar_identity_op. So we fix here a quick meta
+// to indicate whether a functor allows linear access, just always answering 'yes' except for
+// scalar_identity_op.
+// FIXME move this to functor_traits adding a functor_default
+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
+// where we only require them to have the same _real_ scalar type so one may multiply, say, float by complex<float>.
+// 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 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_allows_mixing_real_and_complex<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
+
+
+/** \internal
+  * \brief Template functor to add a scalar to a fixed other one
+  * \sa class CwiseUnaryOp, Array::operator+
+  */
+/* If you wonder why doing the pset1() in packetOp() is an optimization check scalar_multiple_op */
+template<typename Scalar>
+struct scalar_add_op {
+  typedef typename packet_traits<Scalar>::type Packet;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  inline scalar_add_op(const scalar_add_op& other) : m_other(other.m_other) { }
+  inline scalar_add_op(const Scalar& other) : m_other(other) { }
+  inline Scalar operator() (const Scalar& a) const { return a + m_other; }
+  inline const Packet packetOp(const Packet& a) const
+  { return internal::padd(a, pset1<Packet>(m_other)); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_add_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
+
+/** \internal
+  * \brief Template functor to compute the square root of a scalar
+  * \sa class CwiseUnaryOp, Cwise::sqrt()
+  */
+template<typename Scalar> struct scalar_sqrt_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::sqrt(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sqrt_op<Scalar> >
+{ enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasSqrt
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the cosine of a scalar
+  * \sa class CwiseUnaryOp, ArrayBase::cos()
+  */
+template<typename Scalar> struct scalar_cos_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
+  inline Scalar operator() (const Scalar& a) const { return internal::cos(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cos_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasCos
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the sine of a scalar
+  * \sa class CwiseUnaryOp, ArrayBase::sin()
+  */
+template<typename Scalar> struct scalar_sin_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::sin(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sin_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasSin
+  };
+};
+
+
+/** \internal
+  * \brief Template functor to compute the tan of a scalar
+  * \sa class CwiseUnaryOp, ArrayBase::tan()
+  */
+template<typename Scalar> struct scalar_tan_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::tan(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_tan_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasTan
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the arc cosine of a scalar
+  * \sa class CwiseUnaryOp, ArrayBase::acos()
+  */
+template<typename Scalar> struct scalar_acos_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::acos(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_acos_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasACos
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the arc sine of a scalar
+  * \sa class CwiseUnaryOp, ArrayBase::asin()
+  */
+template<typename Scalar> struct scalar_asin_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
+  inline const Scalar operator() (const Scalar& a) const { return internal::asin(a); }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_asin_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasASin
+  };
+};
+
+/** \internal
+  * \brief Template functor to raise a scalar to a power
+  * \sa class CwiseUnaryOp, Cwise::pow
+  */
+template<typename Scalar>
+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); }
+  const Scalar m_exponent;
+};
+template<typename Scalar>
+struct functor_traits<scalar_pow_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to compute the inverse of a scalar
+  * \sa class CwiseUnaryOp, Cwise::inverse()
+  */
+template<typename Scalar>
+struct scalar_inverse_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)
+  inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
+  template<typename Packet>
+  inline const Packet packetOp(const Packet& a) const
+  { return internal::pdiv(pset1<Packet>(Scalar(1)),a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_inverse_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
+
+/** \internal
+  * \brief Template functor to compute the square of a scalar
+  * \sa class CwiseUnaryOp, Cwise::square()
+  */
+template<typename Scalar>
+struct scalar_square_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
+  inline Scalar operator() (const Scalar& a) const { return a*a; }
+  template<typename Packet>
+  inline const Packet packetOp(const Packet& a) const
+  { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_square_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+/** \internal
+  * \brief Template functor to compute the cube of a scalar
+  * \sa class CwiseUnaryOp, Cwise::cube()
+  */
+template<typename Scalar>
+struct scalar_cube_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
+  inline Scalar operator() (const Scalar& a) const { return a*a*a; }
+  template<typename Packet>
+  inline const Packet packetOp(const Packet& a) const
+  { return internal::pmul(a,pmul(a,a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cube_op<Scalar> >
+{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+// default functor traits for STL functors:
+
+template<typename T>
+struct functor_traits<std::multiplies<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::divides<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::plus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::minus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::negate<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_or<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_and<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_not<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::not_equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binder2nd<T> >
+{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binder1st<T> >
+{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::unary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::binary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+
+#ifdef EIGEN_STDEXT_SUPPORT
+
+template<typename T0,typename T1>
+struct functor_traits<std::project1st<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::project2nd<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select2nd<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select1st<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::unary_compose<T0,T1> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };
+
+template<typename T0,typename T1,typename T2>
+struct functor_traits<std::binary_compose<T0,T1,T2> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };
+
+#endif // EIGEN_STDEXT_SUPPORT
+
+// allow to add new functors and specializations of functor_traits from outside Eigen.
+// this macro is really needed because functor_traits must be specialized after it is declared but before it is used...
+#ifdef EIGEN_FUNCTORS_PLUGIN
+#include EIGEN_FUNCTORS_PLUGIN
+#endif
+
+} // end namespace internal
+
+#endif // EIGEN_FUNCTORS_H

Eigen/src/Core/Fuzzy.h

@@ -0,0 +1,161 @@
+// 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 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FUZZY_H
+#define EIGEN_FUZZY_H
+
+namespace internal
+{
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isApprox_selector
+{
+  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
+  {
+    using std::min;
+    const typename internal::nested<Derived,2>::type nested(x);
+    const typename internal::nested<OtherDerived,2>::type otherNested(y);
+    return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
+  }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isApprox_selector<Derived, OtherDerived, true>
+{
+  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar)
+  {
+    return x.matrix() == y.matrix();
+  }
+};
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_object_selector
+{
+  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
+  {
+    return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum();
+  }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
+{
+  static bool run(const Derived& x, const OtherDerived&, typename Derived::RealScalar)
+  {
+    return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+  }
+};
+
+template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_scalar_selector
+{
+  static bool run(const Derived& x, const typename Derived::RealScalar& y, typename Derived::RealScalar prec)
+  {
+    return x.cwiseAbs2().sum() <= abs2(prec * y);
+  }
+};
+
+template<typename Derived>
+struct isMuchSmallerThan_scalar_selector<Derived, true>
+{
+  static bool run(const Derived& x, const typename Derived::RealScalar&, typename Derived::RealScalar)
+  {
+    return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+  }
+};
+
+} // end namespace internal
+
+
+/** \returns \c true if \c *this is approximately equal to \a other, within the precision
+  * determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
+  * are considered to be approximately equal within precision \f$ p \f$ if
+  * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
+  * L2 norm).
+  *
+  * \note Because of the multiplicativeness of this comparison, one can't use this function
+  * to check whether \c *this is approximately equal to the zero matrix or vector.
+  * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
+  * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
+  * RealScalar&, RealScalar) instead.
+  *
+  * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool DenseBase<Derived>::isApprox(
+  const DenseBase<OtherDerived>& other,
+  RealScalar prec
+) const
+{
+  return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
+  *
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
+  * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
+  * of a reference matrix of same dimensions.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
+  */
+template<typename Derived>
+bool DenseBase<Derived>::isMuchSmallerThan(
+  const typename NumTraits<Scalar>::Real& other,
+  RealScalar prec
+) const
+{
+  return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool DenseBase<Derived>::isMuchSmallerThan(
+  const DenseBase<OtherDerived>& other,
+  RealScalar prec
+) const
+{
+  return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+#endif // EIGEN_FUZZY_H

Eigen/src/Core/GenericPacketMath.h

@@ -0,0 +1,339 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_GENERIC_PACKET_MATH_H
+#define EIGEN_GENERIC_PACKET_MATH_H
+
+namespace internal {
+
+/** \internal
+  * \file GenericPacketMath.h
+  *
+  * Default implementation for types not supported by the vectorization.
+  * In practice these functions are provided to make easier the writing
+  * of generic vectorized code.
+  */
+
+#ifndef EIGEN_DEBUG_ALIGNED_LOAD
+#define EIGEN_DEBUG_ALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
+#define EIGEN_DEBUG_UNALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_ALIGNED_STORE
+#define EIGEN_DEBUG_ALIGNED_STORE
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_STORE
+#define EIGEN_DEBUG_UNALIGNED_STORE
+#endif
+
+struct default_packet_traits
+{
+  enum {
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasNegate = 1,
+    HasAbs    = 1,
+    HasAbs2   = 1,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
+    HasSetLinear = 1,
+
+    HasDiv    = 0,
+    HasSqrt   = 0,
+    HasExp    = 0,
+    HasLog    = 0,
+    HasPow    = 0,
+
+    HasSin    = 0,
+    HasCos    = 0,
+    HasTan    = 0,
+    HasASin   = 0,
+    HasACos   = 0,
+    HasATan   = 0
+  };
+};
+
+template<typename T> struct packet_traits : default_packet_traits
+{
+  typedef T type;
+  enum {
+    Vectorizable = 0,
+    size = 1,
+    AlignedOnScalar = 0
+  };
+  enum {
+    HasAdd    = 0,
+    HasSub    = 0,
+    HasMul    = 0,
+    HasNegate = 0,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasConj   = 0,
+    HasSetLinear = 0
+  };
+};
+
+/** \internal \returns a + b (coeff-wise) */
+template<typename Packet> inline Packet
+padd(const Packet& a,
+        const Packet& b) { return a+b; }
+
+/** \internal \returns a - b (coeff-wise) */
+template<typename Packet> inline Packet
+psub(const Packet& a,
+        const Packet& b) { return a-b; }
+
+/** \internal \returns -a (coeff-wise) */
+template<typename Packet> inline Packet
+pnegate(const Packet& a) { return -a; }
+
+/** \internal \returns conj(a) (coeff-wise) */
+template<typename Packet> inline Packet
+pconj(const Packet& a) { return conj(a); }
+
+/** \internal \returns a * b (coeff-wise) */
+template<typename Packet> inline Packet
+pmul(const Packet& a,
+        const Packet& b) { return a*b; }
+
+/** \internal \returns a / b (coeff-wise) */
+template<typename Packet> inline Packet
+pdiv(const Packet& a,
+        const Packet& b) { return a/b; }
+
+/** \internal \returns the min of \a a and \a b  (coeff-wise) */
+template<typename Packet> inline Packet
+pmin(const Packet& a,
+        const Packet& b) { using std::min; return (min)(a, b); }
+
+/** \internal \returns the max of \a a and \a b  (coeff-wise) */
+template<typename Packet> inline Packet
+pmax(const Packet& a,
+        const Packet& b) { using std::max; return (max)(a, b); }
+
+/** \internal \returns the absolute value of \a a */
+template<typename Packet> inline Packet
+pabs(const Packet& a) { return abs(a); }
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> inline Packet
+pand(const Packet& a, const Packet& b) { return a & b; }
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> inline Packet
+por(const Packet& a, const Packet& b) { return a | b; }
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> inline Packet
+pxor(const Packet& a, const Packet& b) { return a ^ b; }
+
+/** \internal \returns the bitwise andnot of \a a and \a b */
+template<typename Packet> inline Packet
+pandnot(const Packet& a, const Packet& b) { return a & (!b); }
+
+/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
+template<typename Packet> inline Packet
+pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet version of \a *from, (un-aligned load) */
+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]) */
+template<typename Packet> inline Packet
+ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
+template<typename Packet> inline Packet
+pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
+
+/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
+template<typename Scalar> inline typename packet_traits<Scalar>::type
+plset(const Scalar& a) { return a; }
+
+/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal tries to do cache prefetching of \a addr */
+template<typename Scalar> inline void prefetch(const Scalar* addr)
+{
+#if !defined(_MSC_VER)
+__builtin_prefetch(addr);
+#endif
+}
+
+/** \internal \returns the first element of a packet */
+template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
+{ return a; }
+
+/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
+template<typename Packet> inline Packet
+preduxp(const Packet* vecs) { return vecs[0]; }
+
+/** \internal \returns the sum of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
+{ return a; }
+
+/** \internal \returns the product of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
+{ return a; }
+
+/** \internal \returns the min of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
+{ return a; }
+
+/** \internal \returns the max of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
+{ return a; }
+
+/** \internal \returns the reversed elements of \a a*/
+template<typename Packet> inline Packet preverse(const Packet& a)
+{ return a; }
+
+
+/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
+template<typename Packet> inline Packet pcplxflip(const Packet& a)
+{ return Packet(imag(a),real(a)); }
+
+/**************************
+* Special math functions
+***************************/
+
+/** \internal \returns the sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin(const Packet& a) { return sin(a); }
+
+/** \internal \returns the cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos(const Packet& a) { return cos(a); }
+
+/** \internal \returns the tan of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ptan(const Packet& a) { return tan(a); }
+
+/** \internal \returns the arc sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin(const Packet& a) { return asin(a); }
+
+/** \internal \returns the arc cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos(const Packet& a) { return acos(a); }
+
+/** \internal \returns the exp of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp(const Packet& a) { return exp(a); }
+
+/** \internal \returns the log of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog(const Packet& a) { return log(a); }
+
+/** \internal \returns the square-root of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt(const Packet& a) { return sqrt(a); }
+
+/***************************************************************************
+* The following functions might not have to be overwritten for vectorized types
+***************************************************************************/
+
+/** \internal copy a packet with constant coeficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
+// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
+template<typename Packet>
+inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
+{
+  pstore(to, pset1<Packet>(a));
+}
+
+/** \internal \returns a * b + c (coeff-wise) */
+template<typename Packet> inline Packet
+pmadd(const Packet&  a,
+         const Packet&  b,
+         const Packet&  c)
+{ return padd(pmul(a, b),c); }
+
+/** \internal \returns a packet version of \a *from.
+  * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
+template<typename Packet, int LoadMode>
+inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
+{
+  if(LoadMode == Aligned)
+    return pload<Packet>(from);
+  else
+    return ploadu<Packet>(from);
+}
+
+/** \internal copy the packet \a from to \a *to.
+  * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet, int LoadMode>
+inline void pstoret(Scalar* to, const Packet& from)
+{
+  if(LoadMode == Aligned)
+    pstore(to, from);
+  else
+    pstoreu(to, from);
+}
+
+/** \internal default implementation of palign() allowing partial specialization */
+template<int Offset,typename PacketType>
+struct palign_impl
+{
+  // by default data are aligned, so there is nothing to be done :)
+  inline static void run(PacketType&, const PacketType&) {}
+};
+
+/** \internal update \a first using the concatenation of the \a Offset last elements
+  * of \a first and packet_size minus \a Offset first elements of \a second */
+template<int Offset,typename PacketType>
+inline void palign(PacketType& first, const PacketType& second)
+{
+  palign_impl<Offset,PacketType>::run(first,second);
+}
+
+/***************************************************************************
+* Fast complex products (GCC generates a function call which is very slow)
+***************************************************************************/
+
+template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
+{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
+{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+} // end namespace internal
+
+#endif // EIGEN_GENERIC_PACKET_MATH_H
+

Eigen/src/Core/GlobalFunctions.h

@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_GLOBAL_FUNCTIONS_H
+#define EIGEN_GLOBAL_FUNCTIONS_H
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(NAME,FUNCTOR) \
+  template<typename Derived> \
+  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
+  NAME(const Eigen::ArrayBase<Derived>& x) { \
+    return x.derived(); \
+  }
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
+  \
+  template<typename Derived> \
+  struct NAME##_retval<ArrayBase<Derived> > \
+  { \
+    typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
+  }; \
+  template<typename Derived> \
+  struct NAME##_impl<ArrayBase<Derived> > \
+  { \
+    static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
+    { \
+      return x.derived(); \
+    } \
+  };
+
+
+namespace std
+{
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(real,scalar_real_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(imag,scalar_imag_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sin,scalar_sin_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(cos,scalar_cos_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(asin,scalar_asin_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(acos,scalar_acos_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(tan,scalar_tan_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(exp,scalar_exp_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(log,scalar_log_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(abs,scalar_abs_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sqrt,scalar_sqrt_op)
+
+  template<typename Derived>
+  inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
+  pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) { \
+    return x.derived().pow(exponent); \
+  }
+}
+
+namespace Eigen
+{
+  namespace internal
+  {
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sin,scalar_sin_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(cos,scalar_cos_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(asin,scalar_asin_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(acos,scalar_acos_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(tan,scalar_tan_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(exp,scalar_exp_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(log,scalar_log_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs,scalar_abs_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
+    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sqrt,scalar_sqrt_op)
+  }
+}
+
+// TODO: cleanly disable those functions that are not supported on Array (internal::real_ref, internal::random, internal::isApprox...)
+
+#endif // EIGEN_GLOBAL_FUNCTIONS_H

Eigen/src/Core/IO.h

@@ -0,0 +1,260 @@
+// 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 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_IO_H
+#define EIGEN_IO_H
+
+enum { DontAlignCols = 1 };
+enum { StreamPrecision = -1,
+       FullPrecision = -2 };
+
+namespace internal {
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);
+}
+
+/** \class IOFormat
+  * \ingroup Core_Module
+  *
+  * \brief Stores a set of parameters controlling the way matrices are printed
+  *
+  * List of available parameters:
+  *  - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
+  *                 The default is the special value \c StreamPrecision which means to use the
+  *                 stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
+  *                 \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
+  *                 type.
+  *  - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which
+  *             allows to disable the alignment of columns, resulting in faster code.
+  *  - \b coeffSeparator string printed between two coefficients of the same row
+  *  - \b rowSeparator string printed between two rows
+  *  - \b rowPrefix string printed at the beginning of each row
+  *  - \b rowSuffix string printed at the end of each row
+  *  - \b matPrefix string printed at the beginning of the matrix
+  *  - \b matSuffix string printed at the end of the matrix
+  *
+  * Example: \include IOFormat.cpp
+  * Output: \verbinclude IOFormat.out
+  *
+  * \sa DenseBase::format(), class WithFormat
+  */
+struct IOFormat
+{
+  /** Default contructor, see class IOFormat for the meaning of the parameters */
+  IOFormat(int _precision = StreamPrecision, int _flags = 0,
+    const std::string& _coeffSeparator = " ",
+    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 = "";
+    int i = int(matSuffix.length())-1;
+    while (i>=0 && matSuffix[i]!='\n')
+    {
+      rowSpacer += ' ';
+      i--;
+    }
+  }
+  std::string matPrefix, matSuffix;
+  std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
+  std::string coeffSeparator;
+  int precision;
+  int flags;
+};
+
+/** \class WithFormat
+  * \ingroup Core_Module
+  *
+  * \brief Pseudo expression providing matrix output with given format
+  *
+  * \param ExpressionType the type of the object on which IO stream operations are performed
+  *
+  * This class represents an expression with stream operators controlled by a given IOFormat.
+  * It is the return type of DenseBase::format()
+  * and most of the time this is the only way it is used.
+  *
+  * See class IOFormat for some examples.
+  *
+  * \sa DenseBase::format(), class IOFormat
+  */
+template<typename ExpressionType>
+class WithFormat
+{
+  public:
+
+    WithFormat(const ExpressionType& matrix, const IOFormat& format)
+      : m_matrix(matrix), m_format(format)
+    {}
+
+    friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
+    {
+      return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
+    }
+
+  protected:
+    const typename ExpressionType::Nested m_matrix;
+    IOFormat m_format;
+};
+
+/** \returns a WithFormat proxy object allowing to print a matrix the with given
+  * format \a fmt.
+  *
+  * See class IOFormat for some examples.
+  *
+  * \sa class IOFormat, class WithFormat
+  */
+template<typename Derived>
+inline const WithFormat<Derived>
+DenseBase<Derived>::format(const IOFormat& fmt) const
+{
+  return WithFormat<Derived>(derived(), fmt);
+}
+
+namespace internal {
+
+template<typename Scalar, bool IsInteger>
+struct significant_decimals_default_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline int run()
+  {
+    using std::ceil;
+    return cast<RealScalar,int>(ceil(-log(NumTraits<RealScalar>::epsilon())/log(RealScalar(10))));
+  }
+};
+
+template<typename Scalar>
+struct significant_decimals_default_impl<Scalar, true>
+{
+  static inline int run()
+  {
+    return 0;
+  }
+};
+
+template<typename Scalar>
+struct significant_decimals_impl
+  : significant_decimals_default_impl<Scalar, NumTraits<Scalar>::IsInteger>
+{};
+
+/** \internal
+  * print the matrix \a _m to the output stream \a s using the output format \a fmt */
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
+{
+  if(_m.size() == 0)
+  {
+    s << fmt.matPrefix << fmt.matSuffix;
+    return s;
+  }
+  
+  const typename Derived::Nested m = _m;
+  typedef typename Derived::Scalar Scalar;
+  typedef typename Derived::Index Index;
+
+  Index width = 0;
+
+  std::streamsize explicit_precision;
+  if(fmt.precision == StreamPrecision)
+  {
+    explicit_precision = 0;
+  }
+  else if(fmt.precision == FullPrecision)
+  {
+    if (NumTraits<Scalar>::IsInteger)
+    {
+      explicit_precision = 0;
+    }
+    else
+    {
+      explicit_precision = significant_decimals_impl<Scalar>::run();
+    }
+  }
+  else
+  {
+    explicit_precision = fmt.precision;
+  }
+
+  bool align_cols = !(fmt.flags & DontAlignCols);
+  if(align_cols)
+  {
+    // compute the largest width
+    for(Index j = 1; j < m.cols(); ++j)
+      for(Index i = 0; i < m.rows(); ++i)
+      {
+        std::stringstream sstr;
+        if(explicit_precision) sstr.precision(explicit_precision);
+        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)
+  {
+    if (i)
+      s << fmt.rowSpacer;
+    s << fmt.rowPrefix;
+    if(width) s.width(width);
+    s << m.coeff(i, 0);
+    for(Index j = 1; j < m.cols(); ++j)
+    {
+      s << fmt.coeffSeparator;
+      if (width) s.width(width);
+      s << m.coeff(i, j);
+    }
+    s << fmt.rowSuffix;
+    if( i < m.rows() - 1)
+      s << fmt.rowSeparator;
+  }
+  s << fmt.matSuffix;
+  if(explicit_precision) s.precision(old_precision);
+  return s;
+}
+
+} // end namespace internal
+
+/** \relates DenseBase
+  *
+  * Outputs the matrix, to the given stream.
+  *
+  * If you wish to print the matrix with a format different than the default, use DenseBase::format().
+  *
+  * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
+  * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
+  *
+  * \sa DenseBase::format()
+  */
+template<typename Derived>
+std::ostream & operator <<
+(std::ostream & s,
+ const DenseBase<Derived> & m)
+{
+  return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
+}
+
+#endif // EIGEN_IO_H

Eigen/src/Core/Map.h

@@ -0,0 +1,203 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MAP_H
+#define EIGEN_MAP_H
+
+/** \class Map
+  * \ingroup Core_Module
+  *
+  * \brief A matrix or vector expression mapping an existing array of data.
+  *
+  * \tparam PlainObjectType the equivalent matrix type of the mapped data
+  * \tparam MapOptions specifies whether the pointer is \c #Aligned, or \c #Unaligned.
+  *                The default is \c #Unaligned.
+  * \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
+  *                   of an ordinary, contiguous array. This can be overridden by specifying strides.
+  *                   The type passed here must be a specialization of the Stride template, see examples below.
+  *
+  * This class represents a matrix or vector expression mapping an existing array of data.
+  * It can be used to let Eigen interface without any overhead with non-Eigen data structures,
+  * such as plain C arrays or structures from other libraries. By default, it assumes that the
+  * data is laid out contiguously in memory. You can however override this by explicitly specifying
+  * inner and outer strides.
+  *
+  * Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
+  * \include Map_simple.cpp
+  * Output: \verbinclude Map_simple.out
+  *
+  * If you need to map non-contiguous arrays, you can do so by specifying strides:
+  *
+  * Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
+  * increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
+  * fixed value.
+  * \include Map_inner_stride.cpp
+  * Output: \verbinclude Map_inner_stride.out
+  *
+  * Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
+  * as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
+  * Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
+  * a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
+  * is  \c Dynamic
+  * \include Map_outer_stride.cpp
+  * Output: \verbinclude Map_outer_stride.out
+  *
+  * For more details and for an example of specifying both an inner and an outer stride, see class Stride.
+  *
+  * \b Tip: to change the array of data mapped by a Map object, you can use the C++
+  * placement new syntax:
+  *
+  * Example: \include Map_placement_new.cpp
+  * Output: \verbinclude Map_placement_new.out
+  *
+  * This class is the return type of PlainObjectBase::Map() but can also be used directly.
+  *
+  * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+  */
+
+namespace internal {
+template<typename PlainObjectType, int MapOptions, typename StrideType>
+struct traits<Map<PlainObjectType, MapOptions, StrideType> >
+  : public traits<PlainObjectType>
+{
+  typedef traits<PlainObjectType> TraitsBase;
+  typedef typename PlainObjectType::Index Index;
+  typedef typename PlainObjectType::Scalar Scalar;
+  enum {
+    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+                             ? int(PlainObjectType::InnerStrideAtCompileTime)
+                             : int(StrideType::InnerStrideAtCompileTime),
+    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+                             ? int(PlainObjectType::OuterStrideAtCompileTime)
+                             : int(StrideType::OuterStrideAtCompileTime),
+    HasNoInnerStride = InnerStrideAtCompileTime == 1,
+    HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,
+    HasNoStride = HasNoInnerStride && HasNoOuterStride,
+    IsAligned = bool(EIGEN_ALIGN) && ((int(MapOptions)&Aligned)==Aligned),
+    IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic,
+    KeepsPacketAccess = bool(HasNoInnerStride)
+                        && ( bool(IsDynamicSize)
+                           || HasNoOuterStride
+                           || ( OuterStrideAtCompileTime!=Dynamic
+                           && ((static_cast<int>(sizeof(Scalar))*OuterStrideAtCompileTime)%16)==0 ) ),
+    Flags0 = TraitsBase::Flags & (~NestByRefBit),
+    Flags1 = IsAligned ? (int(Flags0) | AlignedBit) : (int(Flags0) & ~AlignedBit),
+    Flags2 = (bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime))
+           ? int(Flags1) : int(Flags1 & ~LinearAccessBit),
+    Flags3 = is_lvalue<PlainObjectType>::value ? int(Flags2) : (int(Flags2) & ~LvalueBit),
+    Flags = KeepsPacketAccess ? int(Flags3) : (int(Flags3) & ~PacketAccessBit)
+  };
+private:
+  enum { Options }; // Expressions don't have Options
+};
+}
+
+template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
+  : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
+{
+  public:
+
+    typedef MapBase<Map> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Map)
+
+    typedef typename Base::PointerType PointerType;
+#if EIGEN2_SUPPORT_STAGE <= STAGE30_FULL_EIGEN3_API
+    typedef const Scalar* PointerArgType;
+    inline PointerType cast_to_pointer_type(PointerArgType ptr) { return const_cast<PointerType>(ptr); }
+#else
+    typedef PointerType PointerArgType;
+    inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
+#endif
+
+    inline Index innerStride() const
+    {
+      return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
+    }
+
+    inline Index outerStride() const
+    {
+      return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+           : IsVectorAtCompileTime ? this->size()
+           : int(Flags)&RowMajorBit ? this->cols()
+           : this->rows();
+    }
+
+    /** Constructor in the fixed-size case.
+      *
+      * \param data pointer to the array to map
+      * \param stride optional Stride object, passing the strides.
+      */
+    inline Map(PointerArgType data, const StrideType& stride = StrideType())
+      : Base(cast_to_pointer_type(data)), m_stride(stride)
+    {
+      PlainObjectType::Base::_check_template_params();
+    }
+
+    /** Constructor in the dynamic-size vector case.
+      *
+      * \param data pointer to the array to map
+      * \param size the size of the vector expression
+      * \param stride optional Stride object, passing the strides.
+      */
+    inline Map(PointerArgType data, Index size, const StrideType& stride = StrideType())
+      : Base(cast_to_pointer_type(data), size), m_stride(stride)
+    {
+      PlainObjectType::Base::_check_template_params();
+    }
+
+    /** Constructor in the dynamic-size matrix case.
+      *
+      * \param data pointer to the array to map
+      * \param rows the number of rows of the matrix expression
+      * \param cols the number of columns of the matrix expression
+      * \param stride optional Stride object, passing the strides.
+      */
+    inline Map(PointerArgType data, Index rows, Index cols, const StrideType& stride = StrideType())
+      : Base(cast_to_pointer_type(data), rows, cols), m_stride(stride)
+    {
+      PlainObjectType::Base::_check_template_params();
+    }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+
+  protected:
+    StrideType m_stride;
+};
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+inline Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
+  ::Array(const Scalar *data)
+{
+  this->_set_noalias(Eigen::Map<const Array>(data));
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+inline Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
+  ::Matrix(const Scalar *data)
+{
+  this->_set_noalias(Eigen::Map<const Matrix>(data));
+}
+
+#endif // EIGEN_MAP_H

Eigen/src/Core/MapBase.h

@@ -0,0 +1,255 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MAPBASE_H
+#define EIGEN_MAPBASE_H
+
+#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
+      EIGEN_STATIC_ASSERT((int(internal::traits<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
+                          YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
+
+
+/** \class MapBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for Map and Block expression with direct access
+  *
+  * \sa class Map, class Block
+  */
+template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
+  : public internal::dense_xpr_base<Derived>::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<Derived>::type Base;
+    enum {
+      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+      SizeAtCompileTime = Base::SizeAtCompileTime
+    };
+
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    typedef typename internal::conditional<
+                         bool(internal::is_lvalue<Derived>::value),
+                         Scalar *,
+                         const Scalar *>::type
+                     PointerType;
+
+    using Base::derived;
+//    using Base::RowsAtCompileTime;
+//    using Base::ColsAtCompileTime;
+//    using Base::SizeAtCompileTime;
+    using Base::MaxRowsAtCompileTime;
+    using Base::MaxColsAtCompileTime;
+    using Base::MaxSizeAtCompileTime;
+    using Base::IsVectorAtCompileTime;
+    using Base::Flags;
+    using Base::IsRowMajor;
+
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::coeff;
+    using Base::coeffRef;
+    using Base::lazyAssign;
+    using Base::eval;
+
+    using Base::innerStride;
+    using Base::outerStride;
+    using Base::rowStride;
+    using Base::colStride;
+
+    // bug 217 - compile error on ICC 11.1
+    using Base::operator=;
+
+    typedef typename Base::CoeffReturnType CoeffReturnType;
+
+    inline Index rows() const { return m_rows.value(); }
+    inline Index cols() const { return m_cols.value(); }
+
+    /** Returns a pointer to the first coefficient of the matrix or vector.
+      *
+      * \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
+      *
+      * \sa innerStride(), outerStride()
+      */
+    inline const Scalar* data() const { return m_data; }
+
+    inline const Scalar& coeff(Index row, Index col) const
+    {
+      return m_data[col * colStride() + row * rowStride()];
+    }
+
+    inline const Scalar& coeff(Index index) const
+    {
+      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+      return m_data[index * innerStride()];
+    }
+
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return this->m_data[col * colStride() + row * rowStride()];
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+      return this->m_data[index * innerStride()];
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(Index row, Index col) const
+    {
+      return internal::ploadt<PacketScalar, LoadMode>
+               (m_data + (col * colStride() + row * rowStride()));
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(Index index) const
+    {
+      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+      return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
+    }
+
+    inline MapBase(PointerType data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+    {
+      EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+      checkSanity();
+    }
+
+    inline MapBase(PointerType data, Index size)
+            : m_data(data),
+              m_rows(RowsAtCompileTime == Dynamic ? size : Index(RowsAtCompileTime)),
+              m_cols(ColsAtCompileTime == Dynamic ? size : Index(ColsAtCompileTime))
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+      eigen_assert(size >= 0);
+      eigen_assert(data == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
+      checkSanity();
+    }
+
+    inline MapBase(PointerType data, Index rows, Index cols)
+            : m_data(data), m_rows(rows), m_cols(cols)
+    {
+      eigen_assert( (data == 0)
+              || (   rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+                  && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
+      checkSanity();
+    }
+
+  protected:
+
+    void checkSanity() const
+    {
+      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(internal::traits<Derived>::Flags&PacketAccessBit,
+                                        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");
+    }
+
+    PointerType m_data;
+    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+};
+
+template<typename Derived> class MapBase<Derived, WriteAccessors>
+  : public MapBase<Derived, ReadOnlyAccessors>
+{
+  public:
+
+    typedef MapBase<Derived, ReadOnlyAccessors> Base;
+
+    typedef typename Base::Scalar Scalar;
+    typedef typename Base::PacketScalar PacketScalar;
+    typedef typename Base::Index Index;
+    typedef typename Base::PointerType PointerType;
+
+    using Base::derived;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::coeff;
+    using Base::coeffRef;
+
+    using Base::innerStride;
+    using Base::outerStride;
+    using Base::rowStride;
+    using Base::colStride;
+
+    typedef typename internal::conditional<
+                    internal::is_lvalue<Derived>::value,
+                    Scalar,
+                    const Scalar
+                  >::type ScalarWithConstIfNotLvalue;
+
+    inline const Scalar* data() const { return this->m_data; }
+    inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
+
+    inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
+    {
+      return this->m_data[col * colStride() + row * rowStride()];
+    }
+
+    inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+      return this->m_data[index * innerStride()];
+    }
+
+    template<int StoreMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
+               (this->m_data + (col * colStride() + row * rowStride()), x);
+    }
+
+    template<int StoreMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
+                (this->m_data + index * innerStride(), x);
+    }
+
+    explicit inline MapBase(PointerType data) : Base(data) {}
+    inline MapBase(PointerType data, Index size) : Base(data, size) {}
+    inline MapBase(PointerType data, Index rows, Index cols) : Base(data, rows, cols) {}
+
+    Derived& operator=(const MapBase& other)
+    {
+      Base::Base::operator=(other);
+      return derived();
+    }
+
+    using Base::Base::operator=;
+};
+
+
+#endif // EIGEN_MAPBASE_H

Eigen/src/Core/MathFunctions.h

@@ -0,0 +1,843 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATHFUNCTIONS_H
+#define EIGEN_MATHFUNCTIONS_H
+
+namespace internal {
+
+/** \internal \struct global_math_functions_filtering_base
+  *
+  * What it does:
+  * Defines a typedef 'type' as follows:
+  * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
+  *   global_math_functions_filtering_base<T>::type is a typedef for it.
+  * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
+  *
+  * How it's used:
+  * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
+  * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
+  * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
+  * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
+  * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
+  *
+  * How it's implemented:
+  * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
+  * the typename dummy by an integer template parameter, it doesn't work anymore!
+  */
+
+template<typename T, typename dummy = void>
+struct global_math_functions_filtering_base
+{
+  typedef T type;
+};
+
+template<typename T> struct always_void { typedef void type; };
+
+template<typename T>
+struct global_math_functions_filtering_base
+  <T,
+   typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
+  >
+{
+  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_RETVAL(func, scalar) typename func##_retval<typename global_math_functions_filtering_base<scalar>::type>::type
+
+
+/****************************************************************************
+* Implementation of real                                                 *
+****************************************************************************/
+
+template<typename Scalar>
+struct real_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
+  {
+    return x;
+  }
+};
+
+template<typename RealScalar>
+struct real_impl<std::complex<RealScalar> >
+{
+  static inline RealScalar run(const std::complex<RealScalar>& x)
+  {
+    using std::real;
+    return real(x);
+  }
+};
+
+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>
+struct imag_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar&)
+  {
+    return RealScalar(0);
+  }
+};
+
+template<typename RealScalar>
+struct imag_impl<std::complex<RealScalar> >
+{
+  static inline RealScalar run(const std::complex<RealScalar>& x)
+  {
+    using std::imag;
+    return imag(x);
+  }
+};
+
+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                                             *
+****************************************************************************/
+
+template<typename Scalar>
+struct real_ref_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar& run(Scalar& x)
+  {
+    return reinterpret_cast<RealScalar*>(&x)[0];
+  }
+  static inline const RealScalar& run(const Scalar& x)
+  {
+    return reinterpret_cast<const RealScalar*>(&x)[0];
+  }
+};
+
+template<typename Scalar>
+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                                             *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct imag_ref_default_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar& run(Scalar& x)
+  {
+    return reinterpret_cast<RealScalar*>(&x)[1];
+  }
+  static inline const RealScalar& run(const Scalar& x)
+  {
+    return reinterpret_cast<RealScalar*>(&x)[1];
+  }
+};
+
+template<typename Scalar>
+struct imag_ref_default_impl<Scalar, false>
+{
+  static inline Scalar run(Scalar&)
+  {
+    return Scalar(0);
+  }
+  static inline const Scalar run(const Scalar&)
+  {
+    return Scalar(0);
+  }
+};
+
+template<typename Scalar>
+struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+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>
+struct conj_impl
+{
+  static inline Scalar run(const Scalar& x)
+  {
+    return x;
+  }
+};
+
+template<typename RealScalar>
+struct conj_impl<std::complex<RealScalar> >
+{
+  static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x)
+  {
+    using std::conj;
+    return conj(x);
+  }
+};
+
+template<typename Scalar>
+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 abs                                                  *
+****************************************************************************/
+
+template<typename Scalar>
+struct abs_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
+  {
+    using std::abs;
+    return abs(x);
+  }
+};
+
+template<typename Scalar>
+struct abs_retval
+{
+  typedef typename NumTraits<Scalar>::Real type;
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(abs, Scalar) abs(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(abs, Scalar)::run(x);
+}
+
+/****************************************************************************
+* Implementation of abs2                                                 *
+****************************************************************************/
+
+template<typename Scalar>
+struct abs2_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
+  {
+    return x*x;
+  }
+};
+
+template<typename RealScalar>
+struct abs2_impl<std::complex<RealScalar> >
+{
+  static inline RealScalar run(const std::complex<RealScalar>& x)
+  {
+    using std::norm;
+    return norm(x);
+  }
+};
+
+template<typename Scalar>
+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                                                *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct norm1_default_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
+  {
+    return abs(real(x)) + abs(imag(x));
+  }
+};
+
+template<typename Scalar>
+struct norm1_default_impl<Scalar, false>
+{
+  static inline Scalar run(const Scalar& x)
+  {
+    return abs(x);
+  }
+};
+
+template<typename Scalar>
+struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+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                                                *
+****************************************************************************/
+
+template<typename Scalar>
+struct hypot_impl
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x, const Scalar& y)
+  {
+    using std::max;
+    using std::min;
+    RealScalar _x = abs(x);
+    RealScalar _y = abs(y);
+    RealScalar p = (max)(_x, _y);
+    RealScalar q = (min)(_x, _y);
+    RealScalar qp = q/p;
+    return p * sqrt(RealScalar(1) + qp*qp);
+  }
+};
+
+template<typename Scalar>
+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                                                 *
+****************************************************************************/
+
+template<typename OldType, typename NewType>
+struct cast_impl
+{
+  static inline NewType run(const OldType& x)
+  {
+    return static_cast<NewType>(x);
+  }
+};
+
+// here, for once, we're plainly returning NewType: we don't want cast to do weird things.
+
+template<typename OldType, typename NewType>
+inline NewType cast(const OldType& x)
+{
+  return cast_impl<OldType, NewType>::run(x);
+}
+
+/****************************************************************************
+* Implementation of sqrt                                                 *
+****************************************************************************/
+
+template<typename Scalar, bool IsInteger>
+struct sqrt_default_impl
+{
+  static inline Scalar run(const Scalar& x)
+  {
+    using std::sqrt;
+    return sqrt(x);
+  }
+};
+
+template<typename Scalar>
+struct sqrt_default_impl<Scalar, true>
+{
+  static inline Scalar run(const Scalar&)
+  {
+#ifdef EIGEN2_SUPPORT
+    eigen_assert(!NumTraits<Scalar>::IsInteger);
+#else
+    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+#endif
+    return Scalar(0);
+  }
+};
+
+template<typename Scalar>
+struct sqrt_impl : sqrt_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct sqrt_retval
+{
+  typedef Scalar type;
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
+}
+
+/****************************************************************************
+* Implementation of standard unary real functions (exp, log, sin, cos, ...  *
+****************************************************************************/
+
+// This macro instanciate all the necessary template mechanism which is common to all unary real functions.
+#define EIGEN_MATHFUNC_STANDARD_REAL_UNARY(NAME) \
+  template<typename Scalar, bool IsInteger> struct NAME##_default_impl {            \
+    static inline Scalar run(const Scalar& x) { using std::NAME; return NAME(x); }  \
+  };                                                                                \
+  template<typename Scalar> struct NAME##_default_impl<Scalar, true> {              \
+    static inline Scalar run(const Scalar&) {                                       \
+      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)                                       \
+      return Scalar(0);                                                             \
+    }                                                                               \
+  };                                                                                \
+  template<typename Scalar> struct NAME##_impl                                      \
+    : NAME##_default_impl<Scalar, NumTraits<Scalar>::IsInteger>                     \
+  {};                                                                               \
+  template<typename Scalar> struct NAME##_retval { typedef Scalar type; };          \
+  template<typename Scalar>                                                         \
+  inline EIGEN_MATHFUNC_RETVAL(NAME, Scalar) NAME(const Scalar& x) {                \
+    return EIGEN_MATHFUNC_IMPL(NAME, Scalar)::run(x);                               \
+  }
+
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(exp)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(log)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(sin)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(cos)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(tan)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(asin)
+EIGEN_MATHFUNC_STANDARD_REAL_UNARY(acos)
+
+/****************************************************************************
+* Implementation of atan2                                                *
+****************************************************************************/
+
+template<typename Scalar, bool IsInteger>
+struct atan2_default_impl
+{
+  typedef Scalar retval;
+  static inline Scalar run(const Scalar& x, const Scalar& y)
+  {
+    using std::atan2;
+    return atan2(x, y);
+  }
+};
+
+template<typename Scalar>
+struct atan2_default_impl<Scalar, true>
+{
+  static inline Scalar run(const Scalar&, const Scalar&)
+  {
+    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+    return Scalar(0);
+  }
+};
+
+template<typename Scalar>
+struct atan2_impl : atan2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct atan2_retval
+{
+  typedef Scalar type;
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(atan2, Scalar) atan2(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(atan2, Scalar)::run(x, y);
+}
+
+/****************************************************************************
+* Implementation of pow                                                  *
+****************************************************************************/
+
+template<typename Scalar, bool IsInteger>
+struct pow_default_impl
+{
+  typedef Scalar retval;
+  static inline Scalar run(const Scalar& x, const Scalar& y)
+  {
+    using std::pow;
+    return pow(x, y);
+  }
+};
+
+template<typename Scalar>
+struct pow_default_impl<Scalar, true>
+{
+  static inline Scalar run(Scalar x, Scalar y)
+  {
+    Scalar res = 1;
+    eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
+    if(y & 1) res *= x;
+    y >>= 1;
+    while(y)
+    {
+      x *= x;
+      if(y&1) res *= x;
+      y >>= 1;
+    }
+    return res;
+  }
+};
+
+template<typename Scalar>
+struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+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                                               *
+****************************************************************************/
+
+template<typename Scalar,
+         bool IsComplex,
+         bool IsInteger>
+struct random_default_impl {};
+
+template<typename Scalar>
+struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct random_retval
+{
+  typedef Scalar type;
+};
+
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, false>
+{
+  static inline Scalar run(const Scalar& x, const Scalar& y)
+  {
+    return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
+  }
+  static inline Scalar run()
+  {
+    return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
+  }
+};
+
+enum {
+  floor_log2_terminate,
+  floor_log2_move_up,
+  floor_log2_move_down,
+  floor_log2_bogus
+};
+
+template<unsigned int n, int lower, int upper> struct floor_log2_selector
+{
+  enum { middle = (lower + upper) / 2,
+         value = (upper <= lower + 1) ? int(floor_log2_terminate)
+               : (n < (1 << middle)) ? int(floor_log2_move_down)
+               : (n==0) ? int(floor_log2_bogus)
+               : int(floor_log2_move_up)
+  };
+};
+
+template<unsigned int n,
+         int lower = 0,
+         int upper = sizeof(unsigned int) * CHAR_BIT - 1,
+         int selector = floor_log2_selector<n, lower, upper>::value>
+struct floor_log2 {};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_move_down>
+{
+  enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_move_up>
+{
+  enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_terminate>
+{
+  enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
+};
+
+template<unsigned int n, int lower, int upper>
+struct floor_log2<n, lower, upper, floor_log2_bogus>
+{
+  // no value, error at compile time
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, true>
+{
+  typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+
+  static inline Scalar run(const Scalar& x, const Scalar& y)
+  {
+    return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));
+  }
+
+  static inline Scalar run()
+  {
+#ifdef EIGEN_MAKING_DOCS
+    return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
+#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))
+    };
+    Scalar x = Scalar(std::rand() >> shift);
+    Scalar offset = NumTraits<Scalar>::IsSigned ? Scalar(1 << (rand_bits-1)) : Scalar(0);
+    return x - offset;
+#endif
+  }
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, true, false>
+{
+  static inline Scalar run(const Scalar& x, const Scalar& y)
+  {
+    return Scalar(random(real(x), real(y)),
+                  random(imag(x), imag(y)));
+  }
+  static inline Scalar run()
+  {
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    return Scalar(random<RealScalar>(), random<RealScalar>());
+  }
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
+{
+  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
+}
+
+/****************************************************************************
+* Implementation of fuzzy comparisons                                       *
+****************************************************************************/
+
+template<typename Scalar,
+         bool IsComplex,
+         bool IsInteger>
+struct scalar_fuzzy_default_impl {};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, false>
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  template<typename OtherScalar>
+  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+  {
+    return abs(x) <= abs(y) * prec;
+  }
+  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
+  {
+    using std::min;
+    return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
+  }
+  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
+  {
+    return x <= y || isApprox(x, y, prec);
+  }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, true>
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  template<typename OtherScalar>
+  static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
+  {
+    return x == Scalar(0);
+  }
+  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
+  {
+    return x == y;
+  }
+  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
+  {
+    return x <= y;
+  }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, true, false>
+{
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  template<typename OtherScalar>
+  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+  {
+    return abs2(x) <= 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;
+  }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar, typename OtherScalar>
+inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
+                                   typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+  return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool isApprox(const Scalar& x, const Scalar& y,
+                          typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+  return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
+}
+
+template<typename Scalar>
+inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
+                                    typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+{
+  return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
+}
+
+/******************************************
+***  The special case of the  bool type ***
+******************************************/
+
+template<> struct random_impl<bool>
+{
+  static inline bool run()
+  {
+    return random<int>(0,1)==0 ? false : true;
+  }
+};
+
+template<> struct scalar_fuzzy_impl<bool>
+{
+  typedef bool RealScalar;
+  
+  template<typename OtherScalar>
+  static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
+  {
+    return !x;
+  }
+  
+  static inline bool isApprox(bool x, bool y, bool)
+  {
+    return x == y;
+  }
+
+  static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
+  {
+    return (!x) || y;
+  }
+  
+};
+
+} // end namespace internal
+
+#endif // EIGEN_MATHFUNCTIONS_H

Eigen/src/Core/Matrix.h

@@ -0,0 +1,435 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIX_H
+#define EIGEN_MATRIX_H
+
+/** \class Matrix
+  * \ingroup Core_Module
+  *
+  * \brief The matrix class, also used for vectors and row-vectors
+  *
+  * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
+  * Vectors are matrices with one column, and row-vectors are matrices with one row.
+  *
+  * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
+  *
+  * The first three template parameters are required:
+  * \tparam _Scalar \anchor matrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.
+  *                 User defined sclar types are supported as well (see \ref user_defined_scalars "here").
+  * \tparam _Rows Number of rows, or \b Dynamic
+  * \tparam _Cols Number of columns, or \b Dynamic
+  *
+  * The remaining template parameters are optional -- in most cases you don't have to worry about them.
+  * \tparam _Options \anchor matrix_tparam_options A combination of either \b #RowMajor or \b #ColMajor, and of either
+  *                 \b #AutoAlign or \b #DontAlign.
+  *                 The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
+  *                 for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
+  * \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
+  * \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
+  *
+  * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
+  *
+  * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
+  * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
+  * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
+  *
+  * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
+  * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
+  *
+  * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
+  * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
+  *
+  * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
+  *
+  * You can access elements of vectors and matrices using normal subscripting:
+  *
+  * \code
+  * Eigen::VectorXd v(10);
+  * v[0] = 0.1;
+  * v[1] = 0.2;
+  * v(0) = 0.3;
+  * v(1) = 0.4;
+  *
+  * Eigen::MatrixXi m(10, 10);
+  * m(0, 1) = 1;
+  * m(0, 2) = 2;
+  * m(0, 3) = 3;
+  * \endcode
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
+  *
+  * <i><b>Some notes:</b></i>
+  *
+  * <dl>
+  * <dt><b>\anchor dense Dense versus sparse:</b></dt>
+  * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
+  *
+  * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
+  * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
+  *
+  * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
+  * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
+  * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
+  * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
+  *
+  * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
+  * variables, and the array of coefficients is allocated dynamically on the heap.
+  *
+  * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
+  * If you want this behavior, see the Sparse module.</dd>
+  *
+  * <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
+  * <dd>In most cases, one just leaves these parameters to the default values.
+  * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
+  * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
+  * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
+  * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
+  * </dl>
+  *
+  * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, 
+  * \ref TopicStorageOrders 
+  */
+
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  typedef _Scalar Scalar;
+  typedef Dense StorageKind;
+  typedef DenseIndex Index;
+  typedef MatrixXpr XprKind;
+  enum {
+    RowsAtCompileTime = _Rows,
+    ColsAtCompileTime = _Cols,
+    MaxRowsAtCompileTime = _MaxRows,
+    MaxColsAtCompileTime = _MaxCols,
+    Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
+    CoeffReadCost = NumTraits<Scalar>::ReadCost,
+    Options = _Options,
+    InnerStrideAtCompileTime = 1,
+    OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime
+  };
+};
+}
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+class Matrix
+  : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  public:
+
+    /** \brief Base class typedef.
+      * \sa PlainObjectBase
+      */
+    typedef PlainObjectBase<Matrix> Base;
+
+    enum { Options = _Options };
+
+    EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
+
+    typedef typename Base::PlainObject PlainObject;
+
+    using Base::base;
+    using Base::coeffRef;
+
+    /**
+      * \brief Assigns matrices to each other.
+      *
+      * \note This is a special case of the templated operator=. Its purpose is
+      * to prevent a default operator= from hiding the templated operator=.
+      *
+      * \callgraph
+      */
+    EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
+    {
+      return Base::_set(other);
+    }
+
+    /** \internal
+      * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+      *
+      * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+      * it will be initialized.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      return Base::_set(other);
+    }
+
+    /* Here, doxygen failed to copy the brief information when using \copydoc */
+
+    /**
+      * \brief Copies the generic expression \a other into *this.
+      * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
+    {
+      return Base::operator=(other);
+    }
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
+    {
+      return Base::operator=(func);
+    }
+
+    /** \brief Default constructor.
+      *
+      * For fixed-size matrices, does nothing.
+      *
+      * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+      * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+      * a matrix to 0 is not supported.
+      *
+      * \sa resize(Index,Index)
+      */
+    EIGEN_STRONG_INLINE explicit Matrix() : Base()
+    {
+      Base::_check_template_params();
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+    // FIXME is it still needed
+    Matrix(internal::constructor_without_unaligned_array_assert)
+      : Base(internal::constructor_without_unaligned_array_assert())
+    { Base::_check_template_params(); EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED }
+
+    /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
+      *
+      * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+      * it is redundant to pass the dimension here, so it makes more sense to use the default
+      * constructor Matrix() instead.
+      */
+    EIGEN_STRONG_INLINE explicit Matrix(Index dim)
+      : Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
+      eigen_assert(dim >= 0);
+      eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
+    {
+      Base::_check_template_params();
+      Base::template _init2<T0,T1>(x, y);
+    }
+    #else
+    /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
+      *
+      * This is useful for dynamic-size matrices. For fixed-size matrices,
+      * it is redundant to pass these parameters, so one should use the default constructor
+      * Matrix() instead. */
+    Matrix(Index rows, Index cols);
+    /** \brief Constructs an initialized 2D vector with given coefficients */
+    Matrix(const Scalar& x, const Scalar& y);
+    #endif
+
+    /** \brief Constructs an initialized 3D vector with given coefficients */
+    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+    }
+    /** \brief Constructs an initialized 4D vector with given coefficients */
+    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
+    {
+      Base::_check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+      m_storage.data()[3] = w;
+    }
+
+    explicit Matrix(const Scalar *data);
+
+    /** \brief Constructor copying the value of the expression \a other */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
+             : Base(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      // This test resides here, to bring the error messages closer to the user. Normally, these checks
+      // are performed deeply within the library, thus causing long and scary error traces.
+      EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+      Base::_check_template_params();
+      Base::_set_noalias(other);
+    }
+    /** \brief Copy constructor */
+    EIGEN_STRONG_INLINE Matrix(const Matrix& other)
+            : Base(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      Base::_check_template_params();
+      Base::_set_noalias(other);
+    }
+    /** \brief Copy constructor with in-place evaluation */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived>& other)
+    {
+      Base::_check_template_params();
+      Base::resize(other.rows(), other.cols());
+      other.evalTo(*this);
+    }
+
+    /** \brief Copy constructor for generic expressions.
+      * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
+      : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+    {
+      Base::_check_template_params();
+      Base::resize(other.rows(), other.cols());
+      // FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
+      //              go for pure _set() implementations, right?
+      *this = other;
+    }
+
+    /** \internal
+      * \brief Override MatrixBase::swap() since for dynamic-sized matrices
+      * of same type it is enough to swap the data pointers.
+      */
+    template<typename OtherDerived>
+    void swap(MatrixBase<OtherDerived> const & other)
+    { this->_swap(other.derived()); }
+
+    inline Index innerStride() const { return 1; }
+    inline Index outerStride() const { return this->innerSize(); }
+
+    /////////// Geometry module ///////////
+
+    template<typename OtherDerived>
+    explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    template<typename OtherDerived>
+    Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived>
+    explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    template<typename OtherDerived>
+    Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    #endif
+
+    // allow to extend Matrix outside Eigen
+    #ifdef EIGEN_MATRIX_PLUGIN
+    #include EIGEN_MATRIX_PLUGIN
+    #endif
+
+  protected:
+    template <typename Derived, typename OtherDerived, bool IsVector>
+    friend struct internal::conservative_resize_like_impl;
+
+    using Base::m_storage;
+};
+
+/** \defgroup matrixtypedefs Global matrix typedefs
+  *
+  * \ingroup Core_Module
+  *
+  * Eigen defines several typedef shortcuts for most common matrix and vector types.
+  *
+  * The general patterns are the following:
+  *
+  * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+  * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+  * for complex double.
+  *
+  * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
+  *
+  * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
+  * a fixed-size vector of 4 complex floats.
+  *
+  * \sa class Matrix
+  */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, 1>    Vector##SizeSuffix##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, 1, Size>    RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+
+#undef EIGEN_MAKE_TYPEDEFS_LARGE
+
+#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
+using Eigen::Matrix##SizeSuffix##TypeSuffix; \
+using Eigen::Vector##SizeSuffix##TypeSuffix; \
+using Eigen::RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(TypeSuffix) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
+
+#define EIGEN_USING_MATRIX_TYPEDEFS \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(i) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(f) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(d) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cf) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cd)
+
+#endif // EIGEN_MATRIX_H

Eigen/src/Core/MatrixBase.h

@@ -0,0 +1,521 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIXBASE_H
+#define EIGEN_MATRIXBASE_H
+
+/** \class MatrixBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for all dense matrices, vectors, and expressions
+  *
+  * This class is the base that is inherited by all matrix, vector, and related expression
+  * types. Most of the Eigen API is contained in this class, and its base classes. Other important
+  * classes for the Eigen API are Matrix, and VectorwiseOp.
+  *
+  * Note that some methods are defined in other modules such as the \ref LU_Module LU module
+  * for all functions related to matrix inversions.
+  *
+  * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
+  *
+  * When writing a function taking Eigen objects as argument, if you want your function
+  * to take as argument any matrix, vector, or expression, just let it take a
+  * MatrixBase argument. As an example, here is a function printFirstRow which, given
+  * a matrix, vector, or expression \a x, prints the first row of \a x.
+  *
+  * \code
+    template<typename Derived>
+    void printFirstRow(const Eigen::MatrixBase<Derived>& x)
+    {
+      cout << x.row(0) << endl;
+    }
+  * \endcode
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived> class MatrixBase
+  : public DenseBase<Derived>
+{
+  public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef MatrixBase StorageBaseType;
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    typedef DenseBase<Derived> Base;
+    using Base::RowsAtCompileTime;
+    using Base::ColsAtCompileTime;
+    using Base::SizeAtCompileTime;
+    using Base::MaxRowsAtCompileTime;
+    using Base::MaxColsAtCompileTime;
+    using Base::MaxSizeAtCompileTime;
+    using Base::IsVectorAtCompileTime;
+    using Base::Flags;
+    using Base::CoeffReadCost;
+
+    using Base::derived;
+    using Base::const_cast_derived;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::coeff;
+    using Base::coeffRef;
+    using Base::lazyAssign;
+    using Base::eval;
+    using Base::operator+=;
+    using Base::operator-=;
+    using Base::operator*=;
+    using Base::operator/=;
+
+    typedef typename Base::CoeffReturnType CoeffReturnType;
+    typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
+    typedef typename Base::RowXpr RowXpr;
+    typedef typename Base::ColXpr ColXpr;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** type of the equivalent square matrix */
+    typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
+                          EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** \returns the size of the main diagonal, which is min(rows(),cols()).
+      * \sa rows(), cols(), SizeAtCompileTime. */
+    inline Index diagonalSize() const { return (std::min)(rows(),cols()); }
+
+    /** \brief The plain matrix type corresponding to this expression.
+      *
+      * This is not necessarily exactly the return type of eval(). In the case of plain matrices,
+      * the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
+      * that the return type of eval() is either PlainObject or const PlainObject&.
+      */
+    typedef Matrix<typename internal::traits<Derived>::Scalar,
+                internal::traits<Derived>::RowsAtCompileTime,
+                internal::traits<Derived>::ColsAtCompileTime,
+                AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                internal::traits<Derived>::MaxRowsAtCompileTime,
+                internal::traits<Derived>::MaxColsAtCompileTime
+          > PlainObject;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal Represents a matrix with all coefficients equal to one another*/
+    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+    /** \internal the return type of MatrixBase::adjoint() */
+    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+                        CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
+                        ConstTransposeReturnType
+                     >::type AdjointReturnType;
+    /** \internal Return type of eigenvalues() */
+    typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
+    /** \internal the return type of identity */
+    typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,Derived> IdentityReturnType;
+    /** \internal the return type of unit vectors */
+    typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
+                  internal::traits<Derived>::RowsAtCompileTime,
+                  internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
+#   include "../plugins/CommonCwiseUnaryOps.h"
+#   include "../plugins/CommonCwiseBinaryOps.h"
+#   include "../plugins/MatrixCwiseUnaryOps.h"
+#   include "../plugins/MatrixCwiseBinaryOps.h"
+#   ifdef EIGEN_MATRIXBASE_PLUGIN
+#     include EIGEN_MATRIXBASE_PLUGIN
+#   endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+
+    /** Special case of the template operator=, in order to prevent the compiler
+      * from generating a default operator= (issue hit with g++ 4.1)
+      */
+    Derived& operator=(const MatrixBase& other);
+
+    // We cannot inherit here via Base::operator= since it is causing
+    // trouble with MSVC.
+
+    template <typename OtherDerived>
+    Derived& operator=(const DenseBase<OtherDerived>& other);
+
+    template <typename OtherDerived>
+    Derived& operator=(const EigenBase<OtherDerived>& other);
+
+    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);
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    template<typename OtherDerived>
+    Derived& operator+=(const MatrixBase<OtherDerived>& other);
+    template<typename OtherDerived>
+    Derived& operator-=(const MatrixBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    const typename ProductReturnType<Derived,OtherDerived>::Type
+    operator*(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    const typename LazyProductReturnType<Derived,OtherDerived>::Type
+    lazyProduct(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    Derived& operator*=(const EigenBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    void applyOnTheLeft(const EigenBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    void applyOnTheRight(const EigenBase<OtherDerived>& other);
+
+    template<typename DiagonalDerived>
+    const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
+    operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
+
+    template<typename OtherDerived>
+    typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+    dot(const MatrixBase<OtherDerived>& other) const;
+
+    #ifdef EIGEN2_SUPPORT
+      template<typename OtherDerived>
+      Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
+    #endif
+
+    RealScalar squaredNorm() const;
+    RealScalar norm() const;
+    RealScalar stableNorm() const;
+    RealScalar blueNorm() const;
+    RealScalar hypotNorm() const;
+    const PlainObject normalized() const;
+    void normalize();
+
+    const AdjointReturnType adjoint() const;
+    void adjointInPlace();
+
+    typedef Diagonal<Derived> DiagonalReturnType;
+    DiagonalReturnType diagonal();
+    typedef const Diagonal<const Derived> ConstDiagonalReturnType;
+    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;
+
+    // Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
+    // On the other hand they confuse MSVC8...
+    #if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
+    typename MatrixBase::template DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
+    typename MatrixBase::template ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
+    #else
+    typename DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
+    typename ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
+    #endif
+
+    #ifdef EIGEN2_SUPPORT
+    template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
+    template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
+    
+    // huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
+    // of an integer constant. Solution: overload the part() method template wrt template parameters list.
+    // Note: replacing next line by "template<template<typename T, int n> class U>" produces a mysterious error C2082 in MSVC.
+    template<template<typename, int> class U>
+    const DiagonalWrapper<ConstDiagonalReturnType> part() const
+    { return diagonal().asDiagonal(); }
+    #endif // EIGEN2_SUPPORT
+
+    template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
+    template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
+
+    template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
+    template<unsigned int Mode> typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
+
+    template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
+    template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
+
+    template<unsigned int UpLo> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
+    template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
+
+    const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
+                                         typename NumTraits<Scalar>::Real m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
+    static const IdentityReturnType Identity();
+    static const IdentityReturnType Identity(Index rows, Index cols);
+    static const BasisReturnType Unit(Index size, Index i);
+    static const BasisReturnType Unit(Index i);
+    static const BasisReturnType UnitX();
+    static const BasisReturnType UnitY();
+    static const BasisReturnType UnitZ();
+    static const BasisReturnType UnitW();
+
+    const DiagonalWrapper<const Derived> asDiagonal() const;
+    const PermutationWrapper<const Derived> asPermutation() const;
+
+    Derived& setIdentity();
+    Derived& setIdentity(Index rows, Index cols);
+
+    bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+
+    bool isUpperTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isLowerTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+
+    template<typename OtherDerived>
+    bool isOrthogonal(const MatrixBase<OtherDerived>& other,
+                      RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+
+    /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
+      * \warning When using floating point scalar values you probably should rather use a
+      *          fuzzy comparison such as isApprox()
+      * \sa isApprox(), operator!= */
+    template<typename OtherDerived>
+    inline bool operator==(const MatrixBase<OtherDerived>& other) const
+    { return cwiseEqual(other).all(); }
+
+    /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
+      * \warning When using floating point scalar values you probably should rather use a
+      *          fuzzy comparison such as isApprox()
+      * \sa isApprox(), operator== */
+    template<typename OtherDerived>
+    inline bool operator!=(const MatrixBase<OtherDerived>& other) const
+    { return cwiseNotEqual(other).any(); }
+
+    NoAlias<Derived,Eigen::MatrixBase > noalias();
+
+    inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
+    inline ForceAlignedAccess<Derived> forceAlignedAccess();
+    template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
+    template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
+
+    Scalar trace() const;
+
+/////////// Array module ///////////
+
+    template<int p> RealScalar lpNorm() const;
+
+    MatrixBase<Derived>& matrix() { return *this; }
+    const MatrixBase<Derived>& matrix() const { return *this; }
+
+    /** \returns an \link ArrayBase Array \endlink expression of this matrix
+      * \sa ArrayBase::matrix() */
+    ArrayWrapper<Derived> array() { return derived(); }
+    const ArrayWrapper<Derived> array() const { return derived(); }
+
+/////////// LU module ///////////
+
+    const FullPivLU<PlainObject> fullPivLu() const;
+    const PartialPivLU<PlainObject> partialPivLu() const;
+
+    #if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+    const LU<PlainObject> lu() const;
+    #endif
+
+    #ifdef EIGEN2_SUPPORT
+    const LU<PlainObject> eigen2_lu() const;
+    #endif
+
+    #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+    const PartialPivLU<PlainObject> lu() const;
+    #endif
+    
+    #ifdef EIGEN2_SUPPORT
+    template<typename ResultType>
+    void computeInverse(MatrixBase<ResultType> *result) const {
+      *result = this->inverse();
+    }
+    #endif
+
+    const internal::inverse_impl<Derived> inverse() const;
+    template<typename ResultType>
+    void computeInverseAndDetWithCheck(
+      ResultType& inverse,
+      typename ResultType::Scalar& determinant,
+      bool& invertible,
+      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+    ) const;
+    template<typename ResultType>
+    void computeInverseWithCheck(
+      ResultType& inverse,
+      bool& invertible,
+      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+    ) const;
+    Scalar determinant() const;
+
+/////////// Cholesky module ///////////
+
+    const LLT<PlainObject>  llt() const;
+    const LDLT<PlainObject> ldlt() const;
+
+/////////// QR module ///////////
+
+    const HouseholderQR<PlainObject> householderQr() const;
+    const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
+    const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
+    
+    #ifdef EIGEN2_SUPPORT
+    const QR<PlainObject> qr() const;
+    #endif
+
+    EigenvaluesReturnType eigenvalues() const;
+    RealScalar operatorNorm() const;
+
+/////////// SVD module ///////////
+
+    JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
+
+    #ifdef EIGEN2_SUPPORT
+    SVD<PlainObject> svd() const;
+    #endif
+
+/////////// Geometry module ///////////
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /// \internal helper struct to form the return type of the cross product
+    template<typename OtherDerived> struct cross_product_return_type {
+      typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
+      typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
+    };
+    #endif // EIGEN_PARSED_BY_DOXYGEN
+    template<typename OtherDerived>
+    typename cross_product_return_type<OtherDerived>::type
+    cross(const MatrixBase<OtherDerived>& other) const;
+    template<typename OtherDerived>
+    PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
+    PlainObject unitOrthogonal(void) const;
+    Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
+    
+    #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+    ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
+    // put this as separate enum value to work around possible GCC 4.3 bug (?)
+    enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
+    typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
+    HomogeneousReturnType homogeneous() const;
+    #endif
+    
+    enum {
+      SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
+    };
+    typedef Block<const Derived,
+                  internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
+                  internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
+    typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
+                const ConstStartMinusOne > HNormalizedReturnType;
+
+    const HNormalizedReturnType hnormalized() const;
+
+////////// Householder module ///////////
+
+    void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
+    template<typename EssentialPart>
+    void makeHouseholder(EssentialPart& essential,
+                         Scalar& tau, RealScalar& beta) const;
+    template<typename EssentialPart>
+    void applyHouseholderOnTheLeft(const EssentialPart& essential,
+                                   const Scalar& tau,
+                                   Scalar* workspace);
+    template<typename EssentialPart>
+    void applyHouseholderOnTheRight(const EssentialPart& essential,
+                                    const Scalar& tau,
+                                    Scalar* workspace);
+
+///////// Jacobi module /////////
+
+    template<typename OtherScalar>
+    void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+    template<typename OtherScalar>
+    void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+
+///////// MatrixFunctions module /////////
+
+    typedef typename internal::stem_function<Scalar>::type StemFunction;
+    const MatrixExponentialReturnValue<Derived> exp() const;
+    const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
+    const MatrixFunctionReturnValue<Derived> cosh() const;
+    const MatrixFunctionReturnValue<Derived> sinh() const;
+    const MatrixFunctionReturnValue<Derived> cos() const;
+    const MatrixFunctionReturnValue<Derived> sin() const;
+
+#ifdef EIGEN2_SUPPORT
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+                                      EvalBeforeAssigningBit>& other);
+
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
+                                      EvalBeforeAssigningBit>& other);
+
+    /** \deprecated because .lazy() is deprecated
+      * Overloaded for cache friendly product evaluation */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
+    { return lazyAssign(other._expression()); }
+
+    template<unsigned int Added>
+    const Flagged<Derived, Added, 0> marked() const;
+    const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
+
+    inline const Cwise<Derived> cwise() const;
+    inline Cwise<Derived> cwise();
+
+    VectorBlock<Derived> start(Index size);
+    const VectorBlock<const Derived> start(Index size) const;
+    VectorBlock<Derived> end(Index size);
+    const VectorBlock<const Derived> end(Index size) const;
+    template<int Size> VectorBlock<Derived,Size> start();
+    template<int Size> const VectorBlock<const Derived,Size> start() const;
+    template<int Size> VectorBlock<Derived,Size> end();
+    template<int Size> const VectorBlock<const Derived,Size> end() const;
+
+    Minor<Derived> minor(Index row, Index col);
+    const Minor<Derived> minor(Index row, Index col) const;
+#endif
+
+  protected:
+    MatrixBase() : Base() {}
+
+  private:
+    explicit MatrixBase(int);
+    MatrixBase(int,int);
+    template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
+  protected:
+    // mixing arrays and matrices is not legal
+    template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
+    {EIGEN_STATIC_ASSERT(sizeof(typename OtherDerived::Scalar)==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);}
+    // mixing arrays and matrices is not legal
+    template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
+    {EIGEN_STATIC_ASSERT(sizeof(typename OtherDerived::Scalar)==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);}
+};
+
+#endif // EIGEN_MATRIXBASE_H

Eigen/src/Core/NestByValue.h

@@ -0,0 +1,122 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_NESTBYVALUE_H
+#define EIGEN_NESTBYVALUE_H
+
+/** \class NestByValue
+  * \ingroup Core_Module
+  *
+  * \brief Expression which must be nested by value
+  *
+  * \param ExpressionType the type of the object of which we are requiring nesting-by-value
+  *
+  * This class is the return type of MatrixBase::nestByValue()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::nestByValue()
+  */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
+{};
+}
+
+template<typename ExpressionType> class NestByValue
+  : public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<NestByValue>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
+
+    inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
+
+    inline Index rows() const { return m_expression.rows(); }
+    inline Index cols() const { return m_expression.cols(); }
+    inline Index outerStride() const { return m_expression.outerStride(); }
+    inline Index innerStride() const { return m_expression.innerStride(); }
+
+    inline const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_expression.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return m_expression.coeff(index);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return m_expression.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return m_expression.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+    operator const ExpressionType&() const { return m_expression; }
+
+  protected:
+    const ExpressionType m_expression;
+};
+
+/** \returns an expression of the temporary version of *this.
+  */
+template<typename Derived>
+inline const NestByValue<Derived>
+DenseBase<Derived>::nestByValue() const
+{
+  return NestByValue<Derived>(derived());
+}
+
+#endif // EIGEN_NESTBYVALUE_H

Eigen/src/Core/NoAlias.h

@@ -0,0 +1,136 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_NOALIAS_H
+#define EIGEN_NOALIAS_H
+
+/** \class NoAlias
+  * \ingroup Core_Module
+  *
+  * \brief Pseudo expression providing an operator = assuming no aliasing
+  *
+  * \param ExpressionType the type of the object on which to do the lazy assignment
+  *
+  * This class represents an expression with special assignment operators
+  * assuming no aliasing between the target expression and the source expression.
+  * More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
+  * It is the return type of MatrixBase::noalias()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::noalias()
+  */
+template<typename ExpressionType, template <typename> class StorageBase>
+class NoAlias
+{
+    typedef typename ExpressionType::Scalar Scalar;
+  public:
+    NoAlias(ExpressionType& expression) : m_expression(expression) {}
+
+    /** Behaves like MatrixBase::lazyAssign(other)
+      * \sa MatrixBase::lazyAssign() */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
+    { return internal::assign_selector<ExpressionType,OtherDerived,false>::run(m_expression,other.derived()); }
+
+    /** \sa MatrixBase::operator+= */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
+    {
+      typedef SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
+      SelfAdder tmp(m_expression);
+      typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
+      typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
+      internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
+      return m_expression;
+    }
+
+    /** \sa MatrixBase::operator-= */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
+    {
+      typedef SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
+      SelfAdder tmp(m_expression);
+      typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
+      typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
+      internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
+      return m_expression;
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE ExpressionType& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+    { other.derived().addTo(m_expression); return m_expression; }
+
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE ExpressionType& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+    { other.derived().subTo(m_expression); return m_expression; }
+
+    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 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()); }
+#endif
+
+  protected:
+    ExpressionType& m_expression;
+};
+
+/** \returns a pseudo expression of \c *this with an operator= assuming
+  * no aliasing between \c *this and the source expression.
+  *
+  * More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
+  * Currently, even though several expressions may alias, only product
+  * expressions have this flag. Therefore, noalias() is only usefull when
+  * the source expression contains a matrix product.
+  *
+  * Here are some examples where noalias is usefull:
+  * \code
+  * D.noalias()  = A * B;
+  * D.noalias() += A.transpose() * B;
+  * D.noalias() -= 2 * A * B.adjoint();
+  * \endcode
+  *
+  * On the other hand the following example will lead to a \b wrong result:
+  * \code
+  * A.noalias() = A * B;
+  * \endcode
+  * because the result matrix A is also an operand of the matrix product. Therefore,
+  * there is no alternative than evaluating A * B in a temporary, that is the default
+  * behavior when you write:
+  * \code
+  * A = A * B;
+  * \endcode
+  *
+  * \sa class NoAlias
+  */
+template<typename Derived>
+NoAlias<Derived,MatrixBase> MatrixBase<Derived>::noalias()
+{
+  return derived();
+}
+
+#endif // EIGEN_NOALIAS_H

Eigen/src/Core/NumTraits.h

@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_NUMTRAITS_H
+#define EIGEN_NUMTRAITS_H
+
+/** \class NumTraits
+  * \ingroup Core_Module
+  *
+  * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
+  *
+  * \param T the numeric type at hand
+  *
+  * This class stores enums, typedefs and static methods giving information about a numeric type.
+  *
+  * The provided data consists of:
+  * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
+  *     then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
+  *     is a typedef to \a U.
+  * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
+  *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
+  *     \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
+  *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
+  *     only intended as a helper for code that needs to explicitly promote types.
+  * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
+  *     this means, just use \a T here.
+  * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
+  *     type, and to 0 otherwise.
+  * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
+  *     and to \c 0 otherwise.
+  * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
+  *     to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
+  *     Stay vague here. No need to do architecture-specific stuff.
+  * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
+  * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
+  *     be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
+  * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T.
+  * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
+  *     value by the fuzzy comparison operators.
+  * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
+  */
+
+template<typename T> struct GenericNumTraits
+{
+  enum {
+    IsInteger = std::numeric_limits<T>::is_integer,
+    IsSigned = std::numeric_limits<T>::is_signed,
+    IsComplex = 0,
+    RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+
+  typedef T Real;
+  typedef typename internal::conditional<
+                     IsInteger,
+                     typename internal::conditional<sizeof(T)<=2, float, double>::type,
+                     T
+                   >::type NonInteger;
+  typedef T Nested;
+
+  inline static Real epsilon() { return std::numeric_limits<T>::epsilon(); }
+  inline static Real dummy_precision()
+  {
+    // make sure to override this for floating-point types
+    return Real(0);
+  }
+  inline static T highest() { return (std::numeric_limits<T>::max)(); }
+  inline static T lowest()  { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); }
+  
+#ifdef EIGEN2_SUPPORT
+  enum {
+    HasFloatingPoint = !IsInteger
+  };
+  typedef NonInteger FloatingPoint;
+#endif
+};
+
+template<typename T> struct NumTraits : GenericNumTraits<T>
+{};
+
+template<> struct NumTraits<float>
+  : GenericNumTraits<float>
+{
+  inline static float dummy_precision() { return 1e-5f; }
+};
+
+template<> struct NumTraits<double> : GenericNumTraits<double>
+{
+  inline static double dummy_precision() { return 1e-12; }
+};
+
+template<> struct NumTraits<long double>
+  : GenericNumTraits<long double>
+{
+  static inline long double dummy_precision() { return 1e-15l; }
+};
+
+template<typename _Real> struct NumTraits<std::complex<_Real> >
+  : GenericNumTraits<std::complex<_Real> >
+{
+  typedef _Real Real;
+  enum {
+    IsComplex = 1,
+    RequireInitialization = NumTraits<_Real>::RequireInitialization,
+    ReadCost = 2 * NumTraits<_Real>::ReadCost,
+    AddCost = 2 * NumTraits<Real>::AddCost,
+    MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
+  };
+
+  inline static Real epsilon() { return NumTraits<Real>::epsilon(); }
+  inline static Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
+{
+  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
+  typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
+  typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
+  typedef ArrayType & Nested;
+  
+  enum {
+    IsComplex = NumTraits<Scalar>::IsComplex,
+    IsInteger = NumTraits<Scalar>::IsInteger,
+    IsSigned  = NumTraits<Scalar>::IsSigned,
+    RequireInitialization = 1,
+    ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
+    AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
+    MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
+  };
+};
+
+
+
+#endif // EIGEN_NUMTRAITS_H

Eigen/src/Core/PermutationMatrix.h

@@ -0,0 +1,696 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PERMUTATIONMATRIX_H
+#define EIGEN_PERMUTATIONMATRIX_H
+
+template<int RowCol,typename IndicesType,typename MatrixType, typename StorageKind> class PermutedImpl;
+
+/** \class PermutationBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for permutations
+  *
+  * \param Derived the derived class
+  *
+  * This class is the base class for all expressions representing a permutation matrix,
+  * internally stored as a vector of integers.
+  * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
+  * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
+  *  \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
+  * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
+  *  \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
+  *
+  * Permutation matrices are square and invertible.
+  *
+  * Notice that in addition to the member functions and operators listed here, there also are non-member
+  * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
+  * on either side.
+  *
+  * \sa class PermutationMatrix, class PermutationWrapper
+  */
+
+namespace internal {
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
+struct permut_matrix_product_retval;
+enum PermPermProduct_t {PermPermProduct};
+
+} // end namespace internal
+
+template<typename Derived>
+class PermutationBase : public EigenBase<Derived>
+{
+    typedef internal::traits<Derived> Traits;
+    typedef EigenBase<Derived> Base;
+  public:
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef typename Traits::IndicesType IndicesType;
+    enum {
+      Flags = Traits::Flags,
+      CoeffReadCost = Traits::CoeffReadCost,
+      RowsAtCompileTime = Traits::RowsAtCompileTime,
+      ColsAtCompileTime = Traits::ColsAtCompileTime,
+      MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
+    };
+    typedef typename Traits::Scalar Scalar;
+    typedef typename Traits::Index Index;
+    typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
+            DenseMatrixType;
+    typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,Index>
+            PlainPermutationType;
+    using Base::derived;
+    #endif
+
+    /** Copies the other permutation into *this */
+    template<typename OtherDerived>
+    Derived& operator=(const PermutationBase<OtherDerived>& other)
+    {
+      indices() = other.indices();
+      return derived();
+    }
+
+    /** Assignment from the Transpositions \a tr */
+    template<typename OtherDerived>
+    Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
+    {
+      setIdentity(tr.size());
+      for(Index k=size()-1; k>=0; --k)
+        applyTranspositionOnTheRight(k,tr.coeff(k));
+      return derived();
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    Derived& operator=(const PermutationBase& other)
+    {
+      indices() = other.indices();
+      return derived();
+    }
+    #endif
+
+    /** \returns the number of rows */
+    inline Index rows() const { return indices().size(); }
+
+    /** \returns the number of columns */
+    inline Index cols() const { return indices().size(); }
+
+    /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
+    inline Index size() const { return indices().size(); }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename DenseDerived>
+    void evalTo(MatrixBase<DenseDerived>& other) const
+    {
+      other.setZero();
+      for (int i=0; i<rows();++i)
+        other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
+    }
+    #endif
+
+    /** \returns a Matrix object initialized from this permutation matrix. Notice that it
+      * is inefficient to return this Matrix object by value. For efficiency, favor using
+      * the Matrix constructor taking EigenBase objects.
+      */
+    DenseMatrixType toDenseMatrix() const
+    {
+      return derived();
+    }
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return derived().indices(); }
+    /** \returns a reference to the stored array representing the permutation. */
+    IndicesType& indices() { return derived().indices(); }
+
+    /** Resizes to given size.
+      */
+    inline void resize(Index size)
+    {
+      indices().resize(size);
+    }
+
+    /** Sets *this to be the identity permutation matrix */
+    void setIdentity()
+    {
+      for(Index i = 0; i < size(); ++i)
+        indices().coeffRef(i) = i;
+    }
+
+    /** Sets *this to be the identity permutation matrix of given size.
+      */
+    void setIdentity(Index size)
+    {
+      resize(size);
+      setIdentity();
+    }
+
+    /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
+      *
+      * \returns a reference to *this.
+      *
+      * \warning This is much slower than applyTranspositionOnTheRight(int,int):
+      * this has linear complexity and requires a lot of branching.
+      *
+      * \sa applyTranspositionOnTheRight(int,int)
+      */
+    Derived& applyTranspositionOnTheLeft(Index i, Index j)
+    {
+      eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+      for(Index k = 0; k < size(); ++k)
+      {
+        if(indices().coeff(k) == i) indices().coeffRef(k) = j;
+        else if(indices().coeff(k) == j) indices().coeffRef(k) = i;
+      }
+      return derived();
+    }
+
+    /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
+      *
+      * \returns a reference to *this.
+      *
+      * This is a fast operation, it only consists in swapping two indices.
+      *
+      * \sa applyTranspositionOnTheLeft(int,int)
+      */
+    Derived& applyTranspositionOnTheRight(Index i, Index j)
+    {
+      eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+      std::swap(indices().coeffRef(i), indices().coeffRef(j));
+      return derived();
+    }
+
+    /** \returns the inverse permutation matrix.
+      *
+      * \note \note_try_to_help_rvo
+      */
+    inline Transpose<PermutationBase> inverse() const
+    { return derived(); }
+    /** \returns the tranpose permutation matrix.
+      *
+      * \note \note_try_to_help_rvo
+      */
+    inline Transpose<PermutationBase> transpose() const
+    { return derived(); }
+
+    /**** multiplication helpers to hopefully get RVO ****/
+
+  
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  protected:
+    template<typename OtherDerived>
+    void assignTranspose(const PermutationBase<OtherDerived>& other)
+    {
+      for (int i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
+    }
+    template<typename Lhs,typename Rhs>
+    void assignProduct(const Lhs& lhs, const Rhs& rhs)
+    {
+      eigen_assert(lhs.cols() == rhs.rows());
+      for (int i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
+    }
+#endif
+
+  public:
+
+    /** \returns the product permutation matrix.
+      *
+      * \note \note_try_to_help_rvo
+      */
+    template<typename Other>
+    inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
+    { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
+
+    /** \returns the product of a permutation with another inverse permutation.
+      *
+      * \note \note_try_to_help_rvo
+      */
+    template<typename Other>
+    inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other) const
+    { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
+
+    /** \returns the product of an inverse permutation with another permutation.
+      *
+      * \note \note_try_to_help_rvo
+      */
+    template<typename Other> friend
+    inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
+    { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
+
+  protected:
+
+};
+
+/** \class PermutationMatrix
+  * \ingroup Core_Module
+  *
+  * \brief Permutation matrix
+  *
+  * \param SizeAtCompileTime the number of rows/cols, or Dynamic
+  * \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+  * \param IndexType the interger type of the indices
+  *
+  * This class represents a permutation matrix, internally stored as a vector of integers.
+  *
+  * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
+  */
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
+ : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+  typedef IndexType Index;
+  typedef Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
+{
+    typedef PermutationBase<PermutationMatrix> Base;
+    typedef internal::traits<PermutationMatrix> Traits;
+  public:
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef typename Traits::IndicesType IndicesType;
+    #endif
+
+    inline PermutationMatrix()
+    {}
+
+    /** Constructs an uninitialized permutation matrix of given size.
+      */
+    inline PermutationMatrix(int size) : m_indices(size)
+    {}
+
+    /** Copy constructor. */
+    template<typename OtherDerived>
+    inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
+      : m_indices(other.indices()) {}
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** Standard copy constructor. Defined only to prevent a default copy constructor
+      * from hiding the other templated constructor */
+    inline PermutationMatrix(const PermutationMatrix& other) : m_indices(other.indices()) {}
+    #endif
+
+    /** Generic constructor from expression of the indices. The indices
+      * array has the meaning that the permutations sends each integer i to indices[i].
+      *
+      * \warning It is your responsibility to check that the indices array that you passes actually
+      * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
+      * array's size.
+      */
+    template<typename Other>
+    explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices)
+    {}
+
+    /** Convert the Transpositions \a tr to a permutation matrix */
+    template<typename Other>
+    explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
+      : m_indices(tr.size())
+    {
+      *this = tr;
+    }
+
+    /** Copies the other permutation into *this */
+    template<typename Other>
+    PermutationMatrix& operator=(const PermutationBase<Other>& other)
+    {
+      m_indices = other.indices();
+      return *this;
+    }
+
+    /** Assignment from the Transpositions \a tr */
+    template<typename Other>
+    PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
+    {
+      return Base::operator=(tr.derived());
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    PermutationMatrix& operator=(const PermutationMatrix& other)
+    {
+      m_indices = other.m_indices;
+      return *this;
+    }
+    #endif
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return m_indices; }
+    /** \returns a reference to the stored array representing the permutation. */
+    IndicesType& indices() { return m_indices; }
+
+
+    /**** multiplication helpers to hopefully get RVO ****/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename Other>
+    PermutationMatrix(const Transpose<PermutationBase<Other> >& other)
+      : m_indices(other.nestedPermutation().size())
+    {
+      for (int i=0; i<m_indices.size();++i) m_indices.coeffRef(other.nestedPermutation().indices().coeff(i)) = i;
+    }
+    template<typename Lhs,typename Rhs>
+    PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
+      : m_indices(lhs.indices().size())
+    {
+      Base::assignProduct(lhs,rhs);
+    }
+#endif
+
+  protected:
+
+    IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
+ : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+  typedef IndexType Index;
+  typedef Map<const Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess>
+  : public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
+{
+    typedef PermutationBase<Map> Base;
+    typedef internal::traits<Map> Traits;
+  public:
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef typename Traits::IndicesType IndicesType;
+    typedef typename IndicesType::Scalar Index;
+    #endif
+
+    inline Map(const Index* indices)
+      : m_indices(indices)
+    {}
+
+    inline Map(const Index* indices, Index size)
+      : m_indices(indices,size)
+    {}
+
+    /** Copies the other permutation into *this */
+    template<typename Other>
+    Map& operator=(const PermutationBase<Other>& other)
+    { return Base::operator=(other.derived()); }
+
+    /** Assignment from the Transpositions \a tr */
+    template<typename Other>
+    Map& operator=(const TranspositionsBase<Other>& tr)
+    { return Base::operator=(tr.derived()); }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    Map& operator=(const Map& other)
+    {
+      m_indices = other.m_indices;
+      return *this;
+    }
+    #endif
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return m_indices; }
+    /** \returns a reference to the stored array representing the permutation. */
+    IndicesType& indices() { return m_indices; }
+
+  protected:
+
+    IndicesType m_indices;
+};
+
+/** \class PermutationWrapper
+  * \ingroup Core_Module
+  *
+  * \brief Class to view a vector of integers as a permutation matrix
+  *
+  * \param _IndicesType the type of the vector of integer (can be any compatible expression)
+  *
+  * This class allows to view any vector expression of integers as a permutation matrix.
+  *
+  * \sa class PermutationBase, class PermutationMatrix
+  */
+
+struct PermutationStorage {};
+
+template<typename _IndicesType> class TranspositionsWrapper;
+namespace internal {
+template<typename _IndicesType>
+struct traits<PermutationWrapper<_IndicesType> >
+{
+  typedef PermutationStorage StorageKind;
+  typedef typename _IndicesType::Scalar Scalar;
+  typedef typename _IndicesType::Scalar Index;
+  typedef _IndicesType IndicesType;
+  enum {
+    RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
+    ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
+    MaxRowsAtCompileTime = IndicesType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = IndicesType::MaxColsAtCompileTime,
+    Flags = 0,
+    CoeffReadCost = _IndicesType::CoeffReadCost
+  };
+};
+}
+
+template<typename _IndicesType>
+class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
+{
+    typedef PermutationBase<PermutationWrapper> Base;
+    typedef internal::traits<PermutationWrapper> Traits;
+  public:
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef typename Traits::IndicesType IndicesType;
+    #endif
+
+    inline PermutationWrapper(const IndicesType& indices)
+      : m_indices(indices)
+    {}
+
+    /** const version of indices(). */
+    const typename internal::remove_all<typename IndicesType::Nested>::type&
+    indices() const { return m_indices; }
+
+  protected:
+
+    const typename IndicesType::Nested m_indices;
+};
+
+/** \returns the matrix with the permutation applied to the columns.
+  */
+template<typename Derived, typename PermutationDerived>
+inline const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight>
+operator*(const MatrixBase<Derived>& matrix,
+          const PermutationBase<PermutationDerived> &permutation)
+{
+  return internal::permut_matrix_product_retval
+           <PermutationDerived, Derived, OnTheRight>
+           (permutation.derived(), matrix.derived());
+}
+
+/** \returns the matrix with the permutation applied to the rows.
+  */
+template<typename Derived, typename PermutationDerived>
+inline const internal::permut_matrix_product_retval
+               <PermutationDerived, Derived, OnTheLeft>
+operator*(const PermutationBase<PermutationDerived> &permutation,
+          const MatrixBase<Derived>& matrix)
+{
+  return internal::permut_matrix_product_retval
+           <PermutationDerived, Derived, OnTheLeft>
+           (permutation.derived(), matrix.derived());
+}
+
+namespace internal {
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct traits<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+  typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
+struct permut_matrix_product_retval
+ : public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
+{
+    typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+
+    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 int cols() const { return m_matrix.cols(); }
+
+    template<typename Dest> inline void evalTo(Dest& dst) const
+    {
+      const int n = Side==OnTheLeft ? rows() : cols();
+
+      if(is_same<MatrixTypeNestedCleaned,Dest>::value && 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;
+        while(r < m_permutation.size())
+        {
+          // search for the next seed
+          while(r<m_permutation.size() && mask[r]) r++;
+          if(r>=m_permutation.size())
+            break;
+          // we got one, let's follow it until we are back to the seed
+          int k0 = r++;
+          int kPrev = k0;
+          mask.coeffRef(k0) = true;
+          for(int 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>
+                       (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
+
+            mask.coeffRef(k) = true;
+            kPrev = k;
+          }
+        }
+      }
+      else
+      {
+        for(int i = 0; i < n; ++i)
+        {
+          Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
+               (dst, ((Side==OnTheLeft) ^ Transposed) ? m_permutation.indices().coeff(i) : i)
+
+          =
+
+          Block<const MatrixTypeNestedCleaned,Side==OnTheLeft ? 1 : MatrixType::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixType::ColsAtCompileTime>
+               (m_matrix, ((Side==OnTheRight) ^ Transposed) ? m_permutation.indices().coeff(i) : i);
+        }
+      }
+    }
+
+  protected:
+    const PermutationType& m_permutation;
+    const typename MatrixType::Nested m_matrix;
+};
+
+/* Template partial specialization for transposed/inverse permutations */
+
+template<typename Derived>
+struct traits<Transpose<PermutationBase<Derived> > >
+ : traits<Derived>
+{};
+
+} // end namespace internal
+
+template<typename Derived>
+class Transpose<PermutationBase<Derived> >
+  : public EigenBase<Transpose<PermutationBase<Derived> > >
+{
+    typedef Derived PermutationType;
+    typedef typename PermutationType::IndicesType IndicesType;
+    typedef typename PermutationType::PlainPermutationType PlainPermutationType;
+  public:
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    typedef internal::traits<PermutationType> Traits;
+    typedef typename Derived::DenseMatrixType DenseMatrixType;
+    enum {
+      Flags = Traits::Flags,
+      CoeffReadCost = Traits::CoeffReadCost,
+      RowsAtCompileTime = Traits::RowsAtCompileTime,
+      ColsAtCompileTime = Traits::ColsAtCompileTime,
+      MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
+    };
+    typedef typename Traits::Scalar Scalar;
+    #endif
+
+    Transpose(const PermutationType& p) : m_permutation(p) {}
+
+    inline int rows() const { return m_permutation.rows(); }
+    inline int cols() const { return m_permutation.cols(); }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename DenseDerived>
+    void evalTo(MatrixBase<DenseDerived>& other) const
+    {
+      other.setZero();
+      for (int i=0; i<rows();++i)
+        other.coeffRef(i, m_permutation.indices().coeff(i)) = typename DenseDerived::Scalar(1);
+    }
+    #endif
+
+    /** \return the equivalent permutation matrix */
+    PlainPermutationType eval() const { return *this; }
+
+    DenseMatrixType toDenseMatrix() const { return *this; }
+
+    /** \returns the matrix with the inverse permutation applied to the columns.
+      */
+    template<typename OtherDerived> friend
+    inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>
+    operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trPerm)
+    {
+      return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>(trPerm.m_permutation, matrix.derived());
+    }
+
+    /** \returns the matrix with the inverse permutation applied to the rows.
+      */
+    template<typename OtherDerived>
+    inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>
+    operator*(const MatrixBase<OtherDerived>& matrix) const
+    {
+      return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>(m_permutation, matrix.derived());
+    }
+
+    const PermutationType& nestedPermutation() const { return m_permutation; }
+
+  protected:
+    const PermutationType& m_permutation;
+};
+
+template<typename Derived>
+const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
+{
+  return derived();
+}
+
+#endif // EIGEN_PERMUTATIONMATRIX_H

Eigen/src/Core/PlainObjectBase.h

@@ -0,0 +1,755 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DENSESTORAGEBASE_H
+#define EIGEN_DENSESTORAGEBASE_H
+
+#ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
+# define EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=Scalar(0);
+#else
+# define EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+#endif
+
+namespace internal {
+
+template<typename Index>
+EIGEN_ALWAYS_INLINE void check_rows_cols_for_overflow(Index rows, Index cols)
+{
+  // http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242
+  // we assume Index is signed
+  Index max_index = (size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed
+  bool error = (rows < 0  || cols < 0)  ? true
+             : (rows == 0 || cols == 0) ? false
+                                        : (rows > max_index / cols);
+  if (error)
+    throw_std_bad_alloc();
+}
+
+template <typename Derived, typename OtherDerived = Derived, bool IsVector = bool(Derived::IsVectorAtCompileTime)> struct conservative_resize_like_impl;
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;
+
+} // end namespace internal
+
+/**
+  * \brief %Dense storage base class for matrices and arrays.
+  *
+  * This class can be extended with the help of the plugin mechanism described on the page
+  * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_PLAINOBJECTBASE_PLUGIN.
+  *
+  * \sa \ref TopicClassHierarchy
+  */
+template<typename Derived>
+class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
+{
+  public:
+    enum { Options = internal::traits<Derived>::Options };
+    typedef typename internal::dense_xpr_base<Derived>::type Base;
+
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    typedef Derived DenseType;
+
+    using Base::RowsAtCompileTime;
+    using Base::ColsAtCompileTime;
+    using Base::SizeAtCompileTime;
+    using Base::MaxRowsAtCompileTime;
+    using Base::MaxColsAtCompileTime;
+    using Base::MaxSizeAtCompileTime;
+    using Base::IsVectorAtCompileTime;
+    using Base::Flags;
+
+    template<typename PlainObjectType, int MapOptions, typename StrideType> friend class Eigen::Map;
+    friend  class Eigen::Map<Derived, Unaligned>;
+    typedef Eigen::Map<Derived, Unaligned>  MapType;
+    friend  class Eigen::Map<const Derived, Unaligned>;
+    typedef const Eigen::Map<const Derived, Unaligned> ConstMapType;
+    friend  class Eigen::Map<Derived, Aligned>;
+    typedef Eigen::Map<Derived, Aligned> AlignedMapType;
+    friend  class Eigen::Map<const Derived, Aligned>;
+    typedef const Eigen::Map<const Derived, Aligned> ConstAlignedMapType;
+    template<typename StrideType> struct StridedMapType { typedef Eigen::Map<Derived, Unaligned, StrideType> type; };
+    template<typename StrideType> struct StridedConstMapType { typedef Eigen::Map<const Derived, Unaligned, StrideType> type; };
+    template<typename StrideType> struct StridedAlignedMapType { typedef Eigen::Map<Derived, Aligned, StrideType> type; };
+    template<typename StrideType> struct StridedConstAlignedMapType { typedef Eigen::Map<const Derived, Aligned, StrideType> type; };
+
+  protected:
+    DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;
+
+  public:
+    enum { NeedsToAlign = SizeAtCompileTime != Dynamic && (internal::traits<Derived>::Flags & AlignedBit) != 0 };
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+
+    Base& base() { return *static_cast<Base*>(this); }
+    const Base& base() const { return *static_cast<const Base*>(this); }
+
+    EIGEN_STRONG_INLINE Index rows() const { return m_storage.rows(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_storage.cols(); }
+
+    EIGEN_STRONG_INLINE const Scalar& coeff(Index row, Index col) const
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.data()[col + row * m_storage.cols()];
+      else // column-major
+        return m_storage.data()[row + col * m_storage.rows()];
+    }
+
+    EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
+    {
+      return m_storage.data()[index];
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.data()[col + row * m_storage.cols()];
+      else // column-major
+        return m_storage.data()[row + col * m_storage.rows()];
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+    {
+      return m_storage.data()[index];
+    }
+
+    EIGEN_STRONG_INLINE const Scalar& coeffRef(Index row, Index col) const
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.data()[col + row * m_storage.cols()];
+      else // column-major
+        return m_storage.data()[row + col * m_storage.rows()];
+    }
+
+    EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const
+    {
+      return m_storage.data()[index];
+    }
+
+    /** \internal */
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
+    {
+      return internal::ploadt<PacketScalar, LoadMode>
+               (m_storage.data() + (Flags & RowMajorBit
+                                   ? col + row * m_storage.cols()
+                                   : row + col * m_storage.rows()));
+    }
+
+    /** \internal */
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+    {
+      return internal::ploadt<PacketScalar, LoadMode>(m_storage.data() + index);
+    }
+
+    /** \internal */
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
+              (m_storage.data() + (Flags & RowMajorBit
+                                   ? col + row * m_storage.cols()
+                                   : row + col * m_storage.rows()), x);
+    }
+
+    /** \internal */
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& x)
+    {
+      internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);
+    }
+
+    /** \returns a const pointer to the data array of this matrix */
+    EIGEN_STRONG_INLINE const Scalar *data() const
+    { return m_storage.data(); }
+
+    /** \returns a pointer to the data array of this matrix */
+    EIGEN_STRONG_INLINE Scalar *data()
+    { return m_storage.data(); }
+
+    /** Resizes \c *this to a \a rows x \a cols matrix.
+      *
+      * This method is intended for dynamic-size matrices, although it is legal to call it on any
+      * matrix as long as fixed dimensions are left unchanged. If you only want to change the number
+      * of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).
+      *
+      * If the current number of coefficients of \c *this exactly matches the
+      * product \a rows * \a cols, then no memory allocation is performed and
+      * the current values are left unchanged. In all other cases, including
+      * shrinking, the data is reallocated and all previous values are lost.
+      *
+      * Example: \include Matrix_resize_int_int.cpp
+      * Output: \verbinclude Matrix_resize_int_int.out
+      *
+      * \sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)
+      */
+    EIGEN_STRONG_INLINE void resize(Index rows, Index cols)
+    {
+      #ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
+        internal::check_rows_cols_for_overflow(rows, cols);
+        Index size = rows*cols;
+        bool size_changed = size != this->size();
+        m_storage.resize(size, rows, cols);
+        if(size_changed) EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+      #else
+        internal::check_rows_cols_for_overflow(rows, cols);
+        m_storage.resize(rows*cols, rows, cols);
+      #endif
+    }
+
+    /** Resizes \c *this to a vector of length \a size
+      *
+      * \only_for_vectors. This method does not work for
+      * partially dynamic matrices when the static dimension is anything other
+      * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+      *
+      * Example: \include Matrix_resize_int.cpp
+      * Output: \verbinclude Matrix_resize_int.out
+      *
+      * \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)
+      */
+    inline void resize(Index size)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)
+      eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
+      #ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
+        bool size_changed = size != this->size();
+      #endif
+      if(RowsAtCompileTime == 1)
+        m_storage.resize(size, 1, size);
+      else
+        m_storage.resize(size, size, 1);
+      #ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
+        if(size_changed) EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+      #endif
+    }
+
+    /** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \c NoChange
+      * as in the example below.
+      *
+      * Example: \include Matrix_resize_NoChange_int.cpp
+      * Output: \verbinclude Matrix_resize_NoChange_int.out
+      *
+      * \sa resize(Index,Index)
+      */
+    inline void resize(NoChange_t, Index cols)
+    {
+      resize(rows(), cols);
+    }
+
+    /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \c NoChange
+      * as in the example below.
+      *
+      * Example: \include Matrix_resize_int_NoChange.cpp
+      * Output: \verbinclude Matrix_resize_int_NoChange.out
+      *
+      * \sa resize(Index,Index)
+      */
+    inline void resize(Index rows, NoChange_t)
+    {
+      resize(rows, cols());
+    }
+
+    /** Resizes \c *this to have the same dimensions as \a other.
+      * Takes care of doing all the checking that's needed.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void resizeLike(const EigenBase<OtherDerived>& _other)
+    {
+      const OtherDerived& other = _other.derived();
+      internal::check_rows_cols_for_overflow(other.rows(), other.cols());
+      const Index othersize = other.rows()*other.cols();
+      if(RowsAtCompileTime == 1)
+      {
+        eigen_assert(other.rows() == 1 || other.cols() == 1);
+        resize(1, othersize);
+      }
+      else if(ColsAtCompileTime == 1)
+      {
+        eigen_assert(other.rows() == 1 || other.cols() == 1);
+        resize(othersize, 1);
+      }
+      else resize(other.rows(), other.cols());
+    }
+
+    /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+      *
+      * The method is intended for matrices of dynamic size. If you only want to change the number
+      * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+      * conservativeResize(Index, NoChange_t).
+      *
+      * Matrices are resized relative to the top-left element. In case values need to be 
+      * appended to the matrix they will be uninitialized.
+      */
+    EIGEN_STRONG_INLINE void conservativeResize(Index rows, Index cols)
+    {
+      internal::conservative_resize_like_impl<Derived>::run(*this, rows, cols);
+    }
+
+    /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+      *
+      * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+      * the number of columns unchanged.
+      *
+      * In case the matrix is growing, new rows will be uninitialized.
+      */
+    EIGEN_STRONG_INLINE void conservativeResize(Index rows, NoChange_t)
+    {
+      // Note: see the comment in conservativeResize(Index,Index)
+      conservativeResize(rows, cols());
+    }
+
+    /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+      *
+      * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+      * the number of rows unchanged.
+      *
+      * In case the matrix is growing, new columns will be uninitialized.
+      */
+    EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index cols)
+    {
+      // Note: see the comment in conservativeResize(Index,Index)
+      conservativeResize(rows(), cols);
+    }
+
+    /** Resizes the vector to \a size while retaining old values.
+      *
+      * \only_for_vectors. This method does not work for
+      * partially dynamic matrices when the static dimension is anything other
+      * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+      *
+      * When values are appended, they will be uninitialized.
+      */
+    EIGEN_STRONG_INLINE void conservativeResize(Index size)
+    {
+      internal::conservative_resize_like_impl<Derived>::run(*this, size);
+    }
+
+    /** Resizes the matrix to \a rows x \a cols of \c other, while leaving old values untouched.
+      *
+      * The method is intended for matrices of dynamic size. If you only want to change the number
+      * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+      * conservativeResize(Index, NoChange_t).
+      *
+      * Matrices are resized relative to the top-left element. In case values need to be 
+      * appended to the matrix they will copied from \c other.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase<OtherDerived>& other)
+    {
+      internal::conservative_resize_like_impl<Derived,OtherDerived>::run(*this, other);
+    }
+
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other)
+    {
+      return _set(other);
+    }
+
+    /** \sa MatrixBase::lazyAssign() */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase<OtherDerived>& other)
+    {
+      _resize_to_match(other);
+      return Base::lazyAssign(other.derived());
+    }
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue<OtherDerived>& func)
+    {
+      resize(func.rows(), func.cols());
+      return Base::operator=(func);
+    }
+
+    EIGEN_STRONG_INLINE explicit PlainObjectBase() : m_storage()
+    {
+//       _check_template_params();
+//       EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    // FIXME is it still needed ?
+    /** \internal */
+    PlainObjectBase(internal::constructor_without_unaligned_array_assert)
+      : m_storage(internal::constructor_without_unaligned_array_assert())
+    {
+//       _check_template_params(); EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+#endif
+
+    EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols)
+      : m_storage(size, rows, cols)
+    {
+//       _check_template_params();
+//       EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+
+    /** \copydoc MatrixBase::operator=(const EigenBase<OtherDerived>&)
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived> &other)
+    {
+      _resize_to_match(other);
+      Base::operator=(other.derived());
+      return this->derived();
+    }
+
+    /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase<OtherDerived> &other)
+      : m_storage(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
+    {
+      _check_template_params();
+      internal::check_rows_cols_for_overflow(other.derived().rows(), other.derived().cols());
+      Base::operator=(other.derived());
+    }
+
+    /** \name Map
+      * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
+      * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
+      * \a data pointers.
+      *
+      * \see class Map
+      */
+    //@{
+    inline static ConstMapType Map(const Scalar* data)
+    { return ConstMapType(data); }
+    inline static MapType Map(Scalar* data)
+    { return MapType(data); }
+    inline static ConstMapType Map(const Scalar* data, Index size)
+    { return ConstMapType(data, size); }
+    inline static MapType Map(Scalar* data, Index size)
+    { return MapType(data, size); }
+    inline static ConstMapType Map(const Scalar* data, Index rows, Index cols)
+    { return ConstMapType(data, rows, cols); }
+    inline static MapType Map(Scalar* data, Index rows, Index cols)
+    { return MapType(data, rows, cols); }
+
+    inline static ConstAlignedMapType MapAligned(const Scalar* data)
+    { return ConstAlignedMapType(data); }
+    inline static AlignedMapType MapAligned(Scalar* data)
+    { return AlignedMapType(data); }
+    inline static ConstAlignedMapType MapAligned(const Scalar* data, Index size)
+    { return ConstAlignedMapType(data, size); }
+    inline static AlignedMapType MapAligned(Scalar* data, Index size)
+    { return AlignedMapType(data, size); }
+    inline static ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
+    { return ConstAlignedMapType(data, rows, cols); }
+    inline static AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)
+    { return AlignedMapType(data, rows, cols); }
+
+    template<int Outer, int Inner>
+    inline static typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, const Stride<Outer, Inner>& stride)
+    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+
+    template<int Outer, int Inner>
+    inline static typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, const Stride<Outer, Inner>& stride)
+    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+    template<int Outer, int Inner>
+    inline static typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+    //@}
+
+    using Base::setConstant;
+    Derived& setConstant(Index size, const Scalar& value);
+    Derived& setConstant(Index rows, Index cols, const Scalar& value);
+
+    using Base::setZero;
+    Derived& setZero(Index size);
+    Derived& setZero(Index rows, Index cols);
+
+    using Base::setOnes;
+    Derived& setOnes(Index size);
+    Derived& setOnes(Index rows, Index cols);
+
+    using Base::setRandom;
+    Derived& setRandom(Index size);
+    Derived& setRandom(Index rows, Index cols);
+
+    #ifdef EIGEN_PLAINOBJECTBASE_PLUGIN
+    #include EIGEN_PLAINOBJECTBASE_PLUGIN
+    #endif
+
+  protected:
+    /** \internal Resizes *this in preparation for assigning \a other to it.
+      * Takes care of doing all the checking that's needed.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase<OtherDerived>& other)
+    {
+      #ifdef EIGEN_NO_AUTOMATIC_RESIZING
+      eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())
+                 : (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);
+      #else
+      resizeLike(other);
+      #endif
+    }
+
+    /**
+      * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+      *
+      * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+      * it will be initialized.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      *
+      * \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
+      *
+      * \internal
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Derived& _set(const DenseBase<OtherDerived>& other)
+    {
+      _set_selector(other.derived(), typename internal::conditional<static_cast<bool>(int(OtherDerived::Flags) & EvalBeforeAssigningBit), internal::true_type, internal::false_type>::type());
+      return this->derived();
+    }
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::true_type&) { _set_noalias(other.eval()); }
+
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::false_type&) { _set_noalias(other); }
+
+    /** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
+      * is the case when creating a new matrix) so one can enforce lazy evaluation.
+      *
+      * \sa operator=(const MatrixBase<OtherDerived>&), _set()
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase<OtherDerived>& other)
+    {
+      // I don't think we need this resize call since the lazyAssign will anyways resize
+      // and lazyAssign will be called by the assign selector.
+      //_resize_to_match(other);
+      // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
+      // it wouldn't allow to copy a row-vector into a column-vector.
+      return internal::assign_selector<Derived,OtherDerived,false>::run(this->derived(), other.derived());
+    }
+
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE void _init2(Index rows, Index cols, typename internal::enable_if<Base::SizeAtCompileTime!=2,T0>::type* = 0)
+    {
+      eigen_assert(rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+             && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+      internal::check_rows_cols_for_overflow(rows, cols);      
+      m_storage.resize(rows*cols,rows,cols);
+      EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
+    }
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE void _init2(const Scalar& x, const Scalar& y, typename internal::enable_if<Base::SizeAtCompileTime==2,T0>::type* = 0)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+    }
+
+    template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+    friend struct internal::matrix_swap_impl;
+
+    /** \internal generic implementation of swap for dense storage since for dynamic-sized matrices of same type it is enough to swap the
+      * data pointers.
+      */
+    template<typename OtherDerived>
+    void _swap(DenseBase<OtherDerived> const & other)
+    {
+      enum { SwapPointers = internal::is_same<Derived, OtherDerived>::value && Base::SizeAtCompileTime==Dynamic };
+      internal::matrix_swap_impl<Derived, OtherDerived, bool(SwapPointers)>::run(this->derived(), other.const_cast_derived());
+    }
+
+  public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    EIGEN_STRONG_INLINE static void _check_template_params()
+    {
+      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (Options&RowMajor)==RowMajor)
+                        && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (Options&RowMajor)==0)
+                        && ((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0))
+                        && ((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0))
+                        && ((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0))
+                        && ((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0))
+                        && (MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic)
+                        && (MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic)
+                        && (Options & (DontAlign|RowMajor)) == Options),
+        INVALID_MATRIX_TEMPLATE_PARAMETERS)
+    }
+#endif
+
+private:
+    enum { ThisConstantIsPrivateInPlainObjectBase };
+};
+
+template <typename Derived, typename OtherDerived, bool IsVector>
+struct internal::conservative_resize_like_impl
+{
+  typedef typename Derived::Index Index;
+  static void run(DenseBase<Derived>& _this, Index rows, Index cols)
+  {
+    if (_this.rows() == rows && _this.cols() == cols) return;
+    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+
+    if ( ( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows
+         (!Derived::IsRowMajor && _this.rows() == rows) )  // column-major and we change only the number of columns
+    {
+      internal::check_rows_cols_for_overflow(rows, cols);
+      _this.derived().m_storage.conservativeResize(rows*cols,rows,cols);
+    }
+    else
+    {
+      // The storage order does not allow us to use reallocation.
+      typename Derived::PlainObject tmp(rows,cols);
+      const Index common_rows = (std::min)(rows, _this.rows());
+      const Index common_cols = (std::min)(cols, _this.cols());
+      tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+      _this.derived().swap(tmp);
+    }
+  }
+
+  static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+  {
+    if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+    // Note: Here is space for improvement. Basically, for conservativeResize(Index,Index),
+    // neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the
+    // dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or
+    // conservativeResize(NoChange_t, Index cols). For these methods new static asserts like
+    // EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good.
+    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived)
+
+    if ( ( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows
+         (!Derived::IsRowMajor && _this.rows() == other.rows()) )  // column-major and we change only the number of columns
+    {
+      const Index new_rows = other.rows() - _this.rows();
+      const Index new_cols = other.cols() - _this.cols();
+      _this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols());
+      if (new_rows>0)
+        _this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows);
+      else if (new_cols>0)
+        _this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols);
+    }
+    else
+    {
+      // The storage order does not allow us to use reallocation.
+      typename Derived::PlainObject tmp(other);
+      const Index common_rows = (std::min)(tmp.rows(), _this.rows());
+      const Index common_cols = (std::min)(tmp.cols(), _this.cols());
+      tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+      _this.derived().swap(tmp);
+    }
+  }
+};
+
+namespace internal {
+
+template <typename Derived, typename OtherDerived>
+struct conservative_resize_like_impl<Derived,OtherDerived,true>
+{
+  typedef typename Derived::Index Index;
+  static void run(DenseBase<Derived>& _this, Index size)
+  {
+    const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size;
+    const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1;
+    _this.derived().m_storage.conservativeResize(size,new_rows,new_cols);
+  }
+
+  static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+  {
+    if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+    const Index num_new_elements = other.size() - _this.size();
+
+    const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows();
+    const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1;
+    _this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols);
+
+    if (num_new_elements > 0)
+      _this.tail(num_new_elements) = other.tail(num_new_elements);
+  }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+struct matrix_swap_impl
+{
+  static inline void run(MatrixTypeA& a, MatrixTypeB& b)
+  {
+    a.base().swap(b);
+  }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB>
+struct matrix_swap_impl<MatrixTypeA, MatrixTypeB, true>
+{
+  static inline void run(MatrixTypeA& a, MatrixTypeB& b)
+  {
+    static_cast<typename MatrixTypeA::Base&>(a).m_storage.swap(static_cast<typename MatrixTypeB::Base&>(b).m_storage);
+  }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_DENSESTORAGEBASE_H

Eigen/src/Core/Product.h

@@ -0,0 +1,625 @@
+// 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 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PRODUCT_H
+#define EIGEN_PRODUCT_H
+
+/** \class GeneralProduct
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the product of two general matrices or vectors
+  *
+  * \param LhsNested the type used to store the left-hand side
+  * \param RhsNested the type used to store the right-hand side
+  * \param ProductMode the type of the product
+  *
+  * This class represents an expression of the product of two general matrices.
+  * We call a general matrix, a dense matrix with full storage. For instance,
+  * This excludes triangular, selfadjoint, and sparse matrices.
+  * It is the return type of the operator* between general matrices. Its template
+  * arguments are determined automatically by ProductReturnType. Therefore,
+  * GeneralProduct should never be used direclty. To determine the result type of a
+  * function which involves a matrix product, use ProductReturnType::Type.
+  *
+  * \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+  */
+template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
+class GeneralProduct;
+
+enum {
+  Large = 2,
+  Small = 3
+};
+
+namespace internal {
+
+template<int Rows, int Cols, int Depth> struct product_type_selector;
+
+template<int Size, int MaxSize> struct product_size_category
+{
+  enum { is_large = MaxSize == Dynamic ||
+                    Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
+         value = is_large  ? Large
+               : Size == 1 ? 1
+                           : Small
+  };
+};
+
+template<typename Lhs, typename Rhs> struct product_type
+{
+  typedef typename remove_all<Lhs>::type _Lhs;
+  typedef typename remove_all<Rhs>::type _Rhs;
+  enum {
+    MaxRows  = _Lhs::MaxRowsAtCompileTime,
+    Rows  = _Lhs::RowsAtCompileTime,
+    MaxCols  = _Rhs::MaxColsAtCompileTime,
+    Cols  = _Rhs::ColsAtCompileTime,
+    MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
+                                           _Rhs::MaxRowsAtCompileTime),
+    Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
+                                        _Rhs::RowsAtCompileTime),
+    LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+  };
+
+  // the splitting into different lines of code here, introducing the _select enums and the typedef below,
+  // is to work around an internal compiler error with gcc 4.1 and 4.2.
+private:
+  enum {
+    rows_select = product_size_category<Rows,MaxRows>::value,
+    cols_select = product_size_category<Cols,MaxCols>::value,
+    depth_select = product_size_category<Depth,MaxDepth>::value
+  };
+  typedef product_type_selector<rows_select, cols_select, depth_select> selector;
+
+public:
+  enum {
+    value = selector::ret
+  };
+#ifdef EIGEN_DEBUG_PRODUCT
+  static void debug()
+  {
+      EIGEN_DEBUG_VAR(Rows);
+      EIGEN_DEBUG_VAR(Cols);
+      EIGEN_DEBUG_VAR(Depth);
+      EIGEN_DEBUG_VAR(rows_select);
+      EIGEN_DEBUG_VAR(cols_select);
+      EIGEN_DEBUG_VAR(depth_select);
+      EIGEN_DEBUG_VAR(value);
+  }
+#endif
+};
+
+
+/* The following allows to select the kind of product at compile time
+ * based on the three dimensions of the product.
+ * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
+// FIXME I'm not sure the current mapping is the ideal one.
+template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
+template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
+template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
+template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
+template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
+template<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
+template<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
+template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
+template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
+template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
+
+} // end namespace internal
+
+/** \class ProductReturnType
+  * \ingroup Core_Module
+  *
+  * \brief Helper class to get the correct and optimized returned type of operator*
+  *
+  * \param Lhs the type of the left-hand side
+  * \param Rhs the type of the right-hand side
+  * \param ProductMode the type of the product (determined automatically by internal::product_mode)
+  *
+  * This class defines the typename Type representing the optimized product expression
+  * between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
+  * is the recommended way to define the result type of a function returning an expression
+  * which involve a matrix product. The class Product should never be
+  * used directly.
+  *
+  * \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+  */
+template<typename Lhs, typename Rhs, int ProductType>
+struct ProductReturnType
+{
+  // TODO use the nested type to reduce instanciations ????
+//   typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+//   typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+
+  typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
+};
+
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
+{
+  typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
+  typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
+  typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
+};
+
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
+{
+  typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
+  typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
+  typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
+};
+
+// this is a workaround for sun CC
+template<typename Lhs, typename Rhs>
+struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
+{};
+
+/***********************************************************************
+*  Implementation of Inner Vector Vector Product
+***********************************************************************/
+
+// FIXME : maybe the "inner product" could return a Scalar
+// instead of a 1x1 matrix ??
+// Pro: more natural for the user
+// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
+// product ends up to a row-vector times col-vector product... To tackle this use
+// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
+
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
+ : traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
+{};
+
+}
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, InnerProduct>
+  : internal::no_assignment_operator,
+    public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
+{
+    typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
+  public:
+    GeneralProduct(const Lhs& lhs, const Rhs& rhs)
+    {
+      EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+      Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
+    }
+
+    /** Convertion to scalar */
+    operator const typename Base::Scalar() const {
+      return Base::coeff(0,0);
+    }
+};
+
+/***********************************************************************
+*  Implementation of Outer Vector Vector Product
+***********************************************************************/
+
+namespace internal {
+template<int StorageOrder> struct outer_product_selector;
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
+{};
+
+}
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, OuterProduct>
+  : public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
+{
+  public:
+    EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+    GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+    {
+      EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+    }
+
+    template<typename Dest> void scaleAndAddTo(Dest& dest, Scalar alpha) const
+    {
+      internal::outer_product_selector<(int(Dest::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(*this, dest, alpha);
+    }
+};
+
+namespace internal {
+
+template<> struct outer_product_selector<ColMajor> {
+  template<typename ProductType, typename Dest>
+  static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
+    typedef typename Dest::Index Index;
+    // FIXME make sure lhs is sequentially stored
+    // 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)
+      dest.col(j) += (alpha * prod.rhs().coeff(j)) * prod.lhs();
+  }
+};
+
+template<> struct outer_product_selector<RowMajor> {
+  template<typename ProductType, typename Dest>
+  static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
+    typedef typename Dest::Index Index;
+    // FIXME make sure rhs is sequentially stored
+    // 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)
+      dest.row(i) += (alpha * prod.lhs().coeff(i)) * prod.rhs();
+  }
+};
+
+} // end namespace internal
+
+/***********************************************************************
+*  Implementation of General Matrix Vector Product
+***********************************************************************/
+
+/*  According to the shape/flags of the matrix we have to distinghish 3 different cases:
+ *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
+ *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
+ *   3 - all other cases are handled using a simple loop along the outer-storage direction.
+ *  Therefore we need a lower level meta selector.
+ *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
+ */
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
+{};
+
+template<int Side, int StorageOrder, bool BlasCompatible>
+struct gemv_selector;
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, GemvProduct>
+  : public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
+{
+  public:
+    EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+    typedef typename Lhs::Scalar LhsScalar;
+    typedef typename Rhs::Scalar RhsScalar;
+
+    GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+    {
+//       EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
+//         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+    }
+
+    enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
+    typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
+
+    template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
+    {
+      eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
+      internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
+                       bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
+    }
+};
+
+namespace internal {
+
+// The vector is on the left => transposition
+template<int StorageOrder, bool BlasCompatible>
+struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
+{
+  template<typename ProductType, typename Dest>
+  static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
+  {
+    Transpose<Dest> destT(dest);
+    enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
+    gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
+      ::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
+        (prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
+  }
+};
+
+template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
+{
+  EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
+};
+
+template<typename Scalar,int Size>
+struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
+{
+  EIGEN_STRONG_INLINE Scalar* data() { return 0; }
+};
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
+{
+  #if EIGEN_ALIGN_STATICALLY
+  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
+  EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
+  #else
+  // Some architectures cannot align on the stack,
+  // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
+  enum {
+    ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
+    PacketSize      = internal::packet_traits<Scalar>::size
+  };
+  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
+  EIGEN_STRONG_INLINE Scalar* data() {
+    return ForceAlignment
+            ? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
+            : m_data.array;
+  }
+  #endif
+};
+
+template<> struct gemv_selector<OnTheRight,ColMajor,true>
+{
+  template<typename ProductType, typename Dest>
+  static inline void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
+  {
+    typedef typename ProductType::Index Index;
+    typedef typename ProductType::LhsScalar   LhsScalar;
+    typedef typename ProductType::RhsScalar   RhsScalar;
+    typedef typename ProductType::Scalar      ResScalar;
+    typedef typename ProductType::RealScalar  RealScalar;
+    typedef typename ProductType::ActualLhsType ActualLhsType;
+    typedef typename ProductType::ActualRhsType ActualRhsType;
+    typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+    typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+    typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
+
+    const ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
+    const ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+                                  * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+    enum {
+      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+      // on, the other hand it is good for the cache to pack the vector anyways...
+      EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
+      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
+      MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
+    };
+
+    gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+
+    // this is written like this (i.e., with a ?:) to workaround an ICE with ICC 12
+    bool alphaIsCompatible = (!ComplexByReal) ? true : (imag(actualAlpha)==RealScalar(0));
+    bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
+    
+    RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
+
+    ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+                                                  evalToDest ? dest.data() : static_dest.data());
+    
+    if(!evalToDest)
+    {
+      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+      int size = dest.size();
+      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+      #endif
+      if(!alphaIsCompatible)
+      {
+        MappedDest(actualDestPtr, dest.size()).setZero();
+        compatibleAlpha = RhsScalar(1);
+      }
+      else
+        MappedDest(actualDestPtr, dest.size()) = dest;
+    }
+
+    general_matrix_vector_product
+      <Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
+        actualLhs.rows(), actualLhs.cols(),
+        &actualLhs.coeffRef(0,0), actualLhs.outerStride(),
+        actualRhs.data(), actualRhs.innerStride(),
+        actualDestPtr, 1,
+        compatibleAlpha);
+
+    if (!evalToDest)
+    {
+      if(!alphaIsCompatible)
+        dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
+      else
+        dest = MappedDest(actualDestPtr, dest.size());
+    }
+  }
+};
+
+template<> struct gemv_selector<OnTheRight,RowMajor,true>
+{
+  template<typename ProductType, typename Dest>
+  static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
+  {
+    typedef typename ProductType::LhsScalar LhsScalar;
+    typedef typename ProductType::RhsScalar RhsScalar;
+    typedef typename ProductType::Scalar    ResScalar;
+    typedef typename ProductType::Index Index;
+    typedef typename ProductType::ActualLhsType ActualLhsType;
+    typedef typename ProductType::ActualRhsType ActualRhsType;
+    typedef typename ProductType::_ActualRhsType _ActualRhsType;
+    typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
+    typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
+
+    typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
+    typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
+                                  * RhsBlasTraits::extractScalarFactor(prod.rhs());
+
+    enum {
+      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+      // on, the other hand it is good for the cache to pack the vector anyways...
+      DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
+    };
+
+    gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
+
+    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
+        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
+
+    if(!DirectlyUseRhs)
+    {
+      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+      int size = actualRhs.size();
+      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+      #endif
+      Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+    }
+
+    general_matrix_vector_product
+      <Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
+        actualLhs.rows(), actualLhs.cols(),
+        &actualLhs.coeffRef(0,0), actualLhs.outerStride(),
+        actualRhsPtr, 1,
+        &dest.coeffRef(0,0), dest.innerStride(),
+        actualAlpha);
+  }
+};
+
+template<> struct gemv_selector<OnTheRight,ColMajor,false>
+{
+  template<typename ProductType, typename Dest>
+  static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
+  {
+    typedef typename Dest::Index Index;
+    // TODO makes sure dest is sequentially stored in memory, otherwise use a temp
+    const Index size = prod.rhs().rows();
+    for(Index k=0; k<size; ++k)
+      dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
+  }
+};
+
+template<> struct gemv_selector<OnTheRight,RowMajor,false>
+{
+  template<typename ProductType, typename Dest>
+  static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
+  {
+    typedef typename Dest::Index Index;
+    // TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
+    const Index rows = prod.rows();
+    for(Index i=0; i<rows; ++i)
+      dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
+  }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \returns the matrix product of \c *this and \a other.
+  *
+  * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
+  *
+  * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline const typename ProductReturnType<Derived,OtherDerived>::Type
+MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+  // A note regarding the function declaration: In MSVC, this function will sometimes
+  // not be inlined since DenseStorage is an unwindable object for dynamic
+  // matrices and product types are holding a member to store the result.
+  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
+  enum {
+    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
+                   || OtherDerived::RowsAtCompileTime==Dynamic
+                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+  };
+  // note to the lost user:
+  //    * for a dot product use: v1.dot(v2)
+  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+#ifdef EIGEN_DEBUG_PRODUCT
+  internal::product_type<Derived,OtherDerived>::debug();
+#endif
+  return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
+  *
+  * The returned product will behave like any other expressions: the coefficients of the product will be
+  * computed once at a time as requested. This might be useful in some extremely rare cases when only
+  * a small and no coherent fraction of the result's coefficients have to be computed.
+  *
+  * \warning This version of the matrix product can be much much slower. So use it only if you know
+  * what you are doing and that you measured a true speed improvement.
+  *
+  * \sa operator*(const MatrixBase&)
+  */
+template<typename Derived>
+template<typename OtherDerived>
+const typename LazyProductReturnType<Derived,OtherDerived>::Type
+MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
+{
+  enum {
+    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
+                   || OtherDerived::RowsAtCompileTime==Dynamic
+                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+  };
+  // note to the lost user:
+  //    * for a dot product use: v1.dot(v2)
+  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+
+  return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+#endif // EIGEN_PRODUCT_H

Eigen/src/Core/ProductBase.h

@@ -0,0 +1,290 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PRODUCTBASE_H
+#define EIGEN_PRODUCTBASE_H
+
+/** \class ProductBase
+  * \ingroup Core_Module
+  *
+  */
+
+namespace internal {
+template<typename Derived, typename _Lhs, typename _Rhs>
+struct traits<ProductBase<Derived,_Lhs,_Rhs> >
+{
+  typedef MatrixXpr XprKind;
+  typedef typename remove_all<_Lhs>::type Lhs;
+  typedef typename remove_all<_Rhs>::type Rhs;
+  typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+  typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
+                                           typename traits<Rhs>::StorageKind>::ret StorageKind;
+  typedef typename promote_index_type<typename traits<Lhs>::Index,
+                                         typename traits<Rhs>::Index>::type Index;
+  enum {
+    RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
+    ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
+    MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
+    Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
+          | EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
+                  // Note that EvalBeforeNestingBit and NestByRefBit
+                  // are not used in practice because nested is overloaded for products
+    CoeffReadCost = 0 // FIXME why is it needed ?
+  };
+};
+}
+
+#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived) \
+  typedef ProductBase<Derived, Lhs, Rhs > Base; \
+  EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+  typedef typename Base::LhsNested LhsNested; \
+  typedef typename Base::_LhsNested _LhsNested; \
+  typedef typename Base::LhsBlasTraits LhsBlasTraits; \
+  typedef typename Base::ActualLhsType ActualLhsType; \
+  typedef typename Base::_ActualLhsType _ActualLhsType; \
+  typedef typename Base::RhsNested RhsNested; \
+  typedef typename Base::_RhsNested _RhsNested; \
+  typedef typename Base::RhsBlasTraits RhsBlasTraits; \
+  typedef typename Base::ActualRhsType ActualRhsType; \
+  typedef typename Base::_ActualRhsType _ActualRhsType; \
+  using Base::m_lhs; \
+  using Base::m_rhs;
+
+template<typename Derived, typename Lhs, typename Rhs>
+class ProductBase : public MatrixBase<Derived>
+{
+  public:
+    typedef MatrixBase<Derived> Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(ProductBase)
+    
+    typedef typename Lhs::Nested LhsNested;
+    typedef typename internal::remove_all<LhsNested>::type _LhsNested;
+    typedef internal::blas_traits<_LhsNested> LhsBlasTraits;
+    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+    typedef typename internal::remove_all<ActualLhsType>::type _ActualLhsType;
+    typedef typename internal::traits<Lhs>::Scalar LhsScalar;
+
+    typedef typename Rhs::Nested RhsNested;
+    typedef typename internal::remove_all<RhsNested>::type _RhsNested;
+    typedef internal::blas_traits<_RhsNested> RhsBlasTraits;
+    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+    typedef typename internal::remove_all<ActualRhsType>::type _ActualRhsType;
+    typedef typename internal::traits<Rhs>::Scalar RhsScalar;
+
+    // Diagonal of a product: no need to evaluate the arguments because they are going to be evaluated only once
+    typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType;
+
+  public:
+
+    typedef typename Base::PlainObject PlainObject;
+
+    ProductBase(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(); }
+
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst,Scalar(1)); }
+
+    template<typename Dest>
+    inline void addTo(Dest& dst) const { scaleAndAddTo(dst,1); }
+
+    template<typename Dest>
+    inline void subTo(Dest& dst) const { scaleAndAddTo(dst,-1); }
+
+    template<typename Dest>
+    inline void scaleAndAddTo(Dest& dst,Scalar alpha) const { derived().scaleAndAddTo(dst,alpha); }
+
+    const _LhsNested& lhs() const { return m_lhs; }
+    const _RhsNested& rhs() const { return m_rhs; }
+
+    // Implicit conversion to the nested type (trigger the evaluation of the product)
+    operator const PlainObject& () const
+    {
+      m_result.resize(m_lhs.rows(), m_rhs.cols());
+      derived().evalTo(m_result);
+      return m_result;
+    }
+
+    const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal() const
+    { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
+
+    template<int Index>
+    const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal() const
+    { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
+
+    const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal(Index index) const
+    { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs).diagonal(index); }
+
+    // restrict coeff accessors to 1x1 expressions. No need to care about mutators here since this isnt a Lvalue expression
+    typename Base::CoeffReturnType coeff(Index row, Index col) const
+    {
+#ifdef EIGEN2_SUPPORT
+      return lhs().row(row).cwiseProduct(rhs().col(col).transpose()).sum();
+#else
+      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+      eigen_assert(this->rows() == 1 && this->cols() == 1);
+      Matrix<Scalar,1,1> result = *this;
+      return result.coeff(row,col);
+#endif
+    }
+
+    typename Base::CoeffReturnType coeff(Index i) const
+    {
+      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+      eigen_assert(this->rows() == 1 && this->cols() == 1);
+      Matrix<Scalar,1,1> result = *this;
+      return result.coeff(i);
+    }
+
+    const Scalar& coeffRef(Index row, Index col) const
+    {
+      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+      eigen_assert(this->rows() == 1 && this->cols() == 1);
+      return derived().coeffRef(row,col);
+    }
+
+    const Scalar& coeffRef(Index i) const
+    {
+      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+      eigen_assert(this->rows() == 1 && this->cols() == 1);
+      return derived().coeffRef(i);
+    }
+
+  protected:
+
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+
+    mutable PlainObject m_result;
+};
+
+// here we need to overload the nested rule for products
+// such that the nested type is a const reference to a plain matrix
+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;
+};
+}
+
+template<typename NestedProduct>
+class ScaledProduct;
+
+// Note that these two operator* functions are not defined as member
+// functions of ProductBase, because, otherwise we would have to
+// define all overloads defined in MatrixBase. Furthermore, Using
+// "using Base::operator*" would not work with MSVC.
+//
+// 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)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+template<typename Derived,typename Lhs,typename Rhs>
+typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
+                      const ScaledProduct<Derived> >::type
+operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::RealScalar x)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+
+template<typename Derived,typename Lhs,typename Rhs>
+const ScaledProduct<Derived>
+operator*(typename Derived::Scalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+template<typename Derived,typename Lhs,typename Rhs>
+typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
+                      const ScaledProduct<Derived> >::type
+operator*(typename Derived::RealScalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
+{ return ScaledProduct<Derived>(prod.derived(), x); }
+
+namespace internal {
+template<typename NestedProduct>
+struct traits<ScaledProduct<NestedProduct> >
+ : traits<ProductBase<ScaledProduct<NestedProduct>,
+                         typename NestedProduct::_LhsNested,
+                         typename NestedProduct::_RhsNested> >
+{
+  typedef typename traits<NestedProduct>::StorageKind StorageKind;
+};
+}
+
+template<typename NestedProduct>
+class ScaledProduct
+  : public ProductBase<ScaledProduct<NestedProduct>,
+                       typename NestedProduct::_LhsNested,
+                       typename NestedProduct::_RhsNested>
+{
+  public:
+    typedef ProductBase<ScaledProduct<NestedProduct>,
+                       typename NestedProduct::_LhsNested,
+                       typename NestedProduct::_RhsNested> Base;
+    typedef typename Base::Scalar Scalar;
+    typedef typename Base::PlainObject PlainObject;
+//     EIGEN_PRODUCT_PUBLIC_INTERFACE(ScaledProduct)
+
+    ScaledProduct(const NestedProduct& prod, Scalar x)
+    : Base(prod.lhs(),prod.rhs()), m_prod(prod), m_alpha(x) {}
+
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst, Scalar(1)); }
+
+    template<typename Dest>
+    inline void addTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(1)); }
+
+    template<typename Dest>
+    inline void subTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(-1)); }
+
+    template<typename Dest>
+    inline void scaleAndAddTo(Dest& dst,Scalar alpha) const { m_prod.derived().scaleAndAddTo(dst,alpha * m_alpha); }
+
+    const Scalar& alpha() const { return m_alpha; }
+    
+  protected:
+    const NestedProduct& m_prod;
+    Scalar m_alpha;
+};
+
+/** \internal
+  * Overloaded to perform an efficient C = (A*B).lazy() */
+template<typename Derived>
+template<typename ProductDerived, typename Lhs, typename Rhs>
+Derived& MatrixBase<Derived>::lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+{
+  other.derived().evalTo(derived());
+  return derived();
+}
+
+
+#endif // EIGEN_PRODUCTBASE_H

Eigen/src/Core/Random.h

@@ -0,0 +1,163 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_RANDOM_H
+#define EIGEN_RANDOM_H
+
+namespace internal {
+
+template<typename Scalar> struct scalar_random_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_random_op)
+  template<typename Index>
+  inline const Scalar operator() (Index, Index = 0) const { return random<Scalar>(); }
+};
+
+template<typename Scalar>
+struct functor_traits<scalar_random_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };
+
+} // end namespace internal
+
+/** \returns a random matrix expression
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Random() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_random_int_int.cpp
+  * Output: \verbinclude MatrixBase_random_int_int.out
+  *
+  * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+  * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+  * behavior with expressions involving random matrices.
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(Index), MatrixBase::Random()
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random(Index rows, Index cols)
+{
+  return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a random vector expression
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Random() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_random_int.cpp
+  * Output: \verbinclude MatrixBase_random_int.out
+  *
+  * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+  * a temporary vector whenever it is nested in a larger expression. This prevents unexpected
+  * behavior with expressions involving random matrices.
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random()
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random(Index size)
+{
+  return NullaryExpr(size, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a fixed-size random matrix or vector expression
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_random.cpp
+  * Output: \verbinclude MatrixBase_random.out
+  *
+  * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+  * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+  * behavior with expressions involving random matrices.
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random(Index)
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
+DenseBase<Derived>::Random()
+{
+  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
+}
+
+/** Sets all coefficients in this expression to random values.
+  *
+  * Example: \include MatrixBase_setRandom.cpp
+  * Output: \verbinclude MatrixBase_setRandom.out
+  *
+  * \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
+  */
+template<typename Derived>
+inline Derived& DenseBase<Derived>::setRandom()
+{
+  return *this = Random(rows(), cols());
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to random values.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setRandom_int.cpp
+  * Output: \verbinclude Matrix_setRandom_int.out
+  *
+  * \sa MatrixBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, MatrixBase::Random()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index size)
+{
+  resize(size);
+  return setRandom();
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to random values.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setRandom_int_int.cpp
+  * Output: \verbinclude Matrix_setRandom_int_int.out
+  *
+  * \sa MatrixBase::setRandom(), setRandom(Index), class CwiseNullaryOp, MatrixBase::Random()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index rows, Index cols)
+{
+  resize(rows, cols);
+  return setRandom();
+}
+
+#endif // EIGEN_RANDOM_H

Eigen/src/Core/Redux.h

@@ -0,0 +1,404 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REDUX_H
+#define EIGEN_REDUX_H
+
+namespace internal {
+
+// TODO
+//  * implement other kind of vectorization
+//  * factorize code
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Func, typename Derived>
+struct redux_traits
+{
+public:
+  enum {
+    PacketSize = packet_traits<typename Derived::Scalar>::size,
+    InnerMaxSize = int(Derived::IsRowMajor)
+                 ? Derived::MaxColsAtCompileTime
+                 : Derived::MaxRowsAtCompileTime
+  };
+
+  enum {
+    MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
+                  && (functor_traits<Func>::PacketAccess),
+    MayLinearVectorize = MightVectorize && (int(Derived::Flags)&LinearAccessBit),
+    MaySliceVectorize  = MightVectorize && int(InnerMaxSize)>=3*PacketSize
+  };
+
+public:
+  enum {
+    Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
+              : int(MaySliceVectorize)  ? int(SliceVectorizedTraversal)
+                                        : int(DefaultTraversal)
+  };
+
+public:
+  enum {
+    Cost = (  Derived::SizeAtCompileTime == Dynamic
+           || Derived::CoeffReadCost == Dynamic
+           || (Derived::SizeAtCompileTime!=1 && functor_traits<Func>::Cost == Dynamic)
+           ) ? Dynamic
+           : Derived::SizeAtCompileTime * Derived::CoeffReadCost
+               + (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
+    UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
+  };
+
+public:
+  enum {
+    Unrolling = Cost != Dynamic && Cost <= UnrollingLimit
+              ? CompleteUnrolling
+              : NoUnrolling
+  };
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Func, typename Derived, int Start, int Length>
+struct redux_novec_unroller
+{
+  enum {
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func& func)
+  {
+    return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+                redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
+  }
+};
+
+template<typename Func, typename Derived, int Start>
+struct redux_novec_unroller<Func, Derived, Start, 1>
+{
+  enum {
+    outer = Start / Derived::InnerSizeAtCompileTime,
+    inner = Start % Derived::InnerSizeAtCompileTime
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func&)
+  {
+    return mat.coeffByOuterInner(outer, inner);
+  }
+};
+
+// This is actually dead code and will never be called. It is required
+// to prevent false warnings regarding failed inlining though
+// for 0 length run() will never be called at all.
+template<typename Func, typename Derived, int Start>
+struct redux_novec_unroller<Func, Derived, Start, 0>
+{
+  typedef typename Derived::Scalar Scalar;
+  EIGEN_STRONG_INLINE static Scalar run(const Derived&, const Func&) { return Scalar(); }
+};
+
+/*** vectorization ***/
+
+template<typename Func, typename Derived, int Start, int Length>
+struct redux_vec_unroller
+{
+  enum {
+    PacketSize = packet_traits<typename Derived::Scalar>::size,
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename packet_traits<Scalar>::type PacketScalar;
+
+  EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func& func)
+  {
+    return func.packetOp(
+            redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+            redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
+  }
+};
+
+template<typename Func, typename Derived, int Start>
+struct redux_vec_unroller<Func, Derived, Start, 1>
+{
+  enum {
+    index = Start * packet_traits<typename Derived::Scalar>::size,
+    outer = index / int(Derived::InnerSizeAtCompileTime),
+    inner = index % int(Derived::InnerSizeAtCompileTime),
+    alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename packet_traits<Scalar>::type PacketScalar;
+
+  EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func&)
+  {
+    return mat.template packetByOuterInner<alignment>(outer, inner);
+  }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Func, typename Derived,
+         int Traversal = redux_traits<Func, Derived>::Traversal,
+         int Unrolling = redux_traits<Func, Derived>::Unrolling
+>
+struct redux_impl;
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename Derived::Index Index;
+  static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
+  {
+    eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+    Scalar res;
+    res = mat.coeffByOuterInner(0, 0);
+    for(Index i = 1; i < mat.innerSize(); ++i)
+      res = func(res, mat.coeffByOuterInner(0, i));
+    for(Index i = 1; i < mat.outerSize(); ++i)
+      for(Index j = 0; j < mat.innerSize(); ++j)
+        res = func(res, mat.coeffByOuterInner(i, j));
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
+  : public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
+{};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename packet_traits<Scalar>::type PacketScalar;
+  typedef typename Derived::Index Index;
+
+  static Scalar run(const Derived& mat, const Func& func)
+  {
+    const Index size = mat.size();
+    eigen_assert(size && "you are using an empty matrix");
+    const Index packetSize = packet_traits<Scalar>::size;
+    const Index alignedStart = first_aligned(mat);
+    enum {
+      alignment = bool(Derived::Flags & DirectAccessBit) || bool(Derived::Flags & AlignedBit)
+                ? Aligned : Unaligned
+    };
+    const Index alignedSize = ((size-alignedStart)/packetSize)*packetSize;
+    const Index alignedEnd = alignedStart + alignedSize;
+    Scalar res;
+    if(alignedSize)
+    {
+      PacketScalar packet_res = mat.template packet<alignment>(alignedStart);
+      for(Index index = alignedStart + packetSize; index < alignedEnd; index += packetSize)
+        packet_res = func.packetOp(packet_res, mat.template packet<alignment>(index));
+      res = func.predux(packet_res);
+
+      for(Index index = 0; index < alignedStart; ++index)
+        res = func(res,mat.coeff(index));
+
+      for(Index index = alignedEnd; index < size; ++index)
+        res = func(res,mat.coeff(index));
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = mat.coeff(0);
+      for(Index index = 1; index < size; ++index)
+        res = func(res,mat.coeff(index));
+    }
+
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, SliceVectorizedTraversal, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename packet_traits<Scalar>::type PacketScalar;
+  typedef typename Derived::Index Index;
+
+  static Scalar run(const Derived& mat, const Func& func)
+  {
+    eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+    const Index innerSize = mat.innerSize();
+    const Index outerSize = mat.outerSize();
+    enum {
+      packetSize = packet_traits<Scalar>::size
+    };
+    const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
+    Scalar res;
+    if(packetedInnerSize)
+    {
+      PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
+      for(Index j=0; j<outerSize; ++j)
+        for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
+          packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned>(j,i));
+
+      res = func.predux(packet_res);
+      for(Index j=0; j<outerSize; ++j)
+        for(Index i=packetedInnerSize; i<innerSize; ++i)
+          res = func(res, mat.coeffByOuterInner(j,i));
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
+    }
+
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename packet_traits<Scalar>::type PacketScalar;
+  enum {
+    PacketSize = packet_traits<Scalar>::size,
+    Size = Derived::SizeAtCompileTime,
+    VectorizedSize = (Size / PacketSize) * PacketSize
+  };
+  EIGEN_STRONG_INLINE static Scalar run(const Derived& mat, const Func& func)
+  {
+    eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
+    Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
+    if (VectorizedSize != Size)
+      res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
+    return res;
+  }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Part 4 : public API
+***************************************************************************/
+
+
+/** \returns the result of a full redux operation on the whole matrix or vector using \a func
+  *
+  * The template parameter \a BinaryOp is the type of the functor \a func which must be
+  * an associative operator. Both current STL and TR1 functor styles are handled.
+  *
+  * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
+  */
+template<typename Derived>
+template<typename Func>
+EIGEN_STRONG_INLINE typename internal::result_of<Func(typename internal::traits<Derived>::Scalar)>::type
+DenseBase<Derived>::redux(const Func& func) const
+{
+  typedef typename internal::remove_all<typename Derived::Nested>::type ThisNested;
+  return internal::redux_impl<Func, ThisNested>
+            ::run(derived(), func);
+}
+
+/** \returns the minimum of all coefficients of *this
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff() const
+{
+  return this->redux(Eigen::internal::scalar_min_op<Scalar>());
+}
+
+/** \returns the maximum of all coefficients of *this
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff() const
+{
+  return this->redux(Eigen::internal::scalar_max_op<Scalar>());
+}
+
+/** \returns the sum of all coefficients of *this
+  *
+  * \sa trace(), prod(), mean()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::sum() const
+{
+  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+    return Scalar(0);
+  return this->redux(Eigen::internal::scalar_sum_op<Scalar>());
+}
+
+/** \returns the mean of all coefficients of *this
+*
+* \sa trace(), prod(), sum()
+*/
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::mean() const
+{
+  return Scalar(this->redux(Eigen::internal::scalar_sum_op<Scalar>())) / Scalar(this->size());
+}
+
+/** \returns the product of all coefficients of *this
+  *
+  * Example: \include MatrixBase_prod.cpp
+  * Output: \verbinclude MatrixBase_prod.out
+  *
+  * \sa sum(), mean(), trace()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::prod() const
+{
+  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+    return Scalar(1);
+  return this->redux(Eigen::internal::scalar_product_op<Scalar>());
+}
+
+/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
+  *
+  * \c *this can be any matrix, not necessarily square.
+  *
+  * \sa diagonal(), sum()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+MatrixBase<Derived>::trace() const
+{
+  return derived().diagonal().sum();
+}
+
+#endif // EIGEN_REDUX_H

Eigen/src/Core/Replicate.h

@@ -0,0 +1,184 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REPLICATE_H
+#define EIGEN_REPLICATE_H
+
+/**
+  * \class Replicate
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the multiple replication of a matrix or vector
+  *
+  * \param MatrixType the type of the object we are replicating
+  *
+  * This class represents an expression of the multiple replication of a matrix or vector.
+  * It is the return type of DenseBase::replicate() and most of the time
+  * this is the only way it is used.
+  *
+  * \sa DenseBase::replicate()
+  */
+
+namespace internal {
+template<typename MatrixType,int RowFactor,int ColFactor>
+struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
+ : traits<MatrixType>
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename traits<MatrixType>::StorageKind StorageKind;
+  typedef typename traits<MatrixType>::XprKind XprKind;
+  enum {
+    Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor
+  };
+  typedef typename nested<MatrixType,Factor>::type MatrixTypeNested;
+  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic
+                      ? Dynamic
+                      : RowFactor * MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic
+                      ? Dynamic
+                      : ColFactor * MatrixType::ColsAtCompileTime,
+   //FIXME we don't propagate the max sizes !!!
+    MaxRowsAtCompileTime = RowsAtCompileTime,
+    MaxColsAtCompileTime = ColsAtCompileTime,
+    IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1
+               : MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0
+               : (MatrixType::Flags & RowMajorBit) ? 1 : 0,
+    Flags = (_MatrixTypeNested::Flags & HereditaryBits & ~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0),
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+}
+
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
+  : public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type
+{
+    typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;
+    typedef typename internal::traits<Replicate>::_MatrixTypeNested _MatrixTypeNested;
+  public:
+
+    typedef typename internal::dense_xpr_base<Replicate>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)
+
+    template<typename OriginalMatrixType>
+    inline explicit Replicate(const OriginalMatrixType& matrix)
+      : m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)
+    {
+      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
+                          THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+      eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);
+    }
+
+    template<typename OriginalMatrixType>
+    inline Replicate(const OriginalMatrixType& matrix, int rowFactor, int colFactor)
+      : m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)
+    {
+      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
+                          THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+    }
+
+    inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
+    inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
+
+    inline Scalar coeff(Index row, Index col) const
+    {
+      // try to avoid using modulo; this is a pure optimization strategy
+      const Index actual_row  = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
+                            : RowFactor==1 ? row
+                            : row%m_matrix.rows();
+      const Index actual_col  = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
+                            : ColFactor==1 ? col
+                            : col%m_matrix.cols();
+
+      return m_matrix.coeff(actual_row, actual_col);
+    }
+    template<int LoadMode>
+    inline PacketScalar packet(Index row, Index col) const
+    {
+      const Index actual_row  = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
+                            : RowFactor==1 ? row
+                            : row%m_matrix.rows();
+      const Index actual_col  = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
+                            : ColFactor==1 ? col
+                            : col%m_matrix.cols();
+
+      return m_matrix.template packet<LoadMode>(actual_row, actual_col);
+    }
+
+
+  protected:
+    const MatrixTypeNested m_matrix;
+    const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;
+    const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;
+};
+
+/**
+  * \return an expression of the replication of \c *this
+  *
+  * Example: \include MatrixBase_replicate.cpp
+  * Output: \verbinclude MatrixBase_replicate.out
+  *
+  * \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
+  */
+template<typename Derived>
+template<int RowFactor, int ColFactor>
+inline const Replicate<Derived,RowFactor,ColFactor>
+DenseBase<Derived>::replicate() const
+{
+  return Replicate<Derived,RowFactor,ColFactor>(derived());
+}
+
+/**
+  * \return an expression of the replication of \c *this
+  *
+  * Example: \include MatrixBase_replicate_int_int.cpp
+  * Output: \verbinclude MatrixBase_replicate_int_int.out
+  *
+  * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
+  */
+template<typename Derived>
+inline const Replicate<Derived,Dynamic,Dynamic>
+DenseBase<Derived>::replicate(Index rowFactor,Index colFactor) const
+{
+  return Replicate<Derived,Dynamic,Dynamic>(derived(),rowFactor,colFactor);
+}
+
+/**
+  * \return an expression of the replication of each column (or row) of \c *this
+  *
+  * Example: \include DirectionWise_replicate_int.cpp
+  * Output: \verbinclude DirectionWise_replicate_int.out
+  *
+  * \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate
+  */
+template<typename ExpressionType, int Direction>
+const typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+VectorwiseOp<ExpressionType,Direction>::replicate(Index factor) const
+{
+  return typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+          (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+}
+
+#endif // EIGEN_REPLICATE_H

Eigen/src/Core/ReturnByValue.h

@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_RETURNBYVALUE_H
+#define EIGEN_RETURNBYVALUE_H
+
+/** \class ReturnByValue
+  * \ingroup Core_Module
+  *
+  */
+
+namespace internal {
+
+template<typename Derived>
+struct traits<ReturnByValue<Derived> >
+  : public traits<typename traits<Derived>::ReturnType>
+{
+  enum {
+    // We're disabling the DirectAccess because e.g. the constructor of
+    // the Block-with-DirectAccess expression requires to have a coeffRef method.
+    // Also, we don't want to have to implement the stride stuff.
+    Flags = (traits<typename traits<Derived>::ReturnType>::Flags
+             | EvalBeforeNestingBit) & ~DirectAccessBit
+  };
+};
+
+/* The ReturnByValue object doesn't even have a coeff() method.
+ * So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix.
+ * So internal::nested always gives the plain return matrix type.
+ *
+ * FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ??
+ */
+template<typename Derived,int n,typename PlainObject>
+struct nested<ReturnByValue<Derived>, n, PlainObject>
+{
+  typedef typename traits<Derived>::ReturnType type;
+};
+
+} // end namespace internal
+
+template<typename Derived> class ReturnByValue
+  : public internal::dense_xpr_base< ReturnByValue<Derived> >::type
+{
+  public:
+    typedef typename internal::traits<Derived>::ReturnType ReturnType;
+
+    typedef typename internal::dense_xpr_base<ReturnByValue>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue)
+
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const
+    { static_cast<const Derived*>(this)->evalTo(dst); }
+    inline Index rows() const { return static_cast<const Derived*>(this)->rows(); }
+    inline Index cols() const { return static_cast<const Derived*>(this)->cols(); }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT
+    class Unusable{
+      Unusable(const Unusable&) {}
+      Unusable& operator=(const Unusable&) {return *this;}
+    };
+    const Unusable& coeff(Index) const { return *reinterpret_cast<const Unusable*>(this); }
+    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); }
+#endif
+};
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+  other.evalTo(derived());
+  return derived();
+}
+
+#endif // EIGEN_RETURNBYVALUE_H

Eigen/src/Core/Reverse.h

@@ -0,0 +1,230 @@
+// 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) 2009 Ricard Marxer <email@ricardmarxer.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REVERSE_H
+#define EIGEN_REVERSE_H
+
+/** \class Reverse
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the reverse of a vector or matrix
+  *
+  * \param MatrixType the type of the object of which we are taking the reverse
+  *
+  * This class represents an expression of the reverse of a vector.
+  * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::reverse(), VectorwiseOp::reverse()
+  */
+
+namespace internal {
+
+template<typename MatrixType, int Direction>
+struct traits<Reverse<MatrixType, Direction> >
+ : traits<MatrixType>
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename traits<MatrixType>::StorageKind StorageKind;
+  typedef typename traits<MatrixType>::XprKind XprKind;
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+
+    // let's enable LinearAccess only with vectorization because of the product overhead
+    LinearAccess = ( (Direction==BothDirections) && (int(_MatrixTypeNested::Flags)&PacketAccessBit) )
+                 ? LinearAccessBit : 0,
+
+    Flags = int(_MatrixTypeNested::Flags) & (HereditaryBits | LvalueBit | PacketAccessBit | LinearAccess),
+
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename PacketScalar, bool ReversePacket> struct reverse_packet_cond
+{
+  static inline PacketScalar run(const PacketScalar& x) { return preverse(x); }
+};
+
+template<typename PacketScalar> struct reverse_packet_cond<PacketScalar,false>
+{
+  static inline PacketScalar run(const PacketScalar& x) { return x; }
+};
+
+} // end namespace internal 
+
+template<typename MatrixType, int Direction> class Reverse
+  : public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<Reverse>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Reverse)
+    using Base::IsRowMajor;
+
+    // next line is necessary because otherwise const version of operator()
+    // is hidden by non-const version defined in this file
+    using Base::operator(); 
+
+  protected:
+    enum {
+      PacketSize = internal::packet_traits<Scalar>::size,
+      IsColMajor = !IsRowMajor,
+      ReverseRow = (Direction == Vertical)   || (Direction == BothDirections),
+      ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
+      OffsetRow  = ReverseRow && IsColMajor ? PacketSize : 1,
+      OffsetCol  = ReverseCol && IsRowMajor ? PacketSize : 1,
+      ReversePacket = (Direction == BothDirections)
+                    || ((Direction == Vertical)   && IsColMajor)
+                    || ((Direction == Horizontal) && IsRowMajor)
+    };
+    typedef internal::reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;
+  public:
+
+    inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+
+    inline Index innerStride() const
+    {
+      return -m_matrix.innerStride();
+    }
+
+    inline Scalar& operator()(Index row, Index col)
+    {
+      eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+      return coeffRef(row, col);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(ReverseRow ? m_matrix.rows() - row - 1 : row,
+                                                    ReverseCol ? m_matrix.cols() - col - 1 : col);
+    }
+
+    inline CoeffReturnType coeff(Index row, Index col) const
+    {
+      return m_matrix.coeff(ReverseRow ? m_matrix.rows() - row - 1 : row,
+                            ReverseCol ? m_matrix.cols() - col - 1 : col);
+    }
+
+    inline CoeffReturnType coeff(Index index) const
+    {
+      return m_matrix.coeff(m_matrix.size() - index - 1);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(m_matrix.size() - index - 1);
+    }
+
+    inline Scalar& operator()(Index index)
+    {
+      eigen_assert(index >= 0 && index < m_matrix.size());
+      return coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return reverse_packet::run(m_matrix.template packet<LoadMode>(
+                                    ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+                                    ReverseCol ? m_matrix.cols() - col - OffsetCol : col));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(
+                                      ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+                                      ReverseCol ? m_matrix.cols() - col - OffsetCol : col,
+                                      reverse_packet::run(x));
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return internal::preverse(m_matrix.template packet<LoadMode>( m_matrix.size() - index - PacketSize ));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(m_matrix.size() - index - PacketSize, internal::preverse(x));
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \returns an expression of the reverse of *this.
+  *
+  * Example: \include MatrixBase_reverse.cpp
+  * Output: \verbinclude MatrixBase_reverse.out
+  *
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::ReverseReturnType
+DenseBase<Derived>::reverse()
+{
+  return derived();
+}
+
+/** This is the const version of reverse(). */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstReverseReturnType
+DenseBase<Derived>::reverse() const
+{
+  return derived();
+}
+
+/** This is the "in place" version of reverse: it reverses \c *this.
+  *
+  * In most cases it is probably better to simply use the reversed expression
+  * of a matrix. However, when reversing the matrix data itself is really needed,
+  * then this "in-place" version is probably the right choice because it provides
+  * the following additional features:
+  *  - less error prone: doing the same operation with .reverse() requires special care:
+  *    \code m = m.reverse().eval(); \endcode
+  *  - this API allows to avoid creating a temporary (the current implementation creates a temporary, but that could be avoided using swap)
+  *  - it allows future optimizations (cache friendliness, etc.)
+  *
+  * \sa reverse() */
+template<typename Derived>
+inline void DenseBase<Derived>::reverseInPlace()
+{
+  derived() = derived().reverse().eval();
+}
+
+
+#endif // EIGEN_REVERSE_H

Eigen/src/Core/Select.h

@@ -0,0 +1,158 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SELECT_H
+#define EIGEN_SELECT_H
+
+/** \class Select
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
+  *
+  * \param ConditionMatrixType the type of the \em condition expression which must be a boolean matrix
+  * \param ThenMatrixType the type of the \em then expression
+  * \param ElseMatrixType the type of the \em else expression
+  *
+  * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+  * It is the return type of DenseBase::select() and most of the time this is the only way it is used.
+  *
+  * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
+  */
+
+namespace internal {
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+ : traits<ThenMatrixType>
+{
+  typedef typename traits<ThenMatrixType>::Scalar Scalar;
+  typedef Dense StorageKind;
+  typedef typename traits<ThenMatrixType>::XprKind XprKind;
+  typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
+  typedef typename ThenMatrixType::Nested ThenMatrixNested;
+  typedef typename ElseMatrixType::Nested ElseMatrixNested;
+  enum {
+    RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
+    Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & HereditaryBits,
+    CoeffReadCost = traits<typename remove_all<ConditionMatrixNested>::type>::CoeffReadCost
+                  + EIGEN_SIZE_MAX(traits<typename remove_all<ThenMatrixNested>::type>::CoeffReadCost,
+                                   traits<typename remove_all<ElseMatrixNested>::type>::CoeffReadCost)
+  };
+};
+}
+
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+class Select : internal::no_assignment_operator,
+  public internal::dense_xpr_base< Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<Select>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Select)
+
+    Select(const ConditionMatrixType& conditionMatrix,
+           const ThenMatrixType& thenMatrix,
+           const ElseMatrixType& elseMatrix)
+      : m_condition(conditionMatrix), m_then(thenMatrix), m_else(elseMatrix)
+    {
+      eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
+      eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
+    }
+
+    Index rows() const { return m_condition.rows(); }
+    Index cols() const { return m_condition.cols(); }
+
+    const Scalar coeff(Index i, Index j) const
+    {
+      if (m_condition.coeff(i,j))
+        return m_then.coeff(i,j);
+      else
+        return m_else.coeff(i,j);
+    }
+
+    const Scalar coeff(Index i) const
+    {
+      if (m_condition.coeff(i))
+        return m_then.coeff(i);
+      else
+        return m_else.coeff(i);
+    }
+
+  protected:
+    const typename ConditionMatrixType::Nested m_condition;
+    const typename ThenMatrixType::Nested m_then;
+    const typename ElseMatrixType::Nested m_else;
+};
+
+
+/** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
+  * if \c *this(i,j), and \a elseMatrix(i,j) otherwise.
+  *
+  * Example: \include MatrixBase_select.cpp
+  * Output: \verbinclude MatrixBase_select.out
+  *
+  * \sa class Select
+  */
+template<typename Derived>
+template<typename ThenDerived,typename ElseDerived>
+inline const Select<Derived,ThenDerived,ElseDerived>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+                            const DenseBase<ElseDerived>& elseMatrix) const
+{
+  return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+  * the \em else expression being a scalar value.
+  *
+  * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+  */
+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
+{
+  return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
+    derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+  * the \em then expression being a scalar value.
+  *
+  * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+  */
+template<typename Derived>
+template<typename ElseDerived>
+inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
+DenseBase<Derived>::select(typename ElseDerived::Scalar thenScalar,
+                            const DenseBase<ElseDerived>& elseMatrix) const
+{
+  return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
+    derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
+}
+
+#endif // EIGEN_SELECT_H

Eigen/src/Core/SelfAdjointView.h

@@ -0,0 +1,325 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SELFADJOINTMATRIX_H
+#define EIGEN_SELFADJOINTMATRIX_H
+
+/** \class SelfAdjointView
+  * \ingroup Core_Module
+  *
+  *
+  * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
+  *
+  * \param MatrixType the type of the dense matrix storing the coefficients
+  * \param TriangularPart can be either \c #Lower or \c #Upper
+  *
+  * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
+  * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
+  * and most of the time this is the only way that it is used.
+  *
+  * \sa class TriangularBase, MatrixBase::selfadjointView()
+  */
+
+namespace internal {
+template<typename MatrixType, unsigned int UpLo>
+struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
+{
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+  typedef MatrixType ExpressionType;
+  typedef typename MatrixType::PlainObject DenseMatrixType;
+  enum {
+    Mode = UpLo | SelfAdjoint,
+    Flags =  MatrixTypeNestedCleaned::Flags & (HereditaryBits)
+           & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)), // FIXME these flags should be preserved
+    CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
+  };
+};
+}
+
+template <typename Lhs, int LhsMode, bool LhsIsVector,
+          typename Rhs, int RhsMode, bool RhsIsVector>
+struct SelfadjointProductMatrix;
+
+// FIXME could also be called SelfAdjointWrapper to be consistent with DiagonalWrapper ??
+template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
+  : public TriangularBase<SelfAdjointView<MatrixType, UpLo> >
+{
+  public:
+
+    typedef TriangularBase<SelfAdjointView> Base;
+    typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
+    typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
+
+    /** \brief The type of coefficients in this matrix */
+    typedef typename internal::traits<SelfAdjointView>::Scalar Scalar; 
+
+    typedef typename MatrixType::Index Index;
+
+    enum {
+      Mode = internal::traits<SelfAdjointView>::Mode
+    };
+    typedef typename MatrixType::PlainObject PlainObject;
+
+    inline SelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
+    {}
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+    inline Index outerStride() const { return m_matrix.outerStride(); }
+    inline Index innerStride() const { return m_matrix.innerStride(); }
+
+    /** \sa MatrixBase::coeff()
+      * \warning the coordinates must fit into the referenced triangular part
+      */
+    inline Scalar coeff(Index row, Index col) const
+    {
+      Base::check_coordinates_internal(row, col);
+      return m_matrix.coeff(row, col);
+    }
+
+    /** \sa MatrixBase::coeffRef()
+      * \warning the coordinates must fit into the referenced triangular part
+      */
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      Base::check_coordinates_internal(row, col);
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    /** \internal */
+    const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
+
+    const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+    MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
+
+    /** Efficient self-adjoint matrix times vector/matrix product */
+    template<typename OtherDerived>
+    SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
+    operator*(const MatrixBase<OtherDerived>& rhs) const
+    {
+      return SelfadjointProductMatrix
+              <MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
+              (m_matrix, rhs.derived());
+    }
+
+    /** Efficient vector/matrix times self-adjoint matrix product */
+    template<typename OtherDerived> friend
+    SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
+    operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
+    {
+      return SelfadjointProductMatrix
+              <OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
+              (lhs.derived(),rhs.m_matrix);
+    }
+
+    /** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
+      * \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
+      * \returns a reference to \c *this
+      *
+      * The vectors \a u and \c v \b must be column vectors, however they can be
+      * a adjoint expression without any overhead. Only the meaningful triangular
+      * part of the matrix is updated, the rest is left unchanged.
+      *
+      * \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));
+
+    /** 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.
+      *
+      * \returns a reference to \c *this
+      *
+      * Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
+      * call this function with u.adjoint().
+      *
+      * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
+      */
+    template<typename DerivedU>
+    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, Scalar alpha = Scalar(1));
+
+/////////// Cholesky module ///////////
+
+    const LLT<PlainObject, UpLo> llt() const;
+    const LDLT<PlainObject, UpLo> ldlt() const;
+
+/////////// Eigenvalue module ///////////
+
+    /** Real part of #Scalar */
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    /** Return type of eigenvalues() */
+    typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+    EigenvaluesReturnType eigenvalues() const;
+    RealScalar operatorNorm() const;
+    
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived>
+    SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      enum {
+        OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
+      };
+      m_matrix.const_cast_derived().template triangularView<UpLo>() = other;
+      m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.adjoint();
+      return *this;
+    }
+    template<typename OtherMatrixType, unsigned int OtherMode>
+    SelfAdjointView& operator=(const TriangularView<OtherMatrixType, OtherMode>& other)
+    {
+      enum {
+        OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
+      };
+      m_matrix.const_cast_derived().template triangularView<UpLo>() = other.toDenseMatrix();
+      m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.toDenseMatrix().adjoint();
+      return *this;
+    }
+    #endif
+
+  protected:
+    const MatrixTypeNested m_matrix;
+};
+
+
+// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
+// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
+// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
+// {
+//   return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
+// }
+
+// selfadjoint to dense matrix
+
+namespace internal {
+
+template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount, ClearOpposite>
+{
+  enum {
+    col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+  };
+
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    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));
+    else if(row < col)
+      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, 0, ClearOpposite>
+{
+  inline static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount, ClearOpposite>
+{
+  enum {
+    col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+  };
+
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    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));
+    else if(row > col)
+      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, 0, ClearOpposite>
+{
+  inline static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      for(Index i = 0; i < j; ++i)
+      {
+        dst.copyCoeff(i, j, src);
+        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+      }
+      dst.copyCoeff(j, j, src);
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dynamic, ClearOpposite>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+  typedef typename Derived1::Index Index;
+    for(Index i = 0; i < dst.rows(); ++i)
+    {
+      for(Index j = 0; j < i; ++j)
+      {
+        dst.copyCoeff(i, j, src);
+        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+      }
+      dst.copyCoeff(i, i, src);
+    }
+  }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView() const
+{
+  return derived();
+}
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView()
+{
+  return derived();
+}
+
+#endif // EIGEN_SELFADJOINTMATRIX_H

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SELFCWISEBINARYOP_H
+#define EIGEN_SELFCWISEBINARYOP_H
+
+/** \class SelfCwiseBinaryOp
+  * \ingroup Core_Module
+  *
+  * \internal
+  *
+  * \brief Internal helper class for optimizing operators like +=, -=
+  *
+  * This is a pseudo expression class re-implementing the copyCoeff/copyPacket
+  * method to directly performs a +=/-= operations in an optimal way. In particular,
+  * this allows to make sure that the input/output data are loaded only once using
+  * aligned packet loads.
+  *
+  * \sa class SwapWrapper for a similar trick.
+  */
+
+namespace internal {
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct traits<SelfCwiseBinaryOp<BinaryOp,Lhs,Rhs> >
+  : traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >
+{
+  enum {
+    // Note that it is still a good idea to preserve the DirectAccessBit
+    // so that assign can correctly align the data.
+    Flags = traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >::Flags | (Lhs::Flags&DirectAccessBit) | (Lhs::Flags&LvalueBit),
+    OuterStrideAtCompileTime = Lhs::OuterStrideAtCompileTime,
+    InnerStrideAtCompileTime = Lhs::InnerStrideAtCompileTime
+  };
+};
+}
+
+template<typename BinaryOp, typename Lhs, typename Rhs> class SelfCwiseBinaryOp
+  : public internal::dense_xpr_base< SelfCwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<SelfCwiseBinaryOp>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(SelfCwiseBinaryOp)
+
+    typedef typename internal::packet_traits<Scalar>::type Packet;
+
+    inline SelfCwiseBinaryOp(Lhs& xpr, const BinaryOp& func = BinaryOp()) : m_matrix(xpr), m_functor(func) {}
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+    inline Index outerStride() const { return m_matrix.outerStride(); }
+    inline Index innerStride() const { return m_matrix.innerStride(); }
+    inline const Scalar* data() const { return m_matrix.data(); }
+
+    // note that this function is needed by assign to correctly align loads/stores
+    // TODO make Assign use .data()
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(Lhs)
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_matrix.coeffRef(row, col);
+    }
+
+    // note that this function is needed by assign to correctly align loads/stores
+    // TODO make Assign use .data()
+    inline Scalar& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(Lhs)
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(row >= 0 && row < rows()
+                         && col >= 0 && col < cols());
+      Scalar& tmp = m_matrix.coeffRef(row,col);
+      tmp = m_functor(tmp, _other.coeff(row,col));
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(index >= 0 && index < m_matrix.size());
+      Scalar& tmp = m_matrix.coeffRef(index);
+      tmp = m_functor(tmp, _other.coeff(index));
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      m_matrix.template writePacket<StoreMode>(row, col,
+        m_functor.packetOp(m_matrix.template packet<StoreMode>(row, col),_other.template packet<LoadMode>(row, col)) );
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(index >= 0 && index < m_matrix.size());
+      m_matrix.template writePacket<StoreMode>(index,
+        m_functor.packetOp(m_matrix.template packet<StoreMode>(index),_other.template packet<LoadMode>(index)) );
+    }
+
+    // reimplement lazyAssign to handle complex *= real
+    // see CwiseBinaryOp ctor for details
+    template<typename RhsDerived>
+    EIGEN_STRONG_INLINE SelfCwiseBinaryOp& lazyAssign(const DenseBase<RhsDerived>& rhs)
+    {
+      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs,RhsDerived)
+      EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename RhsDerived::Scalar);
+      
+    #ifdef EIGEN_DEBUG_ASSIGN
+      internal::assign_traits<SelfCwiseBinaryOp, RhsDerived>::debug();
+    #endif
+      eigen_assert(rows() == rhs.rows() && cols() == rhs.cols());
+      internal::assign_impl<SelfCwiseBinaryOp, RhsDerived>::run(*this,rhs.derived());
+    #ifndef EIGEN_NO_DEBUG
+      this->checkTransposeAliasing(rhs.derived());
+    #endif
+      return *this;
+    }
+    
+    // overloaded to honor evaluation of special matrices
+    // maybe another solution would be to not use SelfCwiseBinaryOp
+    // at first...
+    SelfCwiseBinaryOp& operator=(const Rhs& _rhs)
+    {
+      typename internal::nested<Rhs>::type rhs(_rhs);
+      return Base::operator=(rhs);
+    }
+
+  protected:
+    Lhs& m_matrix;
+    const BinaryOp& m_functor;
+
+  private:
+    SelfCwiseBinaryOp& operator=(const SelfCwiseBinaryOp&);
+};
+
+template<typename Derived>
+inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
+{
+  typedef typename Derived::PlainObject PlainObject;
+  SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+  tmp = PlainObject::Constant(rows(),cols(),other);
+  return derived();
+}
+
+template<typename Derived>
+inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
+{
+  typedef typename internal::conditional<NumTraits<Scalar>::IsInteger,
+                                        internal::scalar_quotient_op<Scalar>,
+                                        internal::scalar_product_op<Scalar> >::type BinOp;
+  typedef typename Derived::PlainObject PlainObject;
+  SelfCwiseBinaryOp<BinOp, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+  tmp = PlainObject::Constant(rows(),cols(), NumTraits<Scalar>::IsInteger ? other : Scalar(1)/other);
+  return derived();
+}
+
+#endif // EIGEN_SELFCWISEBINARYOP_H

Eigen/src/Core/SolveTriangular.h

@@ -0,0 +1,263 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SOLVETRIANGULAR_H
+#define EIGEN_SOLVETRIANGULAR_H
+
+namespace internal {
+
+// Forward declarations:
+// The following two routines are implemented in the products/TriangularSolver*.h files
+template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector;
+
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
+struct triangular_solve_matrix;
+
+// small helper struct extracting some traits on the underlying solver operation
+template<typename Lhs, typename Rhs, int Side>
+class trsolve_traits
+{
+  private:
+    enum {
+      RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
+    };
+  public:
+    enum {
+      Unrolling   = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
+                  ? CompleteUnrolling : NoUnrolling,
+      RhsVectors  = RhsIsVectorAtCompileTime ? 1 : Dynamic
+    };
+};
+
+template<typename Lhs, typename Rhs,
+  int Side, // can be OnTheLeft/OnTheRight
+  int Mode, // can be Upper/Lower | UnitDiag
+  int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
+  int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
+  >
+struct triangular_solver_selector;
+
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
+{
+  typedef typename Lhs::Scalar LhsScalar;
+  typedef typename Rhs::Scalar RhsScalar;
+  typedef blas_traits<Lhs> LhsProductTraits;
+  typedef typename LhsProductTraits::ExtractType ActualLhsType;
+  typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
+  static void run(const Lhs& lhs, Rhs& rhs)
+  {
+    ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
+
+    // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
+
+    bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
+
+    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
+                                                  (useRhsDirectly ? rhs.data() : 0));
+                                                  
+    if(!useRhsDirectly)
+      MappedRhs(actualRhs,rhs.size()) = rhs;
+
+    triangular_solve_vector<LhsScalar, RhsScalar, typename Lhs::Index, Side, Mode, LhsProductTraits::NeedToConjugate,
+                            (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
+      ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
+
+    if(!useRhsDirectly)
+      rhs = MappedRhs(actualRhs, rhs.size());
+  }
+};
+
+// the rhs is a matrix
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
+{
+  typedef typename Rhs::Scalar Scalar;
+  typedef typename Rhs::Index Index;
+  typedef blas_traits<Lhs> LhsProductTraits;
+  typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
+  static void run(const Lhs& lhs, Rhs& rhs)
+  {
+    const ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
+    triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
+                               (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
+      ::run(lhs.rows(), Side==OnTheLeft? rhs.cols() : rhs.rows(), &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride());
+  }
+};
+
+/***************************************************************************
+* meta-unrolling implementation
+***************************************************************************/
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size,
+         bool Stop = Index==Size>
+struct triangular_solver_unroller;
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> {
+  enum {
+    IsLower = ((Mode&Lower)==Lower),
+    I = IsLower ? Index : Size - Index - 1,
+    S = IsLower ? 0     : I+1
+  };
+  static void run(const Lhs& lhs, Rhs& rhs)
+  {
+    if (Index>0)
+      rhs.coeffRef(I) -= lhs.row(I).template segment<Index>(S).transpose()
+                         .cwiseProduct(rhs.template segment<Index>(S)).sum();
+
+    if(!(Mode & UnitDiag))
+      rhs.coeffRef(I) /= lhs.coeff(I,I);
+
+    triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs);
+  }
+};
+
+template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> {
+  static void run(const Lhs&, Rhs&) {}
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
+  static void run(const Lhs& lhs, Rhs& rhs)
+  { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
+  static void run(const Lhs& lhs, Rhs& rhs)
+  {
+    Transpose<const Lhs> trLhs(lhs);
+    Transpose<Rhs> trRhs(rhs);
+    
+    triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
+                              ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+                              0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
+  }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* TriangularView methods
+***************************************************************************/
+
+/** "in-place" version of TriangularView::solve() where the result is written in \a other
+  *
+  * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
+  * This function will const_cast it, so constness isn't honored here.
+  *
+  * See TriangularView:solve() for the details.
+  */
+template<typename MatrixType, unsigned int Mode>
+template<int Side, typename OtherDerived>
+void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
+{
+  OtherDerived& other = _other.const_cast_derived();
+  eigen_assert(cols() == rows());
+  eigen_assert( (Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols()) );
+  eigen_assert(!(Mode & ZeroDiag));
+  eigen_assert((Mode & (Upper|Lower)) != 0);
+
+  enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit  && OtherDerived::IsVectorAtCompileTime };
+  typedef typename internal::conditional<copy,
+    typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
+  OtherCopy otherCopy(other);
+
+  internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
+    Side, Mode>::run(nestedExpression(), otherCopy);
+
+  if (copy)
+    other = otherCopy;
+}
+
+/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
+  *
+  * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
+  * \a Side==OnTheLeft (the default), or the right-inverse-multiply  \a other * inverse(\c *this) if
+  * \a Side==OnTheRight.
+  *
+  * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
+  * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
+  * is an upper (resp. lower) triangular matrix.
+  *
+  * Example: \include MatrixBase_marked.cpp
+  * Output: \verbinclude MatrixBase_marked.out
+  *
+  * This function returns an expression of the inverse-multiply and can works in-place if it is assigned
+  * to the same matrix or vector \a other.
+  *
+  * For users coming from BLAS, this function (and more specifically solveInPlace()) offer
+  * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
+  *
+  * \sa TriangularView::solveInPlace()
+  */
+template<typename Derived, unsigned int Mode>
+template<int Side, typename Other>
+const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
+TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const
+{
+  return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
+}
+
+namespace internal {
+
+
+template<int Side, typename TriangularType, typename Rhs>
+struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+  typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
+};
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
+ : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+  typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
+  typedef ReturnByValue<triangular_solve_retval> Base;
+  typedef typename Base::Index Index;
+
+  triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
+    : m_triangularMatrix(tri), m_rhs(rhs)
+  {}
+
+  inline Index rows() const { return m_rhs.rows(); }
+  inline Index cols() const { return m_rhs.cols(); }
+
+  template<typename Dest> inline void evalTo(Dest& dst) const
+  {
+    if(!(is_same<RhsNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_rhs)))
+      dst = m_rhs;
+    m_triangularMatrix.template solveInPlace<Side>(dst);
+  }
+
+  protected:
+    const TriangularType& m_triangularMatrix;
+    const typename Rhs::Nested m_rhs;
+};
+
+} // namespace internal
+
+#endif // EIGEN_SOLVETRIANGULAR_H

Eigen/src/Core/StableNorm.h

@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STABLENORM_H
+#define EIGEN_STABLENORM_H
+
+namespace internal {
+template<typename ExpressionType, typename Scalar>
+inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
+{
+  Scalar max = bl.cwiseAbs().maxCoeff();
+  if (max>scale)
+  {
+    ssq = ssq * abs2(scale/max);
+    scale = max;
+    invScale = Scalar(1)/scale;
+  }
+  // TODO if the max is much much smaller than the current scale,
+  // then we can neglect this sub vector
+  ssq += (bl*invScale).squaredNorm();
+}
+}
+
+/** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
+  * This version use a blockwise two passes algorithm:
+  *  1 - find the absolute largest coefficient \c s
+  *  2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
+  *
+  * For architecture/scalar types supporting vectorization, this version
+  * is faster than blueNorm(). Otherwise the blueNorm() is much faster.
+  *
+  * \sa norm(), blueNorm(), hypotNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::stableNorm() const
+{
+  using std::min;
+  const Index blockSize = 4096;
+  RealScalar scale = 0;
+  RealScalar invScale = 1;
+  RealScalar ssq = 0; // sum of square
+  enum {
+    Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? 1 : 0
+  };
+  Index n = size();
+  Index bi = internal::first_aligned(derived());
+  if (bi>0)
+    internal::stable_norm_kernel(this->head(bi), ssq, scale, invScale);
+  for (; bi<n; bi+=blockSize)
+    internal::stable_norm_kernel(this->segment(bi,(min)(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
+  return scale * internal::sqrt(ssq);
+}
+
+/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
+  * A Portable Fortran Program to Find the Euclidean Norm of a Vector,
+  * ACM TOMS, Vol 4, Issue 1, 1978.
+  *
+  * For architecture/scalar types without vectorization, this version
+  * is much faster than stableNorm(). Otherwise the stableNorm() is faster.
+  *
+  * \sa norm(), stableNorm(), hypotNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::blueNorm() const
+{
+  using std::pow;
+  using std::min;
+  using std::max;
+  static Index nmax = -1;
+  static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
+  if(nmax <= 0)
+  {
+    int nbig, ibeta, it, iemin, iemax, iexp;
+    RealScalar abig, eps;
+    // This program calculates the machine-dependent constants
+    // bl, b2, slm, s2m, relerr overfl, nmax
+    // 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
+    it    = std::numeric_limits<RealScalar>::digits;        // number of base-beta digits in mantissa
+    iemin = std::numeric_limits<RealScalar>::min_exponent;  // minimum exponent
+    iemax = std::numeric_limits<RealScalar>::max_exponent;  // maximum exponent
+    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
+    iexp  = (iemax + 1 - it)/2;
+    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
+    iexp  = - ((iemax+it)/2);
+    s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));   // scaling factor for upper range
+
+    overfl  = rbig*s2m;             // overflow boundary for abig
+    eps     = RealScalar(pow(double(ibeta), 1-it));
+    relerr  = internal::sqrt(eps);         // tolerance for neglecting asml
+    abig    = RealScalar(1.0/eps - 1.0);
+    if (RealScalar(nbig)>abig)  nmax = int(abig);  // largest safe n
+    else                        nmax = nbig;
+  }
+  Index n = size();
+  RealScalar ab2 = b2 / RealScalar(n);
+  RealScalar asml = RealScalar(0);
+  RealScalar amed = RealScalar(0);
+  RealScalar abig = RealScalar(0);
+  for(Index j=0; j<n; ++j)
+  {
+    RealScalar ax = internal::abs(coeff(j));
+    if(ax > ab2)     abig += internal::abs2(ax*s2m);
+    else if(ax < b1) asml += internal::abs2(ax*s1m);
+    else             amed += internal::abs2(ax);
+  }
+  if(abig > RealScalar(0))
+  {
+    abig = internal::sqrt(abig);
+    if(abig > overfl)
+    {
+      eigen_assert(false && "overflow");
+      return rbig;
+    }
+    if(amed > RealScalar(0))
+    {
+      abig = abig/s2m;
+      amed = internal::sqrt(amed);
+    }
+    else
+      return abig/s2m;
+  }
+  else if(asml > RealScalar(0))
+  {
+    if (amed > RealScalar(0))
+    {
+      abig = internal::sqrt(amed);
+      amed = internal::sqrt(asml) / s1m;
+    }
+    else
+      return internal::sqrt(asml)/s1m;
+  }
+  else
+    return internal::sqrt(amed);
+  asml = (min)(abig, amed);
+  abig = (max)(abig, amed);
+  if(asml <= abig*relerr)
+    return abig;
+  else
+    return abig * internal::sqrt(RealScalar(1) + internal::abs2(asml/abig));
+}
+
+/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
+  * This version use a concatenation of hypot() calls, and it is very slow.
+  *
+  * \sa norm(), stableNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::hypotNorm() const
+{
+  return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
+}
+
+#endif // EIGEN_STABLENORM_H

Eigen/src/Core/Stride.h

@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STRIDE_H
+#define EIGEN_STRIDE_H
+
+/** \class Stride
+  * \ingroup Core_Module
+  *
+  * \brief Holds strides information for Map
+  *
+  * This class holds the strides information for mapping arrays with strides with class Map.
+  *
+  * It holds two values: the inner stride and the outer stride.
+  *
+  * The inner stride is the pointer increment between two consecutive entries within a given row of a
+  * row-major matrix or within a given column of a column-major matrix.
+  *
+  * The outer stride is the pointer increment between two consecutive rows of a row-major matrix or
+  * between two consecutive columns of a column-major matrix.
+  *
+  * These two values can be passed either at compile-time as template parameters, or at runtime as
+  * arguments to the constructor.
+  *
+  * Indeed, this class takes two template parameters:
+  *  \param _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.
+  *  \param _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.
+  *
+  * Here is an example:
+  * \include Map_general_stride.cpp
+  * Output: \verbinclude Map_general_stride.out
+  *
+  * \sa class InnerStride, class OuterStride, \ref TopicStorageOrders
+  */
+template<int _OuterStrideAtCompileTime, int _InnerStrideAtCompileTime>
+class Stride
+{
+  public:
+    typedef DenseIndex Index;
+    enum {
+      InnerStrideAtCompileTime = _InnerStrideAtCompileTime,
+      OuterStrideAtCompileTime = _OuterStrideAtCompileTime
+    };
+
+    /** Default constructor, for use when strides are fixed at compile time */
+    Stride()
+      : m_outer(OuterStrideAtCompileTime), m_inner(InnerStrideAtCompileTime)
+    {
+      eigen_assert(InnerStrideAtCompileTime != Dynamic && OuterStrideAtCompileTime != Dynamic);
+    }
+
+    /** Constructor allowing to pass the strides at runtime */
+    Stride(Index outerStride, Index innerStride)
+      : m_outer(outerStride), m_inner(innerStride)
+    {
+      eigen_assert(innerStride>=0 && outerStride>=0);
+    }
+
+    /** Copy constructor */
+    Stride(const Stride& other)
+      : m_outer(other.outer()), m_inner(other.inner())
+    {}
+
+    /** \returns the outer stride */
+    inline Index outer() const { return m_outer.value(); }
+    /** \returns the inner stride */
+    inline Index inner() const { return m_inner.value(); }
+
+  protected:
+    internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;
+    internal::variable_if_dynamic<Index, InnerStrideAtCompileTime> m_inner;
+};
+
+/** \brief Convenience specialization of Stride to specify only an inner stride
+  * See class Map for some examples */
+template<int Value = Dynamic>
+class InnerStride : public Stride<0, Value>
+{
+    typedef Stride<0, Value> Base;
+  public:
+    typedef DenseIndex Index;
+    InnerStride() : Base() {}
+    InnerStride(Index v) : Base(0, v) {}
+};
+
+/** \brief Convenience specialization of Stride to specify only an outer stride
+  * See class Map for some examples */
+template<int Value = Dynamic>
+class OuterStride : public Stride<Value, 0>
+{
+    typedef Stride<Value, 0> Base;
+  public:
+    typedef DenseIndex Index;
+    OuterStride() : Base() {}
+    OuterStride(Index v) : Base(v,0) {}
+};
+
+#endif // EIGEN_STRIDE_H

Eigen/src/Core/Swap.h

@@ -0,0 +1,126 @@
+// 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>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SWAP_H
+#define EIGEN_SWAP_H
+
+/** \class SwapWrapper
+  * \ingroup Core_Module
+  *
+  * \internal
+  *
+  * \brief Internal helper class for swapping two expressions
+  */
+namespace internal {
+template<typename ExpressionType>
+struct traits<SwapWrapper<ExpressionType> > : traits<ExpressionType> {};
+}
+
+template<typename ExpressionType> class SwapWrapper
+  : public internal::dense_xpr_base<SwapWrapper<ExpressionType> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<SwapWrapper>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(SwapWrapper)
+    typedef typename internal::packet_traits<Scalar>::type Packet;
+
+    inline SwapWrapper(ExpressionType& xpr) : m_expression(xpr) {}
+
+    inline Index rows() const { return m_expression.rows(); }
+    inline Index cols() const { return m_expression.cols(); }
+    inline Index outerStride() const { return m_expression.outerStride(); }
+    inline Index innerStride() const { return m_expression.innerStride(); }
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    inline Scalar& coeffRef(Index row, Index col) const
+    {
+      return m_expression.coeffRef(row, col);
+    }
+
+    inline Scalar& coeffRef(Index index) const
+    {
+      return m_expression.coeffRef(index);
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(row >= 0 && row < rows()
+                         && col >= 0 && col < cols());
+      Scalar tmp = m_expression.coeff(row, col);
+      m_expression.coeffRef(row, col) = _other.coeff(row, col);
+      _other.coeffRef(row, col) = tmp;
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(index >= 0 && index < m_expression.size());
+      Scalar tmp = m_expression.coeff(index);
+      m_expression.coeffRef(index) = _other.coeff(index);
+      _other.coeffRef(index) = tmp;
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      Packet tmp = m_expression.template packet<StoreMode>(row, col);
+      m_expression.template writePacket<StoreMode>(row, col,
+        _other.template packet<LoadMode>(row, col)
+      );
+      _other.template writePacket<LoadMode>(row, col, tmp);
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(Index index, const DenseBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      eigen_internal_assert(index >= 0 && index < m_expression.size());
+      Packet tmp = m_expression.template packet<StoreMode>(index);
+      m_expression.template writePacket<StoreMode>(index,
+        _other.template packet<LoadMode>(index)
+      );
+      _other.template writePacket<LoadMode>(index, tmp);
+    }
+
+  protected:
+    ExpressionType& m_expression;
+};
+
+#endif // EIGEN_SWAP_H

Eigen/src/Core/Transpose.h

@@ -0,0 +1,425 @@
+// 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) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_TRANSPOSE_H
+#define EIGEN_TRANSPOSE_H
+
+/** \class Transpose
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the transpose of a matrix
+  *
+  * \param MatrixType the type of the object of which we are taking the transpose
+  *
+  * This class represents an expression of the transpose of a matrix.
+  * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::transpose(), MatrixBase::adjoint()
+  */
+
+namespace internal {
+template<typename MatrixType>
+struct traits<Transpose<MatrixType> > : traits<MatrixType>
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedPlain;
+  typedef typename traits<MatrixType>::StorageKind StorageKind;
+  typedef typename traits<MatrixType>::XprKind XprKind;
+  enum {
+    RowsAtCompileTime = MatrixType::ColsAtCompileTime,
+    ColsAtCompileTime = MatrixType::RowsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+    Flags0 = MatrixTypeNestedPlain::Flags & ~(LvalueBit | NestByRefBit),
+    Flags1 = Flags0 | FlagsLvalueBit,
+    Flags = Flags1 ^ RowMajorBit,
+    CoeffReadCost = MatrixTypeNestedPlain::CoeffReadCost,
+    InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,
+    OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret
+  };
+};
+}
+
+template<typename MatrixType, typename StorageKind> class TransposeImpl;
+
+template<typename MatrixType> class Transpose
+  : public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>
+{
+  public:
+
+    typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
+
+    inline Transpose(MatrixType& matrix) : m_matrix(matrix) {}
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
+
+    inline Index rows() const { return m_matrix.cols(); }
+    inline Index cols() const { return m_matrix.rows(); }
+
+    /** \returns the nested expression */
+    const typename internal::remove_all<typename MatrixType::Nested>::type&
+    nestedExpression() const { return m_matrix; }
+
+    /** \returns the nested expression */
+    typename internal::remove_all<typename MatrixType::Nested>::type&
+    nestedExpression() { return m_matrix.const_cast_derived(); }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+};
+
+namespace internal {
+
+template<typename MatrixType, bool HasDirectAccess = has_direct_access<MatrixType>::ret>
+struct TransposeImpl_base
+{
+  typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+template<typename MatrixType>
+struct TransposeImpl_base<MatrixType, false>
+{
+  typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+} // end namespace internal
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
+  : public internal::TransposeImpl_base<MatrixType>::type
+{
+  public:
+
+    typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
+
+    inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
+    inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
+
+    typedef typename internal::conditional<
+                       internal::is_lvalue<MatrixType>::value,
+                       Scalar,
+                       const Scalar
+                     >::type ScalarWithConstIfNotLvalue;
+
+    inline ScalarWithConstIfNotLvalue* data() { return derived().nestedExpression().data(); }
+    inline const Scalar* data() const { return derived().nestedExpression().data(); }
+
+    inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+      return derived().nestedExpression().const_cast_derived().coeffRef(col, row);
+    }
+
+    inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+      return derived().nestedExpression().const_cast_derived().coeffRef(index);
+    }
+
+    inline const Scalar& coeffRef(Index row, Index col) const
+    {
+      return derived().nestedExpression().coeffRef(col, row);
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      return derived().nestedExpression().coeffRef(index);
+    }
+
+    inline const CoeffReturnType coeff(Index row, Index col) const
+    {
+      return derived().nestedExpression().coeff(col, row);
+    }
+
+    inline const CoeffReturnType coeff(Index index) const
+    {
+      return derived().nestedExpression().coeff(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index row, Index col) const
+    {
+      return derived().nestedExpression().template packet<LoadMode>(col, row);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      derived().nestedExpression().const_cast_derived().template writePacket<LoadMode>(col, row, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(Index index) const
+    {
+      return derived().nestedExpression().template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      derived().nestedExpression().const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+};
+
+/** \returns an expression of the transpose of *this.
+  *
+  * Example: \include MatrixBase_transpose.cpp
+  * Output: \verbinclude MatrixBase_transpose.out
+  *
+  * \warning If you want to replace a matrix by its own transpose, do \b NOT do this:
+  * \code
+  * m = m.transpose(); // bug!!! caused by aliasing effect
+  * \endcode
+  * Instead, use the transposeInPlace() method:
+  * \code
+  * m.transposeInPlace();
+  * \endcode
+  * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+  * \code
+  * m = m.transpose().eval();
+  * \endcode
+  *
+  * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline Transpose<Derived>
+DenseBase<Derived>::transpose()
+{
+  return derived();
+}
+
+/** This is the const version of transpose().
+  *
+  * Make sure you read the warning for transpose() !
+  *
+  * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstTransposeReturnType
+DenseBase<Derived>::transpose() const
+{
+  return ConstTransposeReturnType(derived());
+}
+
+/** \returns an expression of the adjoint (i.e. conjugate transpose) of *this.
+  *
+  * Example: \include MatrixBase_adjoint.cpp
+  * Output: \verbinclude MatrixBase_adjoint.out
+  *
+  * \warning If you want to replace a matrix by its own adjoint, do \b NOT do this:
+  * \code
+  * m = m.adjoint(); // bug!!! caused by aliasing effect
+  * \endcode
+  * Instead, use the adjointInPlace() method:
+  * \code
+  * m.adjointInPlace();
+  * \endcode
+  * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+  * \code
+  * m = m.adjoint().eval();
+  * \endcode
+  *
+  * \sa adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::AdjointReturnType
+MatrixBase<Derived>::adjoint() const
+{
+  return this->transpose(); // in the complex case, the .conjugate() is be implicit here
+                            // due to implicit conversion to return type
+}
+
+/***************************************************************************
+* "in place" transpose implementation
+***************************************************************************/
+
+namespace internal {
+
+template<typename MatrixType,
+  bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic>
+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());
+  }
+};
+
+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());
+    else
+      m = m.transpose().eval();
+  }
+};
+
+} // end namespace internal
+
+/** This is the "in place" version of transpose(): it replaces \c *this by its own transpose.
+  * Thus, doing
+  * \code
+  * m.transposeInPlace();
+  * \endcode
+  * has the same effect on m as doing
+  * \code
+  * m = m.transpose().eval();
+  * \endcode
+  * and is faster and also safer because in the latter line of code, forgetting the eval() results
+  * in a bug caused by aliasing.
+  *
+  * 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.
+  *
+  * \sa transpose(), adjoint(), adjointInPlace() */
+template<typename Derived>
+inline void DenseBase<Derived>::transposeInPlace()
+{
+  internal::inplace_transpose_selector<Derived>::run(derived());
+}
+
+/***************************************************************************
+* "in place" adjoint implementation
+***************************************************************************/
+
+/** This is the "in place" version of adjoint(): it replaces \c *this by its own transpose.
+  * Thus, doing
+  * \code
+  * m.adjointInPlace();
+  * \endcode
+  * has the same effect on m as doing
+  * \code
+  * m = m.adjoint().eval();
+  * \endcode
+  * and is faster and also safer because in the latter line of code, forgetting the eval() results
+  * in a bug caused by aliasing.
+  *
+  * Notice however that this method is only useful if you want to replace a matrix by its own adjoint.
+  * 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.
+  *
+  * \sa transpose(), adjoint(), transposeInPlace() */
+template<typename Derived>
+inline void MatrixBase<Derived>::adjointInPlace()
+{
+  derived() = adjoint().eval();
+}
+
+#ifndef EIGEN_NO_DEBUG
+
+// The following is to detect aliasing problems in most common cases.
+
+namespace internal {
+
+template<typename BinOp,typename NestedXpr,typename Rhs>
+struct blas_traits<SelfCwiseBinaryOp<BinOp,NestedXpr,Rhs> >
+ : blas_traits<NestedXpr>
+{
+  typedef SelfCwiseBinaryOp<BinOp,NestedXpr,Rhs> XprType;
+  static inline const XprType extract(const XprType& x) { return x; }
+};
+
+template<bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_compile_time_selector
+{
+  enum { ret = bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed };
+};
+
+template<bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_compile_time_selector<DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+  enum { ret =    bool(blas_traits<DerivedA>::IsTransposed) != DestIsTransposed
+               || bool(blas_traits<DerivedB>::IsTransposed) != DestIsTransposed
+  };
+};
+
+template<typename Scalar, bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_run_time_selector
+{
+  static bool run(const Scalar* dest, const OtherDerived& src)
+  {
+    return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src));
+  }
+};
+
+template<typename Scalar, bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+  static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)
+  {
+    return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src.lhs())))
+        || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src.rhs())));
+  }
+};
+
+// the following selector, checkTransposeAliasing_impl, based on MightHaveTransposeAliasing,
+// is because when the condition controlling the assert is known at compile time, ICC emits a warning.
+// This is actually a good warning: in expressions that don't have any transposing, the condition is
+// known at compile time to be false, and using that, we can avoid generating the code of the assert again
+// and again for all these expressions that don't need it.
+
+template<typename Derived, typename OtherDerived,
+         bool MightHaveTransposeAliasing
+                 = check_transpose_aliasing_compile_time_selector
+                     <blas_traits<Derived>::IsTransposed,OtherDerived>::ret
+        >
+struct checkTransposeAliasing_impl
+{
+    static void run(const Derived& dst, const OtherDerived& other)
+    {
+        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() "
+             "or evaluate the rhs into a temporary using .eval()");
+
+    }
+};
+
+template<typename Derived, typename OtherDerived>
+struct checkTransposeAliasing_impl<Derived, OtherDerived, false>
+{
+    static void run(const Derived&, const OtherDerived&)
+    {
+    }
+};
+
+} // end namespace internal
+
+template<typename Derived>
+template<typename OtherDerived>
+void DenseBase<Derived>::checkTransposeAliasing(const OtherDerived& other) const
+{
+    internal::checkTransposeAliasing_impl<Derived, OtherDerived>::run(derived(), other);
+}
+#endif
+
+#endif // EIGEN_TRANSPOSE_H

Eigen/src/Core/Transpositions.h

@@ -0,0 +1,447 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_TRANSPOSITIONS_H
+#define EIGEN_TRANSPOSITIONS_H
+
+/** \class Transpositions
+  * \ingroup Core_Module
+  *
+  * \brief Represents a sequence of transpositions (row/column interchange)
+  *
+  * \param SizeAtCompileTime the number of transpositions, or Dynamic
+  * \param MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+  *
+  * This class represents a permutation transformation as a sequence of \em n transpositions
+  * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
+  * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
+  * the rows \c i and \c indices[i] of the matrix \c M.
+  * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
+  *
+  * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
+  * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
+  * 
+  * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
+  * \code
+  * Transpositions tr;
+  * MatrixXf mat;
+  * mat = tr * mat;
+  * \endcode
+  * In this example, we detect that the matrix appears on both side, and so the transpositions
+  * are applied in-place without any temporary or extra copy.
+  *
+  * \sa class PermutationMatrix
+  */
+
+namespace internal {
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed=false> struct transposition_matrix_product_retval;
+}
+
+template<typename Derived>
+class TranspositionsBase
+{
+    typedef internal::traits<Derived> Traits;
+    
+  public:
+
+    typedef typename Traits::IndicesType IndicesType;
+    typedef typename IndicesType::Scalar Index;
+
+    Derived& derived() { return *static_cast<Derived*>(this); }
+    const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+    /** Copies the \a other transpositions into \c *this */
+    template<typename OtherDerived>
+    Derived& operator=(const TranspositionsBase<OtherDerived>& other)
+    {
+      indices() = other.indices();
+      return derived();
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    Derived& operator=(const TranspositionsBase& other)
+    {
+      indices() = other.indices();
+      return derived();
+    }
+    #endif
+
+    /** \returns the number of transpositions */
+    inline Index size() const { return indices().size(); }
+
+    /** Direct access to the underlying index vector */
+    inline const Index& coeff(Index i) const { return indices().coeff(i); }
+    /** Direct access to the underlying index vector */
+    inline Index& coeffRef(Index i) { return indices().coeffRef(i); }
+    /** Direct access to the underlying index vector */
+    inline const Index& operator()(Index i) const { return indices()(i); }
+    /** Direct access to the underlying index vector */
+    inline Index& operator()(Index i) { return indices()(i); }
+    /** Direct access to the underlying index vector */
+    inline const Index& operator[](Index i) const { return indices()(i); }
+    /** Direct access to the underlying index vector */
+    inline Index& operator[](Index i) { return indices()(i); }
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return derived().indices(); }
+    /** \returns a reference to the stored array representing the transpositions. */
+    IndicesType& indices() { return derived().indices(); }
+
+    /** Resizes to given size. */
+    inline void resize(int size)
+    {
+      indices().resize(size);
+    }
+
+    /** Sets \c *this to represents an identity transformation */
+    void setIdentity()
+    {
+      for(int i = 0; i < indices().size(); ++i)
+        coeffRef(i) = i;
+    }
+
+    // FIXME: do we want such methods ?
+    // might be usefull when the target matrix expression is complex, e.g.:
+    // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
+    /*
+    template<typename MatrixType>
+    void applyForwardToRows(MatrixType& mat) const
+    {
+      for(Index k=0 ; k<size() ; ++k)
+        if(m_indices(k)!=k)
+          mat.row(k).swap(mat.row(m_indices(k)));
+    }
+
+    template<typename MatrixType>
+    void applyBackwardToRows(MatrixType& mat) const
+    {
+      for(Index k=size()-1 ; k>=0 ; --k)
+        if(m_indices(k)!=k)
+          mat.row(k).swap(mat.row(m_indices(k)));
+    }
+    */
+
+    /** \returns the inverse transformation */
+    inline Transpose<TranspositionsBase> inverse() const
+    { return Transpose<TranspositionsBase>(derived()); }
+
+    /** \returns the tranpose transformation */
+    inline Transpose<TranspositionsBase> transpose() const
+    { return Transpose<TranspositionsBase>(derived()); }
+
+  protected:
+};
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
+{
+  typedef IndexType Index;
+  typedef Matrix<Index, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
+class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
+{
+    typedef internal::traits<Transpositions> Traits;
+  public:
+
+    typedef TranspositionsBase<Transpositions> Base;
+    typedef typename Traits::IndicesType IndicesType;
+    typedef typename IndicesType::Scalar Index;
+
+    inline Transpositions() {}
+
+    /** Copy constructor. */
+    template<typename OtherDerived>
+    inline Transpositions(const TranspositionsBase<OtherDerived>& other)
+      : m_indices(other.indices()) {}
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** Standard copy constructor. Defined only to prevent a default copy constructor
+      * from hiding the other templated constructor */
+    inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}
+    #endif
+
+    /** Generic constructor from expression of the transposition indices. */
+    template<typename Other>
+    explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices)
+    {}
+
+    /** Copies the \a other transpositions into \c *this */
+    template<typename OtherDerived>
+    Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
+    {
+      return Base::operator=(other);
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    Transpositions& operator=(const Transpositions& other)
+    {
+      m_indices = other.m_indices;
+      return *this;
+    }
+    #endif
+
+    /** Constructs an uninitialized permutation matrix of given size.
+      */
+    inline Transpositions(Index size) : m_indices(size)
+    {}
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return m_indices; }
+    /** \returns a reference to the stored array representing the transpositions. */
+    IndicesType& indices() { return m_indices; }
+
+  protected:
+
+    IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
+struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,_PacketAccess> >
+{
+  typedef IndexType Index;
+  typedef Map<const Matrix<Index,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int PacketAccess>
+class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess>
+ : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess> >
+{
+    typedef internal::traits<Map> Traits;
+  public:
+
+    typedef TranspositionsBase<Map> Base;
+    typedef typename Traits::IndicesType IndicesType;
+    typedef typename IndicesType::Scalar Index;
+
+    inline Map(const Index* indices)
+      : m_indices(indices)
+    {}
+
+    inline Map(const Index* indices, Index size)
+      : m_indices(indices,size)
+    {}
+
+    /** Copies the \a other transpositions into \c *this */
+    template<typename OtherDerived>
+    Map& operator=(const TranspositionsBase<OtherDerived>& other)
+    {
+      return Base::operator=(other);
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    Map& operator=(const Map& other)
+    {
+      m_indices = other.m_indices;
+      return *this;
+    }
+    #endif
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return m_indices; }
+    
+    /** \returns a reference to the stored array representing the transpositions. */
+    IndicesType& indices() { return m_indices; }
+
+  protected:
+
+    IndicesType m_indices;
+};
+
+namespace internal {
+template<typename _IndicesType>
+struct traits<TranspositionsWrapper<_IndicesType> >
+{
+  typedef typename _IndicesType::Scalar Index;
+  typedef _IndicesType IndicesType;
+};
+}
+
+template<typename _IndicesType>
+class TranspositionsWrapper
+ : public TranspositionsBase<TranspositionsWrapper<_IndicesType> >
+{
+    typedef internal::traits<TranspositionsWrapper> Traits;
+  public:
+
+    typedef TranspositionsBase<TranspositionsWrapper> Base;
+    typedef typename Traits::IndicesType IndicesType;
+    typedef typename IndicesType::Scalar Index;
+
+    inline TranspositionsWrapper(IndicesType& indices)
+      : m_indices(indices)
+    {}
+
+    /** Copies the \a other transpositions into \c *this */
+    template<typename OtherDerived>
+    TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
+    {
+      return Base::operator=(other);
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    TranspositionsWrapper& operator=(const TranspositionsWrapper& other)
+    {
+      m_indices = other.m_indices;
+      return *this;
+    }
+    #endif
+
+    /** const version of indices(). */
+    const IndicesType& indices() const { return m_indices; }
+
+    /** \returns a reference to the stored array representing the transpositions. */
+    IndicesType& indices() { return m_indices; }
+
+  protected:
+
+    const typename IndicesType::Nested m_indices;
+};
+
+/** \returns the \a matrix with the \a transpositions applied to the columns.
+  */
+template<typename Derived, typename TranspositionsDerived>
+inline const internal::transposition_matrix_product_retval<TranspositionsDerived, Derived, OnTheRight>
+operator*(const MatrixBase<Derived>& matrix,
+          const TranspositionsBase<TranspositionsDerived> &transpositions)
+{
+  return internal::transposition_matrix_product_retval
+           <TranspositionsDerived, Derived, OnTheRight>
+           (transpositions.derived(), matrix.derived());
+}
+
+/** \returns the \a matrix with the \a transpositions applied to the rows.
+  */
+template<typename Derived, typename TranspositionDerived>
+inline const internal::transposition_matrix_product_retval
+               <TranspositionDerived, Derived, OnTheLeft>
+operator*(const TranspositionsBase<TranspositionDerived> &transpositions,
+          const MatrixBase<Derived>& matrix)
+{
+  return internal::transposition_matrix_product_retval
+           <TranspositionDerived, Derived, OnTheLeft>
+           (transpositions.derived(), matrix.derived());
+}
+
+namespace internal {
+
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
+struct traits<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
+{
+  typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
+struct transposition_matrix_product_retval
+ : public ReturnByValue<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
+{
+    typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
+    typedef typename TranspositionType::Index Index;
+
+    transposition_matrix_product_retval(const TranspositionType& tr, const MatrixType& matrix)
+      : m_transpositions(tr), m_matrix(matrix)
+    {}
+
+    inline int rows() const { return m_matrix.rows(); }
+    inline int cols() const { return m_matrix.cols(); }
+
+    template<typename Dest> inline void evalTo(Dest& dst) const
+    {
+      const int size = m_transpositions.size();
+      Index j = 0;
+
+      if(!(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix)))
+        dst = m_matrix;
+
+      for(int k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
+        if((j=m_transpositions.coeff(k))!=k)
+        {
+          if(Side==OnTheLeft)
+            dst.row(k).swap(dst.row(j));
+          else if(Side==OnTheRight)
+            dst.col(k).swap(dst.col(j));
+        }
+    }
+
+  protected:
+    const TranspositionType& m_transpositions;
+    const typename MatrixType::Nested m_matrix;
+};
+
+} // end namespace internal
+
+/* Template partial specialization for transposed/inverse transpositions */
+
+template<typename TranspositionsDerived>
+class Transpose<TranspositionsBase<TranspositionsDerived> >
+{
+    typedef TranspositionsDerived TranspositionType;
+    typedef typename TranspositionType::IndicesType IndicesType;
+  public:
+
+    Transpose(const TranspositionType& t) : m_transpositions(t) {}
+
+    inline int size() const { return m_transpositions.size(); }
+
+    /** \returns the \a matrix with the inverse transpositions applied to the columns.
+      */
+    template<typename Derived> friend
+    inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>
+    operator*(const MatrixBase<Derived>& matrix, const Transpose& trt)
+    {
+      return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>(trt.m_transpositions, matrix.derived());
+    }
+
+    /** \returns the \a matrix with the inverse transpositions applied to the rows.
+      */
+    template<typename Derived>
+    inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>
+    operator*(const MatrixBase<Derived>& matrix) const
+    {
+      return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>(m_transpositions, matrix.derived());
+    }
+
+  protected:
+    const TranspositionType& m_transpositions;
+};
+
+#endif // EIGEN_TRANSPOSITIONS_H

Eigen/src/Core/TriangularMatrix.h

@@ -0,0 +1,838 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_TRIANGULARMATRIX_H
+#define EIGEN_TRIANGULARMATRIX_H
+
+namespace internal {
+  
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;
+  
+}
+
+/** \internal
+  *
+  * \class TriangularBase
+  * \ingroup Core_Module
+  *
+  * \brief Base class for triangular part in a matrix
+  */
+template<typename Derived> class TriangularBase : public EigenBase<Derived>
+{
+  public:
+
+    enum {
+      Mode = internal::traits<Derived>::Mode,
+      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime
+    };
+    typedef typename internal::traits<Derived>::Scalar Scalar;
+    typedef typename internal::traits<Derived>::StorageKind StorageKind;
+    typedef typename internal::traits<Derived>::Index Index;
+    typedef typename internal::traits<Derived>::DenseMatrixType DenseMatrixType;
+    typedef DenseMatrixType DenseType;
+
+    inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); }
+
+    inline Index rows() const { return derived().rows(); }
+    inline Index cols() const { return derived().cols(); }
+    inline Index outerStride() const { return derived().outerStride(); }
+    inline Index innerStride() const { return derived().innerStride(); }
+
+    inline Scalar coeff(Index row, Index col) const  { return derived().coeff(row,col); }
+    inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }
+
+    /** \see MatrixBase::copyCoeff(row,col)
+      */
+    template<typename Other>
+    EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)
+    {
+      derived().coeffRef(row, col) = other.coeff(row, col);
+    }
+
+    inline Scalar operator()(Index row, Index col) const
+    {
+      check_coordinates(row, col);
+      return coeff(row,col);
+    }
+    inline Scalar& operator()(Index row, Index col)
+    {
+      check_coordinates(row, col);
+      return coeffRef(row,col);
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+    inline Derived& derived() { return *static_cast<Derived*>(this); }
+    #endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    template<typename DenseDerived>
+    void evalTo(MatrixBase<DenseDerived> &other) const;
+    template<typename DenseDerived>
+    void evalToLazy(MatrixBase<DenseDerived> &other) const;
+
+    DenseMatrixType toDenseMatrix() const
+    {
+      DenseMatrixType res(rows(), cols());
+      evalToLazy(res);
+      return res;
+    }
+
+  protected:
+
+    void check_coordinates(Index row, Index col) const
+    {
+      EIGEN_ONLY_USED_FOR_DEBUG(row);
+      EIGEN_ONLY_USED_FOR_DEBUG(col);
+      eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());
+      const int mode = int(Mode) & ~SelfAdjoint;
+      EIGEN_ONLY_USED_FOR_DEBUG(mode);
+      eigen_assert((mode==Upper && col>=row)
+                || (mode==Lower && col<=row)
+                || ((mode==StrictlyUpper || mode==UnitUpper) && col>row)
+                || ((mode==StrictlyLower || mode==UnitLower) && col<row));
+    }
+
+    #ifdef EIGEN_INTERNAL_DEBUGGING
+    void check_coordinates_internal(Index row, Index col) const
+    {
+      check_coordinates(row, col);
+    }
+    #else
+    void check_coordinates_internal(Index , Index ) const {}
+    #endif
+
+};
+
+/** \class TriangularView
+  * \ingroup Core_Module
+  *
+  * \brief Base class for triangular part in a matrix
+  *
+  * \param MatrixType the type of the object in which we are taking the triangular part
+  * \param Mode the kind of triangular matrix expression to construct. Can be #Upper,
+  *             #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.
+  *             This is in fact a bit field; it must have either #Upper or #Lower, 
+  *             and additionnaly it may have #UnitDiag or #ZeroDiag or neither.
+  *
+  * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
+  * matrices one should speak of "trapezoid" parts. This class is the return type
+  * of MatrixBase::triangularView() and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::triangularView()
+  */
+namespace internal {
+template<typename MatrixType, unsigned int _Mode>
+struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>
+{
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
+  typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
+  typedef MatrixType ExpressionType;
+  typedef typename MatrixType::PlainObject DenseMatrixType;
+  enum {
+    Mode = _Mode,
+    Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode,
+    CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
+  };
+};
+}
+
+template<int Mode, bool LhsIsTriangular,
+         typename Lhs, bool LhsIsVector,
+         typename Rhs, bool RhsIsVector>
+struct TriangularProduct;
+
+template<typename _MatrixType, unsigned int _Mode> class TriangularView
+  : public TriangularBase<TriangularView<_MatrixType, _Mode> >
+{
+  public:
+
+    typedef TriangularBase<TriangularView> Base;
+    typedef typename internal::traits<TriangularView>::Scalar Scalar;
+
+    typedef _MatrixType MatrixType;
+    typedef typename internal::traits<TriangularView>::DenseMatrixType DenseMatrixType;
+    typedef DenseMatrixType PlainObject;
+
+  protected:
+    typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;
+    typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;
+    typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
+
+    typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;
+    
+  public:
+    using Base::evalToLazy;
+  
+
+    typedef typename internal::traits<TriangularView>::StorageKind StorageKind;
+    typedef typename internal::traits<TriangularView>::Index Index;
+
+    enum {
+      Mode = _Mode,
+      TransposeMode = (Mode & Upper ? Lower : 0)
+                    | (Mode & Lower ? Upper : 0)
+                    | (Mode & (UnitDiag))
+                    | (Mode & (ZeroDiag))
+    };
+
+    inline TriangularView(const MatrixType& matrix) : m_matrix(matrix)
+    {}
+
+    inline Index rows() const { return m_matrix.rows(); }
+    inline Index cols() const { return m_matrix.cols(); }
+    inline Index outerStride() const { return m_matrix.outerStride(); }
+    inline Index innerStride() const { return m_matrix.innerStride(); }
+
+    /** \sa MatrixBase::operator+=() */
+    template<typename Other> TriangularView&  operator+=(const DenseBase<Other>& other) { return *this = m_matrix + other.derived(); }
+    /** \sa MatrixBase::operator-=() */
+    template<typename Other> TriangularView&  operator-=(const DenseBase<Other>& other) { return *this = m_matrix - other.derived(); }
+    /** \sa MatrixBase::operator*=() */
+    TriangularView&  operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix * other; }
+    /** \sa MatrixBase::operator/=() */
+    TriangularView&  operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix / other; }
+
+    /** \sa MatrixBase::fill() */
+    void fill(const Scalar& value) { setConstant(value); }
+    /** \sa MatrixBase::setConstant() */
+    TriangularView& setConstant(const Scalar& value)
+    { return *this = MatrixType::Constant(rows(), cols(), value); }
+    /** \sa MatrixBase::setZero() */
+    TriangularView& setZero() { return setConstant(Scalar(0)); }
+    /** \sa MatrixBase::setOnes() */
+    TriangularView& setOnes() { return setConstant(Scalar(1)); }
+
+    /** \sa MatrixBase::coeff()
+      * \warning the coordinates must fit into the referenced triangular part
+      */
+    inline Scalar coeff(Index row, Index col) const
+    {
+      Base::check_coordinates_internal(row, col);
+      return m_matrix.coeff(row, col);
+    }
+
+    /** \sa MatrixBase::coeffRef()
+      * \warning the coordinates must fit into the referenced triangular part
+      */
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      Base::check_coordinates_internal(row, col);
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+    MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
+
+    /** Assigns a triangular matrix to a triangular part of a dense matrix */
+    template<typename OtherDerived>
+    TriangularView& operator=(const TriangularBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    TriangularView& operator=(const MatrixBase<OtherDerived>& other);
+
+    TriangularView& operator=(const TriangularView& other)
+    { return *this = other.nestedExpression(); }
+
+    template<typename OtherDerived>
+    void lazyAssign(const TriangularBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    void lazyAssign(const MatrixBase<OtherDerived>& other);
+
+    /** \sa MatrixBase::conjugate() */
+    inline TriangularView<MatrixConjugateReturnType,Mode> conjugate()
+    { return m_matrix.conjugate(); }
+    /** \sa MatrixBase::conjugate() const */
+    inline const TriangularView<MatrixConjugateReturnType,Mode> conjugate() const
+    { return m_matrix.conjugate(); }
+
+    /** \sa MatrixBase::adjoint() */
+    inline TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> adjoint()
+    { return m_matrix.adjoint(); }
+    /** \sa MatrixBase::adjoint() const */
+    inline const TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> adjoint() const
+    { return m_matrix.adjoint(); }
+
+    /** \sa MatrixBase::transpose() */
+    inline TriangularView<Transpose<MatrixType>,TransposeMode> transpose()
+    {
+      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+      return m_matrix.const_cast_derived().transpose();
+    }
+    /** \sa MatrixBase::transpose() const */
+    inline const TriangularView<Transpose<MatrixType>,TransposeMode> transpose() const
+    { return m_matrix.transpose(); }
+
+    /** Efficient triangular matrix times vector/matrix product */
+    template<typename OtherDerived>
+    TriangularProduct<Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
+    operator*(const MatrixBase<OtherDerived>& rhs) const
+    {
+      return TriangularProduct
+              <Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
+              (m_matrix, rhs.derived());
+    }
+
+    /** Efficient vector/matrix times triangular matrix product */
+    template<typename OtherDerived> friend
+    TriangularProduct<Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+    operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs)
+    {
+      return TriangularProduct
+              <Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+              (lhs.derived(),rhs.m_matrix);
+    }
+
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived>
+    struct eigen2_product_return_type
+    {
+      typedef typename TriangularView<MatrixType,Mode>::DenseMatrixType DenseMatrixType;
+      typedef typename OtherDerived::PlainObject::DenseType OtherPlainObject;
+      typedef typename ProductReturnType<DenseMatrixType, OtherPlainObject>::Type ProdRetType;
+      typedef typename ProdRetType::PlainObject type;
+    };
+    template<typename OtherDerived>
+    const typename eigen2_product_return_type<OtherDerived>::type
+    operator*(const EigenBase<OtherDerived>& rhs) const
+    {
+      typename OtherDerived::PlainObject::DenseType rhsPlainObject;
+      rhs.evalTo(rhsPlainObject);
+      return this->toDenseMatrix() * rhsPlainObject;
+    }
+    template<typename OtherMatrixType>
+    bool isApprox(const TriangularView<OtherMatrixType, Mode>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+    {
+      return this->toDenseMatrix().isApprox(other.toDenseMatrix(), precision);
+    }
+    template<typename OtherDerived>
+    bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
+    {
+      return this->toDenseMatrix().isApprox(other, precision);
+    }
+    #endif // EIGEN2_SUPPORT
+
+    template<int Side, typename Other>
+    inline const internal::triangular_solve_retval<Side,TriangularView, Other>
+    solve(const MatrixBase<Other>& other) const;
+
+    template<int Side, typename OtherDerived>
+    void solveInPlace(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename Other>
+    inline const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other> 
+    solve(const MatrixBase<Other>& other) const
+    { return solve<OnTheLeft>(other); }
+
+    template<typename OtherDerived>
+    void solveInPlace(const MatrixBase<OtherDerived>& other) const
+    { return solveInPlace<OnTheLeft>(other); }
+
+    const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const
+    {
+      EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
+      return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+    }
+    SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()
+    {
+      EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
+      return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+    }
+
+    template<typename OtherDerived>
+    void swap(TriangularBase<OtherDerived> const & other)
+    {
+      TriangularView<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived());
+    }
+
+    template<typename OtherDerived>
+    void swap(MatrixBase<OtherDerived> const & other)
+    {
+      TriangularView<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived());
+    }
+
+    Scalar determinant() const
+    {
+      if (Mode & UnitDiag)
+        return 1;
+      else if (Mode & ZeroDiag)
+        return 0;
+      else
+        return m_matrix.diagonal().prod();
+    }
+    
+    // TODO simplify the following:
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE TriangularView& operator=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+    {
+      setZero();
+      return assignProduct(other,1);
+    }
+    
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE TriangularView& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+    {
+      return assignProduct(other,1);
+    }
+    
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE TriangularView& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
+    {
+      return assignProduct(other,-1);
+    }
+    
+    
+    template<typename ProductDerived>
+    EIGEN_STRONG_INLINE TriangularView& operator=(const ScaledProduct<ProductDerived>& other)
+    {
+      setZero();
+      return assignProduct(other,other.alpha());
+    }
+    
+    template<typename ProductDerived>
+    EIGEN_STRONG_INLINE TriangularView& operator+=(const ScaledProduct<ProductDerived>& other)
+    {
+      return assignProduct(other,other.alpha());
+    }
+    
+    template<typename ProductDerived>
+    EIGEN_STRONG_INLINE TriangularView& operator-=(const ScaledProduct<ProductDerived>& other)
+    {
+      return assignProduct(other,-other.alpha());
+    }
+    
+  protected:
+    
+    template<typename ProductDerived, typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE TriangularView& assignProduct(const ProductBase<ProductDerived, Lhs,Rhs>& prod, const Scalar& alpha);
+
+    const MatrixTypeNested m_matrix;
+};
+
+/***************************************************************************
+* Implementation of triangular evaluation/assignment
+***************************************************************************/
+
+namespace internal {
+
+template<typename Derived1, typename Derived2, unsigned int Mode, int UnrollCount, bool ClearOpposite>
+struct triangular_assignment_selector
+{
+  enum {
+    col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+  };
+  
+  typedef typename Derived1::Scalar Scalar;
+
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    triangular_assignment_selector<Derived1, Derived2, Mode, UnrollCount-1, ClearOpposite>::run(dst, src);
+
+    eigen_assert( Mode == Upper || Mode == Lower
+            || Mode == StrictlyUpper || Mode == StrictlyLower
+            || Mode == UnitUpper || Mode == UnitLower);
+    if((Mode == Upper && row <= col)
+    || (Mode == Lower && row >= col)
+    || (Mode == StrictlyUpper && row < col)
+    || (Mode == StrictlyLower && row > col)
+    || (Mode == UnitUpper && row < col)
+    || (Mode == UnitLower && row > col))
+      dst.copyCoeff(row, col, src);
+    else if(ClearOpposite)
+    {
+      if (Mode&UnitDiag && row==col)
+        dst.coeffRef(row, col) = Scalar(1);
+      else
+        dst.coeffRef(row, col) = Scalar(0);
+    }
+  }
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite>
+{
+  inline static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Upper, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  typedef typename Derived1::Scalar Scalar;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      Index maxi = (std::min)(j, dst.rows()-1);
+      for(Index i = 0; i <= maxi; ++i)
+        dst.copyCoeff(i, j, src);
+      if (ClearOpposite)
+        for(Index i = maxi+1; i < dst.rows(); ++i)
+          dst.coeffRef(i, j) = Scalar(0);
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, Lower, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      for(Index i = j; i < dst.rows(); ++i)
+        dst.copyCoeff(i, j, src);
+      Index maxi = (std::min)(j, dst.rows());
+      if (ClearOpposite)
+        for(Index i = 0; i < maxi; ++i)
+          dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, StrictlyUpper, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      Index maxi = (std::min)(j, dst.rows());
+      for(Index i = 0; i < maxi; ++i)
+        dst.copyCoeff(i, j, src);
+      if (ClearOpposite)
+        for(Index i = maxi; i < dst.rows(); ++i)
+          dst.coeffRef(i, j) = 0;
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, StrictlyLower, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      for(Index i = j+1; i < dst.rows(); ++i)
+        dst.copyCoeff(i, j, src);
+      Index maxi = (std::min)(j, dst.rows()-1);
+      if (ClearOpposite)
+        for(Index i = 0; i <= maxi; ++i)
+          dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, UnitUpper, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      Index maxi = (std::min)(j, dst.rows());
+      for(Index i = 0; i < maxi; ++i)
+        dst.copyCoeff(i, j, src);
+      if (ClearOpposite)
+      {
+        for(Index i = maxi+1; i < dst.rows(); ++i)
+          dst.coeffRef(i, j) = 0;
+      }
+    }
+    dst.diagonal().setOnes();
+  }
+};
+template<typename Derived1, typename Derived2, bool ClearOpposite>
+struct triangular_assignment_selector<Derived1, Derived2, UnitLower, Dynamic, ClearOpposite>
+{
+  typedef typename Derived1::Index Index;
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(Index j = 0; j < dst.cols(); ++j)
+    {
+      Index maxi = (std::min)(j, dst.rows());
+      for(Index i = maxi+1; i < dst.rows(); ++i)
+        dst.copyCoeff(i, j, src);
+      if (ClearOpposite)
+      {
+        for(Index i = 0; i < maxi; ++i)
+          dst.coeffRef(i, j) = 0;
+      }
+    }
+    dst.diagonal().setOnes();
+  }
+};
+
+} // end namespace internal
+
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+inline TriangularView<MatrixType, Mode>&
+TriangularView<MatrixType, Mode>::operator=(const MatrixBase<OtherDerived>& other)
+{
+  if(OtherDerived::Flags & EvalBeforeAssigningBit)
+  {
+    typename internal::plain_matrix_type<OtherDerived>::type other_evaluated(other.rows(), other.cols());
+    other_evaluated.template triangularView<Mode>().lazyAssign(other.derived());
+    lazyAssign(other_evaluated);
+  }
+  else
+    lazyAssign(other.derived());
+  return *this;
+}
+
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived>& other)
+{
+  enum {
+    unroll = MatrixType::SizeAtCompileTime != Dynamic
+          && internal::traits<OtherDerived>::CoeffReadCost != Dynamic
+          && MatrixType::SizeAtCompileTime*internal::traits<OtherDerived>::CoeffReadCost/2 <= EIGEN_UNROLLING_LIMIT
+  };
+  eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
+
+  internal::triangular_assignment_selector
+    <MatrixType, OtherDerived, int(Mode),
+    unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
+    false // do not change the opposite triangular part
+    >::run(m_matrix.const_cast_derived(), other.derived());
+}
+
+
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+inline TriangularView<MatrixType, Mode>&
+TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& other)
+{
+  eigen_assert(Mode == int(OtherDerived::Mode));
+  if(internal::traits<OtherDerived>::Flags & EvalBeforeAssigningBit)
+  {
+    typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols());
+    other_evaluated.template triangularView<Mode>().lazyAssign(other.derived().nestedExpression());
+    lazyAssign(other_evaluated);
+  }
+  else
+    lazyAssign(other.derived().nestedExpression());
+  return *this;
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+void TriangularView<MatrixType, Mode>::lazyAssign(const TriangularBase<OtherDerived>& other)
+{
+  enum {
+    unroll = MatrixType::SizeAtCompileTime != Dynamic
+                   && internal::traits<OtherDerived>::CoeffReadCost != Dynamic
+                   && MatrixType::SizeAtCompileTime * internal::traits<OtherDerived>::CoeffReadCost / 2
+                        <= EIGEN_UNROLLING_LIMIT
+  };
+  eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
+
+  internal::triangular_assignment_selector
+    <MatrixType, OtherDerived, int(Mode),
+    unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
+    false // preserve the opposite triangular part
+    >::run(m_matrix.const_cast_derived(), other.derived().nestedExpression());
+}
+
+/***************************************************************************
+* Implementation of TriangularBase methods
+***************************************************************************/
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+  * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
+{
+  if(internal::traits<Derived>::Flags & EvalBeforeAssigningBit)
+  {
+    typename internal::plain_matrix_type<Derived>::type other_evaluated(rows(), cols());
+    evalToLazy(other_evaluated);
+    other.derived().swap(other_evaluated);
+  }
+  else
+    evalToLazy(other.derived());
+}
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+  * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const
+{
+  enum {
+    unroll = DenseDerived::SizeAtCompileTime != Dynamic
+                   && internal::traits<Derived>::CoeffReadCost != Dynamic
+                   && DenseDerived::SizeAtCompileTime * internal::traits<Derived>::CoeffReadCost / 2
+                        <= EIGEN_UNROLLING_LIMIT
+  };
+  other.derived().resize(this->rows(), this->cols());
+
+  internal::triangular_assignment_selector
+    <DenseDerived, typename internal::traits<Derived>::MatrixTypeNestedCleaned, Derived::Mode,
+    unroll ? int(DenseDerived::SizeAtCompileTime) : Dynamic,
+    true // clear the opposite triangular part
+    >::run(other.derived(), derived().nestedExpression());
+}
+
+/***************************************************************************
+* Implementation of TriangularView methods
+***************************************************************************/
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+#ifdef EIGEN2_SUPPORT
+
+// implementation of part<>(), including the SelfAdjoint case.
+
+namespace internal {
+template<typename MatrixType, unsigned int Mode>
+struct eigen2_part_return_type
+{
+  typedef TriangularView<MatrixType, Mode> type;
+};
+
+template<typename MatrixType>
+struct eigen2_part_return_type<MatrixType, SelfAdjoint>
+{
+  typedef SelfAdjointView<MatrixType, Upper> type;
+};
+}
+
+/** \deprecated use MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+const typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part() const
+{
+  return derived();
+}
+
+/** \deprecated use MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part()
+{
+  return derived();
+}
+#endif
+
+/**
+  * \returns an expression of a triangular view extracted from the current matrix
+  *
+  * The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
+  * \c #Lower, \c #StrictlyLower, \c #UnitLower.
+  *
+  * Example: \include MatrixBase_extract.cpp
+  * Output: \verbinclude MatrixBase_extract.out
+  *
+  * \sa class TriangularView
+  */
+template<typename Derived>
+template<unsigned int Mode>
+typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView()
+{
+  return derived();
+}
+
+/** This is the const version of MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView() const
+{
+  return derived();
+}
+
+/** \returns true if *this is approximately equal to an upper triangular matrix,
+  *          within the precision given by \a prec.
+  *
+  * \sa isLowerTriangular()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
+{
+  RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
+  for(Index j = 0; j < cols(); ++j)
+  {
+    Index maxi = (std::min)(j, rows()-1);
+    for(Index i = 0; i <= maxi; ++i)
+    {
+      RealScalar absValue = internal::abs(coeff(i,j));
+      if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
+    }
+  }
+  RealScalar threshold = maxAbsOnUpperPart * prec;
+  for(Index j = 0; j < cols(); ++j)
+    for(Index i = j+1; i < rows(); ++i)
+      if(internal::abs(coeff(i, j)) > threshold) return false;
+  return true;
+}
+
+/** \returns true if *this is approximately equal to a lower triangular matrix,
+  *          within the precision given by \a prec.
+  *
+  * \sa isUpperTriangular()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
+{
+  RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
+  for(Index j = 0; j < cols(); ++j)
+    for(Index i = j; i < rows(); ++i)
+    {
+      RealScalar absValue = internal::abs(coeff(i,j));
+      if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
+    }
+  RealScalar threshold = maxAbsOnLowerPart * prec;
+  for(Index j = 1; j < cols(); ++j)
+  {
+    Index maxi = (std::min)(j, rows()-1);
+    for(Index i = 0; i < maxi; ++i)
+      if(internal::abs(coeff(i, j)) > threshold) return false;
+  }
+  return true;
+}
+
+#endif // EIGEN_TRIANGULARMATRIX_H

Eigen/src/Core/VectorBlock.h

@@ -0,0 +1,296 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_VECTORBLOCK_H
+#define EIGEN_VECTORBLOCK_H
+
+/** \class VectorBlock
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a fixed-size or dynamic-size sub-vector
+  *
+  * \param VectorType the type of the object in which we are taking a sub-vector
+  * \param Size size of the sub-vector we are taking at compile time (optional)
+  *
+  * This class represents an expression of either a fixed-size or dynamic-size sub-vector.
+  * It is the return type of DenseBase::segment(Index,Index) and DenseBase::segment<int>(Index) and
+  * most of the time this is the only way it is used.
+  *
+  * However, if you want to directly maniputate sub-vector expressions,
+  * for instance if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * Here is an example illustrating the dynamic case:
+  * \include class_VectorBlock.cpp
+  * Output: \verbinclude class_VectorBlock.out
+  *
+  * \note Even though this expression has dynamic size, in the case where \a VectorType
+  * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+  * it does not cause a dynamic memory allocation.
+  *
+  * Here is an example illustrating the fixed-size case:
+  * \include class_FixedVectorBlock.cpp
+  * Output: \verbinclude class_FixedVectorBlock.out
+  *
+  * \sa class Block, DenseBase::segment(Index,Index,Index,Index), DenseBase::segment(Index,Index)
+  */
+
+namespace internal {
+template<typename VectorType, int Size>
+struct traits<VectorBlock<VectorType, Size> >
+  : public traits<Block<VectorType,
+                     traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+                     traits<VectorType>::Flags & RowMajorBit ? Size : 1> >
+{
+};
+}
+
+template<typename VectorType, int Size> class VectorBlock
+  : public Block<VectorType,
+                     internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+                     internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1>
+{
+    typedef Block<VectorType,
+                     internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+                     internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1> Base;
+    enum {
+      IsColVector = !(internal::traits<VectorType>::Flags & RowMajorBit)
+    };
+  public:
+    EIGEN_DENSE_PUBLIC_INTERFACE(VectorBlock)
+
+    using Base::operator=;
+
+    /** Dynamic-size constructor
+      */
+    inline VectorBlock(VectorType& vector, Index start, Index size)
+      : Base(vector,
+             IsColVector ? start : 0, IsColVector ? 0 : start,
+             IsColVector ? size  : 1, IsColVector ? 1 : size)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);
+    }
+
+    /** Fixed-size constructor
+      */
+    inline VectorBlock(VectorType& vector, Index start)
+      : Base(vector, IsColVector ? start : 0, IsColVector ? 0 : start)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);
+    }
+};
+
+
+/** \returns a dynamic-size expression of a segment (i.e. a vector block) in *this.
+  *
+  * \only_for_vectors
+  *
+  * \param start the first coefficient in the segment
+  * \param size the number of coefficients in the segment
+  *
+  * Example: \include MatrixBase_segment_int_int.cpp
+  * Output: \verbinclude MatrixBase_segment_int_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, segment(Index)
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::SegmentReturnType
+DenseBase<Derived>::segment(Index start, Index size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return SegmentReturnType(derived(), start, size);
+}
+
+/** This is the const version of segment(Index,Index).*/
+template<typename Derived>
+inline typename DenseBase<Derived>::ConstSegmentReturnType
+DenseBase<Derived>::segment(Index start, Index size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return ConstSegmentReturnType(derived(), start, size);
+}
+
+/** \returns a dynamic-size expression of the first coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * \param size the number of coefficients in the block
+  *
+  * Example: \include MatrixBase_start_int.cpp
+  * Output: \verbinclude MatrixBase_start_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(Index,Index)
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::SegmentReturnType
+DenseBase<Derived>::head(Index size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return SegmentReturnType(derived(), 0, size);
+}
+
+/** This is the const version of head(Index).*/
+template<typename Derived>
+inline typename DenseBase<Derived>::ConstSegmentReturnType
+DenseBase<Derived>::head(Index size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return ConstSegmentReturnType(derived(), 0, size);
+}
+
+/** \returns a dynamic-size expression of the last coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * \param size the number of coefficients in the block
+  *
+  * Example: \include MatrixBase_end_int.cpp
+  * Output: \verbinclude MatrixBase_end_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(Index,Index)
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::SegmentReturnType
+DenseBase<Derived>::tail(Index size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return SegmentReturnType(derived(), this->size() - size, size);
+}
+
+/** This is the const version of tail(Index).*/
+template<typename Derived>
+inline typename DenseBase<Derived>::ConstSegmentReturnType
+DenseBase<Derived>::tail(Index size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return ConstSegmentReturnType(derived(), this->size() - size, size);
+}
+
+/** \returns a fixed-size expression of a segment (i.e. a vector block) in \c *this
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * \param start the index of the first element of the sub-vector
+  *
+  * Example: \include MatrixBase_template_int_segment.cpp
+  * Output: \verbinclude MatrixBase_template_int_segment.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template FixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::segment(Index start)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename FixedSegmentReturnType<Size>::Type(derived(), start);
+}
+
+/** This is the const version of segment<int>(Index).*/
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template ConstFixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::segment(Index start) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename ConstFixedSegmentReturnType<Size>::Type(derived(), start);
+}
+
+/** \returns a fixed-size expression of the first coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * Example: \include MatrixBase_template_int_start.cpp
+  * Output: \verbinclude MatrixBase_template_int_start.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template FixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::head()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename FixedSegmentReturnType<Size>::Type(derived(), 0);
+}
+
+/** This is the const version of head<int>().*/
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template ConstFixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::head() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename ConstFixedSegmentReturnType<Size>::Type(derived(), 0);
+}
+
+/** \returns a fixed-size expression of the last coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * Example: \include MatrixBase_template_int_end.cpp
+  * Output: \verbinclude MatrixBase_template_int_end.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template FixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::tail()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename FixedSegmentReturnType<Size>::Type(derived(), size() - Size);
+}
+
+/** This is the const version of tail<int>.*/
+template<typename Derived>
+template<int Size>
+inline typename DenseBase<Derived>::template ConstFixedSegmentReturnType<Size>::Type
+DenseBase<Derived>::tail() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename ConstFixedSegmentReturnType<Size>::Type(derived(), size() - Size);
+}
+
+
+#endif // EIGEN_VECTORBLOCK_H

Eigen/src/Core/VectorwiseOp.h

@@ -0,0 +1,557 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PARTIAL_REDUX_H
+#define EIGEN_PARTIAL_REDUX_H
+
+/** \class PartialReduxExpr
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression of a partially reduxed matrix
+  *
+  * \tparam MatrixType the type of the matrix we are applying the redux operation
+  * \tparam MemberOp type of the member functor
+  * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
+  *
+  * This class represents an expression of a partial redux operator of a matrix.
+  * It is the return type of some VectorwiseOp functions,
+  * and most of the time this is the only way it is used.
+  *
+  * \sa class VectorwiseOp
+  */
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr;
+
+namespace internal {
+template<typename MatrixType, typename MemberOp, int Direction>
+struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+ : traits<MatrixType>
+{
+  typedef typename MemberOp::result_type Scalar;
+  typedef typename traits<MatrixType>::StorageKind StorageKind;
+  typedef typename traits<MatrixType>::XprKind XprKind;
+  typedef typename MatrixType::Scalar InputScalar;
+  typedef typename nested<MatrixType>::type MatrixTypeNested;
+  typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
+    Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
+    Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
+    TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime
+  };
+  #if EIGEN_GNUC_AT_LEAST(3,4)
+  typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
+  #else
+  typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
+  #endif
+  enum {
+    CoeffReadCost = TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
+  };
+};
+}
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr : internal::no_assignment_operator,
+  public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type
+{
+  public:
+
+    typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
+    EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
+    typedef typename internal::traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
+    typedef typename internal::traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
+
+    PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
+      : m_matrix(mat), m_functor(func) {}
+
+    Index rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
+    Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
+    {
+      if (Direction==Vertical)
+        return m_functor(m_matrix.col(j));
+      else
+        return m_functor(m_matrix.row(i));
+    }
+
+    const Scalar coeff(Index index) const
+    {
+      if (Direction==Vertical)
+        return m_functor(m_matrix.col(index));
+      else
+        return m_functor(m_matrix.row(index));
+    }
+
+  protected:
+    const MatrixTypeNested m_matrix;
+    const MemberOp m_functor;
+};
+
+#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST)                               \
+  template <typename ResultType>                                        \
+  struct member_##MEMBER {                                           \
+    EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER)                         \
+    typedef ResultType result_type;                                     \
+    template<typename Scalar, int Size> struct Cost                     \
+    { enum { value = COST }; };                                         \
+    template<typename XprType>                                          \
+    EIGEN_STRONG_INLINE ResultType operator()(const XprType& mat) const \
+    { return mat.MEMBER(); } \
+  }
+
+namespace internal {
+
+EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
+EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
+EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
+
+
+template <typename BinaryOp, typename Scalar>
+struct member_redux {
+  typedef typename result_of<
+                     BinaryOp(Scalar)
+                   >::type  result_type;
+  template<typename _Scalar, int Size> struct Cost
+  { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
+  member_redux(const BinaryOp func) : m_functor(func) {}
+  template<typename Derived>
+  inline result_type operator()(const DenseBase<Derived>& mat) const
+  { return mat.redux(m_functor); }
+  const BinaryOp m_functor;
+};
+}
+
+/** \class VectorwiseOp
+  * \ingroup Core_Module
+  *
+  * \brief Pseudo expression providing partial reduction operations
+  *
+  * \param ExpressionType the type of the object on which to do partial reductions
+  * \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
+  *
+  * This class represents a pseudo expression with partial reduction features.
+  * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
+  * and most of the time this is the only way it is used.
+  *
+  * Example: \include MatrixBase_colwise.cpp
+  * Output: \verbinclude MatrixBase_colwise.out
+  *
+  * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
+  */
+template<typename ExpressionType, int Direction> class VectorwiseOp
+{
+  public:
+
+    typedef typename ExpressionType::Scalar Scalar;
+    typedef typename ExpressionType::RealScalar RealScalar;
+    typedef typename ExpressionType::Index Index;
+    typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, ExpressionType&>::type ExpressionTypeNested;
+    typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
+
+    template<template<typename _Scalar> class Functor,
+                      typename Scalar=typename internal::traits<ExpressionType>::Scalar> struct ReturnType
+    {
+      typedef PartialReduxExpr<ExpressionType,
+                               Functor<Scalar>,
+                               Direction
+                              > Type;
+    };
+
+    template<typename BinaryOp> struct ReduxReturnType
+    {
+      typedef PartialReduxExpr<ExpressionType,
+                               internal::member_redux<BinaryOp,typename internal::traits<ExpressionType>::Scalar>,
+                               Direction
+                              > Type;
+    };
+
+    enum {
+      IsVertical   = (Direction==Vertical) ? 1 : 0,
+      IsHorizontal = (Direction==Horizontal) ? 1 : 0
+    };
+
+  protected:
+
+    /** \internal
+      * \returns the i-th subvector according to the \c Direction */
+    typedef typename internal::conditional<Direction==Vertical,
+                               typename ExpressionType::ColXpr,
+                               typename ExpressionType::RowXpr>::type SubVector;
+    SubVector subVector(Index i)
+    {
+      return SubVector(m_matrix.derived(),i);
+    }
+
+    /** \internal
+      * \returns the number of subvectors in the direction \c Direction */
+    Index subVectors() const
+    { return Direction==Vertical?m_matrix.cols():m_matrix.rows(); }
+
+    template<typename OtherDerived> struct ExtendedType {
+      typedef Replicate<OtherDerived,
+                        Direction==Vertical   ? 1 : ExpressionType::RowsAtCompileTime,
+                        Direction==Horizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
+    };
+
+    /** \internal
+      * Replicates a vector to match the size of \c *this */
+    template<typename OtherDerived>
+    typename ExtendedType<OtherDerived>::Type
+    extendedTo(const DenseBase<OtherDerived>& other) const
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
+      return typename ExtendedType<OtherDerived>::Type
+                      (other.derived(),
+                       Direction==Vertical   ? 1 : m_matrix.rows(),
+                       Direction==Horizontal ? 1 : m_matrix.cols());
+    }
+
+  public:
+
+    inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
+
+    /** \internal */
+    inline const ExpressionType& _expression() const { return m_matrix; }
+
+    /** \returns a row or column vector expression of \c *this reduxed by \a func
+      *
+      * The template parameter \a BinaryOp is the type of the functor
+      * of the custom redux operator. Note that func must be an associative operator.
+      *
+      * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
+      */
+    template<typename BinaryOp>
+    const typename ReduxReturnType<BinaryOp>::Type
+    redux(const BinaryOp& func = BinaryOp()) const
+    { return typename ReduxReturnType<BinaryOp>::Type(_expression(), func); }
+
+    /** \returns a row (or column) vector expression of the smallest coefficient
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_minCoeff.cpp
+      * Output: \verbinclude PartialRedux_minCoeff.out
+      *
+      * \sa DenseBase::minCoeff() */
+    const typename ReturnType<internal::member_minCoeff>::Type minCoeff() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the largest coefficient
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_maxCoeff.cpp
+      * Output: \verbinclude PartialRedux_maxCoeff.out
+      *
+      * \sa DenseBase::maxCoeff() */
+    const typename ReturnType<internal::member_maxCoeff>::Type maxCoeff() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the squared norm
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_squaredNorm.cpp
+      * Output: \verbinclude PartialRedux_squaredNorm.out
+      *
+      * \sa DenseBase::squaredNorm() */
+    const typename ReturnType<internal::member_squaredNorm,RealScalar>::Type squaredNorm() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the norm
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_norm.cpp
+      * Output: \verbinclude PartialRedux_norm.out
+      *
+      * \sa DenseBase::norm() */
+    const typename ReturnType<internal::member_norm,RealScalar>::Type norm() const
+    { return _expression(); }
+
+
+    /** \returns a row (or column) vector expression of the norm
+      * of each column (or row) of the referenced expression, using
+      * blue's algorithm.
+      *
+      * \sa DenseBase::blueNorm() */
+    const typename ReturnType<internal::member_blueNorm,RealScalar>::Type blueNorm() const
+    { return _expression(); }
+
+
+    /** \returns a row (or column) vector expression of the norm
+      * of each column (or row) of the referenced expression, avoiding
+      * underflow and overflow.
+      *
+      * \sa DenseBase::stableNorm() */
+    const typename ReturnType<internal::member_stableNorm,RealScalar>::Type stableNorm() const
+    { return _expression(); }
+
+
+    /** \returns a row (or column) vector expression of the norm
+      * of each column (or row) of the referenced expression, avoiding
+      * underflow and overflow using a concatenation of hypot() calls.
+      *
+      * \sa DenseBase::hypotNorm() */
+    const typename ReturnType<internal::member_hypotNorm,RealScalar>::Type hypotNorm() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the sum
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_sum.cpp
+      * Output: \verbinclude PartialRedux_sum.out
+      *
+      * \sa DenseBase::sum() */
+    const typename ReturnType<internal::member_sum>::Type sum() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the mean
+    * of each column (or row) of the referenced expression.
+    *
+    * \sa DenseBase::mean() */
+    const typename ReturnType<internal::member_mean>::Type mean() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * whether \b all coefficients of each respective column (or row) are \c true.
+      *
+      * \sa DenseBase::all() */
+    const typename ReturnType<internal::member_all>::Type all() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * whether \b at \b least one coefficient of each respective column (or row) is \c true.
+      *
+      * \sa DenseBase::any() */
+    const typename ReturnType<internal::member_any>::Type any() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * the number of \c true coefficients of each respective column (or row).
+      *
+      * Example: \include PartialRedux_count.cpp
+      * Output: \verbinclude PartialRedux_count.out
+      *
+      * \sa DenseBase::count() */
+    const PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> count() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the product
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_prod.cpp
+      * Output: \verbinclude PartialRedux_prod.out
+      *
+      * \sa DenseBase::prod() */
+    const typename ReturnType<internal::member_prod>::Type prod() const
+    { return _expression(); }
+
+
+    /** \returns a matrix expression
+      * where each column (or row) are reversed.
+      *
+      * Example: \include Vectorwise_reverse.cpp
+      * Output: \verbinclude Vectorwise_reverse.out
+      *
+      * \sa DenseBase::reverse() */
+    const Reverse<ExpressionType, Direction> reverse() const
+    { return Reverse<ExpressionType, Direction>( _expression() ); }
+
+    typedef Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1> ReplicateReturnType;
+    const ReplicateReturnType replicate(Index factor) const;
+
+    /**
+      * \return an expression of the replication of each column (or row) of \c *this
+      *
+      * Example: \include DirectionWise_replicate.cpp
+      * Output: \verbinclude DirectionWise_replicate.out
+      *
+      * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
+      */
+    // NOTE implemented here because of sunstudio's compilation errors
+    template<int Factor> const Replicate<ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>
+    replicate(Index factor = Factor) const
+    {
+      return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
+          (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+    }
+
+/////////// Artithmetic operators ///////////
+
+    /** Copies the vector \a other to each subvector of \c *this */
+    template<typename OtherDerived>
+    ExpressionType& operator=(const DenseBase<OtherDerived>& other)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+      //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
+      for(Index j=0; j<subVectors(); ++j)
+        subVector(j) = other;
+      return const_cast<ExpressionType&>(m_matrix);
+    }
+
+    /** Adds the vector \a other to each subvector of \c *this */
+    template<typename OtherDerived>
+    ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+      for(Index j=0; j<subVectors(); ++j)
+        subVector(j) += other.derived();
+      return const_cast<ExpressionType&>(m_matrix);
+    }
+
+    /** Substracts the vector \a other to each subvector of \c *this */
+    template<typename OtherDerived>
+    ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+      for(Index j=0; j<subVectors(); ++j)
+        subVector(j) -= other.derived();
+      return const_cast<ExpressionType&>(m_matrix);
+    }
+
+    /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
+    template<typename OtherDerived> EIGEN_STRONG_INLINE
+    CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+                  const ExpressionTypeNestedCleaned,
+                  const typename ExtendedType<OtherDerived>::Type>
+    operator+(const DenseBase<OtherDerived>& other) const
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
+      return m_matrix + extendedTo(other.derived());
+    }
+
+    /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
+    template<typename OtherDerived>
+    CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
+                  const ExpressionTypeNestedCleaned,
+                  const typename ExtendedType<OtherDerived>::Type>
+    operator-(const DenseBase<OtherDerived>& other) const
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
+      return m_matrix - extendedTo(other.derived());
+    }
+
+/////////// Geometry module ///////////
+
+    #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+    Homogeneous<ExpressionType,Direction> homogeneous() const;
+    #endif
+
+    typedef typename ExpressionType::PlainObject CrossReturnType;
+    template<typename OtherDerived>
+    const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
+
+    enum {
+      HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
+                                             : internal::traits<ExpressionType>::ColsAtCompileTime,
+      HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
+    };
+    typedef Block<const ExpressionType,
+                  Direction==Vertical   ? int(HNormalized_SizeMinusOne)
+                                        : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+                  Direction==Horizontal ? int(HNormalized_SizeMinusOne)
+                                        : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+            HNormalized_Block;
+    typedef Block<const ExpressionType,
+                  Direction==Vertical   ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+                  Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+            HNormalized_Factors;
+    typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
+                const HNormalized_Block,
+                const Replicate<HNormalized_Factors,
+                  Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
+                  Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
+            HNormalizedReturnType;
+
+    const HNormalizedReturnType hnormalized() const;
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+  *
+  * Example: \include MatrixBase_colwise.cpp
+  * Output: \verbinclude MatrixBase_colwise.out
+  *
+  * \sa rowwise(), class VectorwiseOp
+  */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstColwiseReturnType
+DenseBase<Derived>::colwise() const
+{
+  return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+  *
+  * \sa rowwise(), class VectorwiseOp
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::ColwiseReturnType
+DenseBase<Derived>::colwise()
+{
+  return derived();
+}
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+  *
+  * Example: \include MatrixBase_rowwise.cpp
+  * Output: \verbinclude MatrixBase_rowwise.out
+  *
+  * \sa colwise(), class VectorwiseOp
+  */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstRowwiseReturnType
+DenseBase<Derived>::rowwise() const
+{
+  return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+  *
+  * \sa colwise(), class VectorwiseOp
+  */
+template<typename Derived>
+inline typename DenseBase<Derived>::RowwiseReturnType
+DenseBase<Derived>::rowwise()
+{
+  return derived();
+}
+
+#endif // EIGEN_PARTIAL_REDUX_H

Eigen/src/Core/Visitor.h

@@ -0,0 +1,248 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_VISITOR_H
+#define EIGEN_VISITOR_H
+
+namespace internal {
+
+template<typename Visitor, typename Derived, int UnrollCount>
+struct visitor_impl
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static void run(const Derived &mat, Visitor& visitor)
+  {
+    visitor_impl<Visitor, Derived, UnrollCount-1>::run(mat, visitor);
+    visitor(mat.coeff(row, col), row, col);
+  }
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, 1>
+{
+  inline static void run(const Derived &mat, Visitor& visitor)
+  {
+    return visitor.init(mat.coeff(0, 0), 0, 0);
+  }
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, Dynamic>
+{
+  typedef typename Derived::Index Index;
+  inline static void run(const Derived& mat, Visitor& visitor)
+  {
+    visitor.init(mat.coeff(0,0), 0, 0);
+    for(Index i = 1; i < mat.rows(); ++i)
+      visitor(mat.coeff(i, 0), i, 0);
+    for(Index j = 1; j < mat.cols(); ++j)
+      for(Index i = 0; i < mat.rows(); ++i)
+        visitor(mat.coeff(i, j), i, j);
+  }
+};
+
+} // end namespace internal
+
+/** Applies the visitor \a visitor to the whole coefficients of the matrix or vector.
+  *
+  * The template parameter \a Visitor is the type of the visitor and provides the following interface:
+  * \code
+  * struct MyVisitor {
+  *   // called for the first coefficient
+  *   void init(const Scalar& value, Index i, Index j);
+  *   // called for all other coefficients
+  *   void operator() (const Scalar& value, Index i, Index j);
+  * };
+  * \endcode
+  *
+  * \note compared to one or two \em for \em loops, visitors offer automatic
+  * unrolling for small fixed size matrix.
+  *
+  * \sa minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()
+  */
+template<typename Derived>
+template<typename Visitor>
+void DenseBase<Derived>::visit(Visitor& visitor) const
+{
+  enum { unroll = SizeAtCompileTime != Dynamic
+                   && CoeffReadCost != Dynamic
+                   && (SizeAtCompileTime == 1 || internal::functor_traits<Visitor>::Cost != Dynamic)
+                   && SizeAtCompileTime * CoeffReadCost + (SizeAtCompileTime-1) * internal::functor_traits<Visitor>::Cost
+                      <= EIGEN_UNROLLING_LIMIT };
+  return internal::visitor_impl<Visitor, Derived,
+      unroll ? int(SizeAtCompileTime) : Dynamic
+    >::run(derived(), visitor);
+}
+
+namespace internal {
+
+/** \internal
+  * \brief Base class to implement min and max visitors
+  */
+template <typename Derived>
+struct coeff_visitor
+{
+  typedef typename Derived::Index Index;
+  typedef typename Derived::Scalar Scalar;
+  Index row, col;
+  Scalar res;
+  inline void init(const Scalar& value, Index i, Index j)
+  {
+    res = value;
+    row = i;
+    col = j;
+  }
+};
+
+/** \internal
+  * \brief Visitor computing the min coefficient with its value and coordinates
+  *
+  * \sa DenseBase::minCoeff(Index*, Index*)
+  */
+template <typename Derived>
+struct min_coeff_visitor : coeff_visitor<Derived>
+{
+  typedef typename Derived::Index Index;
+  typedef typename Derived::Scalar Scalar;
+  void operator() (const Scalar& value, Index i, Index j)
+  {
+    if(value < this->res)
+    {
+      this->res = value;
+      this->row = i;
+      this->col = j;
+    }
+  }
+};
+
+template<typename Scalar>
+struct functor_traits<min_coeff_visitor<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost
+  };
+};
+
+/** \internal
+  * \brief Visitor computing the max coefficient with its value and coordinates
+  *
+  * \sa DenseBase::maxCoeff(Index*, Index*)
+  */
+template <typename Derived>
+struct max_coeff_visitor : coeff_visitor<Derived>
+{
+  typedef typename Derived::Index Index;
+  typedef typename Derived::Scalar Scalar;
+  void operator() (const Scalar& value, Index i, Index j)
+  {
+    if(value > this->res)
+    {
+      this->res = value;
+      this->row = i;
+      this->col = j;
+    }
+  }
+};
+
+template<typename Scalar>
+struct functor_traits<max_coeff_visitor<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost
+  };
+};
+
+} // end namespace internal
+
+/** \returns the minimum of all coefficients of *this
+  * and puts in *row and *col its location.
+  *
+  * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
+  */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* row, IndexType* col) const
+{
+  internal::min_coeff_visitor<Derived> minVisitor;
+  this->visit(minVisitor);
+  *row = minVisitor.row;
+  if (col) *col = minVisitor.col;
+  return minVisitor.res;
+}
+
+/** \returns the minimum of all coefficients of *this
+  * and puts in *index its location.
+  *
+  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
+  */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* index) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  internal::min_coeff_visitor<Derived> minVisitor;
+  this->visit(minVisitor);
+  *index = (RowsAtCompileTime==1) ? minVisitor.col : minVisitor.row;
+  return minVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this
+  * and puts in *row and *col its location.
+  *
+  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+  */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* row, IndexType* col) const
+{
+  internal::max_coeff_visitor<Derived> maxVisitor;
+  this->visit(maxVisitor);
+  *row = maxVisitor.row;
+  if (col) *col = maxVisitor.col;
+  return maxVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this
+  * and puts in *index its location.
+  *
+  * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+  */
+template<typename Derived>
+template<typename IndexType>
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* index) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  internal::max_coeff_visitor<Derived> maxVisitor;
+  this->visit(maxVisitor);
+  *index = (RowsAtCompileTime==1) ? maxVisitor.col : maxVisitor.row;
+  return maxVisitor.res;
+}
+
+#endif // EIGEN_VISITOR_H

Eigen/src/Core/arch/AltiVec/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_AltiVec_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_arch_AltiVec_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/AltiVec COMPONENT Devel
+)

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

@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COMPLEX_ALTIVEC_H
+#define EIGEN_COMPLEX_ALTIVEC_H
+
+namespace internal {
+
+static Packet4ui  p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_ZERO_);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+static Packet16uc p16uc_COMPLEX_RE   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_COMPLEX_IM   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 1), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+static Packet16uc p16uc_COMPLEX_REV  = vec_sld(p16uc_REVERSE, p16uc_REVERSE, 8);//{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
+static Packet16uc p16uc_COMPLEX_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);//{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_PSET_HI = (Packet16uc) vec_mergeh((Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 1));//{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_PSET_LO = (Packet16uc) vec_mergeh((Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 2), (Packet4ui) vec_splat((Packet4ui)p16uc_FORWARD, 3));//{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
+
+//---------- float ----------
+struct Packet2cf
+{
+  EIGEN_STRONG_INLINE Packet2cf() {}
+  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+  Packet4f  v;
+};
+
+template<> struct packet_traits<std::complex<float> >  : default_packet_traits
+{
+  typedef Packet2cf type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size = 2,
+
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasDiv    = 1,
+    HasNegate = 1,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasSetLinear = 0
+  };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
+{
+  Packet2cf res;
+  /* On AltiVec we cannot load 64-bit registers, so wa have to take care of alignment */
+  if((ptrdiff_t(&from) % 16) == 0)
+    res.v = pload<Packet4f>((const float *)&from);
+  else
+    res.v = ploadu<Packet4f>((const float *)&from);
+  res.v = vec_perm(res.v, res.v, p16uc_PSET_HI);
+  return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_add(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_sub(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf((Packet4f)vec_xor((Packet4ui)a.v, p4ui_CONJ_XOR)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  Packet4f v1, v2;
+
+  // Permute and multiply the real parts of a and b
+  v1 = vec_perm(a.v, a.v, p16uc_COMPLEX_RE);
+  // Get the imaginary parts of a
+  v2 = vec_perm(a.v, a.v, p16uc_COMPLEX_IM);
+  // multiply a_re * b 
+  v1 = vec_madd(v1, b.v, p4f_ZERO);
+  // multiply a_im * b and get the conjugate result
+  v2 = vec_madd(v2, b.v, p4f_ZERO);
+  v2 = (Packet4f) vec_xor((Packet4ui)v2, p4ui_CONJ_XOR);
+  // permute back to a proper order
+  v2 = vec_perm(v2, v2, p16uc_COMPLEX_REV);
+  
+  return Packet2cf(vec_add(v1, v2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_or(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_xor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v, vec_nor(b.v,b.v))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
+
+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((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) { vec_dstt((float *)addr, DST_CTRL(2,2,32), DST_CHAN); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
+{
+  std::complex<float> EIGEN_ALIGN16 res[2];
+  pstore((float *)&res, a.v);
+
+  return res[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+  Packet4f rev_a;
+  rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX_REV2);
+  return Packet2cf(rev_a);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+  Packet4f b;
+  b = (Packet4f) vec_sld(a.v, a.v, 8);
+  b = padd(a.v, b);
+  return pfirst(Packet2cf(b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
+{
+  Packet4f b1, b2;
+  
+  b1 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8);
+  b2 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8);
+  b2 = (Packet4f) vec_sld(b2, b2, 8);
+  b2 = padd(b1, b2);
+
+  return Packet2cf(b2);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+  Packet4f b;
+  Packet2cf prod;
+  b = (Packet4f) vec_sld(a.v, a.v, 8);
+  prod = pmul(a, Packet2cf(b));
+
+  return pfirst(prod);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cf>
+{
+  EIGEN_STRONG_INLINE static void run(Packet2cf& first, const Packet2cf& second)
+  {
+    if (Offset==1)
+    {
+      first.v = vec_sld(first.v, second.v, 8);
+    }
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return internal::pmul(a, pconj(b));
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return internal::pmul(pconj(a), b);
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return pconj(internal::pmul(a, b));
+  }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  // TODO optimize it for AltiVec
+  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
+  Packet4f s = vec_madd(b.v, b.v, p4f_ZERO);
+  return Packet2cf(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_COMPLEX_REV))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
+{
+  return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX_REV));
+}
+
+} // end namespace internal
+
+#endif // EIGEN_COMPLEX_ALTIVEC_H

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

@@ -0,0 +1,509 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Konstantinos Margaritis <markos@codex.gr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
+#define EIGEN_PACKET_MATH_ALTIVEC_H
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
+#endif
+
+#ifndef EIGEN_HAS_FUSE_CJMADD
+#define EIGEN_HAS_FUSE_CJMADD 1
+#endif
+
+// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
+#endif
+
+typedef __vector float          Packet4f;
+typedef __vector int            Packet4i;
+typedef __vector unsigned int   Packet4ui;
+typedef __vector __bool int     Packet4bi;
+typedef __vector short int      Packet8i;
+typedef __vector unsigned char  Packet16uc;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
+  Packet4f p4f_##NAME = (Packet4f) vec_splat_s32(X)
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
+  Packet4i p4i_##NAME = vec_splat_s32(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+  Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+  Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+  Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#define DST_CHAN 1
+#define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
+
+// Define global static constants:
+static Packet4f p4f_COUNTDOWN = { 3.0, 2.0, 1.0, 0.0 };
+static Packet4i p4i_COUNTDOWN = { 3, 2, 1, 0 };
+static Packet16uc p16uc_REVERSE = {12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
+static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
+static Packet16uc p16uc_DUPLICATE = {0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7};
+
+static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16);
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1);
+static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0);
+static Packet4f p4f_ZERO_ = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1);
+
+template<> struct packet_traits<float>  : default_packet_traits
+{
+  typedef Packet4f type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=4,
+
+    // FIXME check the Has*
+    HasSin  = 0,
+    HasCos  = 0,
+    HasLog  = 0,
+    HasExp  = 0,
+    HasSqrt = 0
+  };
+};
+template<> struct packet_traits<int>    : default_packet_traits
+{
+  typedef Packet4i type;
+  enum {
+    // FIXME check the Has*
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=4
+  };
+};
+
+template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4}; };
+template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4}; };
+/*
+inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
+{
+  union {
+    Packet4f   v;
+    float n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
+{
+  union {
+    Packet4i   v;
+    int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
+{
+  union {
+    Packet4ui   v;
+    unsigned int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packetbi & v)
+{
+  union {
+    Packet4bi v;
+    unsigned int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+*/
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  float EIGEN_ALIGN16 af[4];
+  af[0] = from;
+  Packet4f vc = vec_ld(0, af);
+  vc = vec_splat(vc, 0);
+  return vc;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
+  int EIGEN_ALIGN16 ai[4];
+  ai[0] = from;
+  Packet4i vc = vec_ld(0, ai);
+  vc = vec_splat(vc, 0);
+  return vc;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return vec_add(pset1<Packet4f>(a), p4f_COUNTDOWN); }
+template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a)     { return vec_add(pset1<Packet4i>(a), p4i_COUNTDOWN); }
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_add(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_add(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_sub(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_sub(a,b); }
+
+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 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
+ *
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+  // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
+  //Set up constants, variables
+  Packet4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
+
+  // Get the absolute values
+  a1  = vec_abs(a);
+  b1  = vec_abs(b);
+
+  // Get the signs using xor
+  Packet4bi sgn = (Packet4bi) vec_cmplt(vec_xor(a, b), p4i_ZERO);
+
+  // Do the multiplication for the asbolute values.
+  bswap = (Packet4i) vec_rl((Packet4ui) b1, (Packet4ui) p4i_MINUS16 );
+  low_prod = vec_mulo((Packet8i) a1, (Packet8i)b1);
+  high_prod = vec_msum((Packet8i) a1, (Packet8i) bswap, p4i_ZERO);
+  high_prod = (Packet4i) vec_sl((Packet4ui) high_prod, (Packet4ui) p4i_MINUS16);
+  prod = vec_add( low_prod, high_prod );
+
+  // NOR the product and select only the negative elements according to the sign mask
+  prod_ = vec_nor(prod, prod);
+  prod_ = vec_sel(p4i_ZERO, prod_, sgn);
+
+  // Add 1 to the result to get the negative numbers
+  v1sel = vec_sel(p4i_ZERO, p4i_ONE, sgn);
+  prod_ = vec_add(prod_, v1sel);
+
+  // Merge the results back to the final vector.
+  prod = vec_sel(prod, prod_, sgn);
+
+  return prod;
+}
+*/
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+  Packet4f t, y_0, y_1, res;
+
+  // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
+  y_0 = vec_re(b);
+
+  // Do one Newton-Raphson iteration to get the needed accuracy
+  t   = vec_nmsub(y_0, b, p4f_ONE);
+  y_1 = vec_madd(y_0, t, y_0);
+
+  res = vec_madd(a, y_1, p4f_ZERO);
+  return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by AltiVec");
+  return pset1<Packet4i>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{
+  EIGEN_DEBUG_ALIGNED_LOAD
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  Packet16uc MSQ, LSQ;
+  Packet16uc mask;
+  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
+  mask = vec_lvsl(0, from);                        // create the permute mask
+  return (Packet4f) vec_perm(MSQ, LSQ, mask);           // align the data
+
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
+{
+  EIGEN_DEBUG_ALIGNED_LOAD
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  Packet16uc MSQ, LSQ;
+  Packet16uc mask;
+  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
+  mask = vec_lvsl(0, from);                        // create the permute mask
+  return (Packet4i) vec_perm(MSQ, LSQ, mask);    // align the data
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
+{
+  Packet4f p;
+  if((ptrdiff_t(&from) % 16) == 0)  p = pload<Packet4f>(from);
+  else                              p = ploadu<Packet4f>(from);
+  return vec_perm(p, p, p16uc_DUPLICATE);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
+{
+  Packet4i p;
+  if((ptrdiff_t(&from) % 16) == 0)  p = pload<Packet4i>(from);
+  else                              p = ploadu<Packet4i>(from);
+  return vec_perm(p, p, p16uc_DUPLICATE);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from)
+{
+  EIGEN_DEBUG_UNALIGNED_STORE
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  // Warning: not thread safe!
+  Packet16uc MSQ, LSQ, edges;
+  Packet16uc edgeAlign, align;
+
+  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
+  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
+  edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
+  align = vec_lvsr( 0, to );                                // permute map to misalign data
+  MSQ = vec_perm(edges,(Packet16uc)from,align);             // misalign the data (MSQ)
+  LSQ = vec_perm((Packet16uc)from,edges,align);             // misalign the data (LSQ)
+  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
+  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from)
+{
+  EIGEN_DEBUG_UNALIGNED_STORE
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  // Warning: not thread safe!
+  Packet16uc MSQ, LSQ, edges;
+  Packet16uc edgeAlign, align;
+
+  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
+  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
+  edges=vec_perm(LSQ, MSQ, edgeAlign);                      // extract the edges
+  align = vec_lvsr( 0, to );                                // permute map to misalign data
+  MSQ = vec_perm(edges, (Packet16uc) from, align);          // misalign the data (MSQ)
+  LSQ = vec_perm((Packet16uc) from, edges, align);          // misalign the data (LSQ)
+  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
+  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
+
+template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
+template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return (Packet4f)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return (Packet4i)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+  Packet4f b, sum;
+  b   = (Packet4f) vec_sld(a, a, 8);
+  sum = vec_add(a, b);
+  b   = (Packet4f) vec_sld(sum, sum, 4);
+  sum = vec_add(sum, b);
+  return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
+{
+  Packet4f v[4], sum[4];
+
+  // It's easier and faster to transpose then add as columns
+  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+  // Do the transpose, first set of moves
+  v[0] = vec_mergeh(vecs[0], vecs[2]);
+  v[1] = vec_mergel(vecs[0], vecs[2]);
+  v[2] = vec_mergeh(vecs[1], vecs[3]);
+  v[3] = vec_mergel(vecs[1], vecs[3]);
+  // Get the resulting vectors
+  sum[0] = vec_mergeh(v[0], v[2]);
+  sum[1] = vec_mergel(v[0], v[2]);
+  sum[2] = vec_mergeh(v[1], v[3]);
+  sum[3] = vec_mergel(v[1], v[3]);
+
+  // Now do the summation:
+  // Lines 0+1
+  sum[0] = vec_add(sum[0], sum[1]);
+  // Lines 2+3
+  sum[1] = vec_add(sum[2], sum[3]);
+  // Add the results
+  sum[0] = vec_add(sum[0], sum[1]);
+
+  return sum[0];
+}
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+  Packet4i sum;
+  sum = vec_sums(a, p4i_ZERO);
+  sum = vec_sld(sum, p4i_ZERO, 12);
+  return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
+{
+  Packet4i v[4], sum[4];
+
+  // It's easier and faster to transpose then add as columns
+  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+  // Do the transpose, first set of moves
+  v[0] = vec_mergeh(vecs[0], vecs[2]);
+  v[1] = vec_mergel(vecs[0], vecs[2]);
+  v[2] = vec_mergeh(vecs[1], vecs[3]);
+  v[3] = vec_mergel(vecs[1], vecs[3]);
+  // Get the resulting vectors
+  sum[0] = vec_mergeh(v[0], v[2]);
+  sum[1] = vec_mergel(v[0], v[2]);
+  sum[2] = vec_mergeh(v[1], v[3]);
+  sum[3] = vec_mergel(v[1], v[3]);
+
+  // Now do the summation:
+  // Lines 0+1
+  sum[0] = vec_add(sum[0], sum[1]);
+  // Lines 2+3
+  sum[1] = vec_add(sum[2], sum[3]);
+  // Add the results
+  sum[0] = vec_add(sum[0], sum[1]);
+
+  return sum[0];
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+  Packet4f prod;
+  prod = pmul(a, (Packet4f)vec_sld(a, a, 8));
+  return pfirst(pmul(prod, (Packet4f)vec_sld(prod, prod, 4)));
+}
+
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+  EIGEN_ALIGN16 int aux[4];
+  pstore(aux, a);
+  return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+  Packet4f b, res;
+  b = vec_min(a, vec_sld(a, a, 8));
+  res = vec_min(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+  Packet4i b, res;
+  b = vec_min(a, vec_sld(a, a, 8));
+  res = vec_min(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+  Packet4f b, res;
+  b = vec_max(a, vec_sld(a, a, 8));
+  res = vec_max(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+  Packet4i b, res;
+  b = vec_max(a, vec_sld(a, a, 8));
+  res = vec_max(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet4f>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4f& first, const Packet4f& second)
+  {
+    if (Offset!=0)
+      first = vec_sld(first, second, Offset*4);
+  }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet4i>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4i& first, const Packet4i& second)
+  {
+    if (Offset!=0)
+      first = vec_sld(first, second, Offset*4);
+  }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_PACKET_MATH_ALTIVEC_H

Eigen/src/Core/arch/CMakeLists.txt

@@ -0,0 +1,4 @@
+ADD_SUBDIRECTORY(SSE)
+ADD_SUBDIRECTORY(AltiVec)
+ADD_SUBDIRECTORY(NEON)
+ADD_SUBDIRECTORY(Default)

Eigen/src/Core/arch/Default/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_Default_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_arch_Default_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/Default COMPONENT Devel
+)

Eigen/src/Core/arch/Default/Settings.h

@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+
+/* All the parameters defined in this file can be specialized in the
+ * architecture specific files, and/or by the user.
+ * More to come... */
+
+#ifndef EIGEN_DEFAULT_SETTINGS_H
+#define EIGEN_DEFAULT_SETTINGS_H
+
+/** Defines the maximal loop size to enable meta unrolling of loops.
+  * Note that the value here is expressed in Eigen's own notion of "number of FLOPS",
+  * it does not correspond to the number of iterations or the number of instructions
+  */
+#ifndef EIGEN_UNROLLING_LIMIT
+#define EIGEN_UNROLLING_LIMIT 100
+#endif
+
+/** Defines the threshold between a "small" and a "large" matrix.
+  * This threshold is mainly used to select the proper product implementation.
+  */
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+/** Defines the maximal width of the blocks used in the triangular product and solver
+  * for vectors (level 2 blas xTRMV and xTRSV). The default is 8.
+  */
+#ifndef EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH
+#define EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH 8
+#endif
+
+
+/** Defines the default number of registers available for that architecture.
+  * Currently it must be 8 or 16. Other values will fail.
+  */
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8
+#endif
+
+#endif // EIGEN_DEFAULT_SETTINGS_H

Eigen/src/Core/arch/NEON/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_NEON_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_arch_NEON_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/NEON COMPONENT Devel
+)

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

@@ -0,0 +1,270 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COMPLEX_NEON_H
+#define EIGEN_COMPLEX_NEON_H
+
+namespace internal {
+
+static uint32x4_t p4ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET4(0x00000000, 0x80000000, 0x00000000, 0x80000000);
+static uint32x2_t p2ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x00000000, 0x80000000);
+
+//---------- float ----------
+struct Packet2cf
+{
+  EIGEN_STRONG_INLINE Packet2cf() {}
+  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+  Packet4f  v;
+};
+
+template<> struct packet_traits<std::complex<float> >  : default_packet_traits
+{
+  typedef Packet2cf type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size = 2,
+
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasDiv    = 1,
+    HasNegate = 1,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasSetLinear = 0
+  };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
+{
+  float32x2_t r64;
+  r64 = vld1_f32((float *)&from);
+
+  return Packet2cf(vcombine_f32(r64, r64));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+  Packet4ui b = vreinterpretq_u32_f32(a.v);
+  return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR)));
+}
+
+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));
+  // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
+  v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));
+  // Multiply the real a with b
+  v1 = vmulq_f32(v1, b.v);
+  // Multiply the imag a with b
+  v2 = vmulq_f32(v2, b.v);
+  // 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));
+  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));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
+
+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((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 std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
+{
+  std::complex<float> EIGEN_ALIGN16 x[2];
+  vst1q_f32((float *)x, a.v);
+  return x[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+  float32x2_t a_lo, a_hi;
+  Packet4f a_r128;
+
+  a_lo = vget_low_f32(a.v);
+  a_hi = vget_high_f32(a.v);
+  a_r128 = vcombine_f32(a_hi, a_lo);
+
+  return Packet2cf(a_r128);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)
+{
+  return Packet2cf(vrev64q_f32(a.v));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+  float32x2_t a1, a2;
+  std::complex<float> s;
+
+  a1 = vget_low_f32(a.v);
+  a2 = vget_high_f32(a.v);
+  a2 = vadd_f32(a1, a2);
+  vst1_f32((float *)&s, a2);
+
+  return s;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
+{
+  Packet4f sum1, sum2, sum;
+
+  // Add the first two 64-bit float32x2_t of vecs[0]
+  sum1 = vcombine_f32(vget_low_f32(vecs[0].v), vget_low_f32(vecs[1].v));
+  sum2 = vcombine_f32(vget_high_f32(vecs[0].v), vget_high_f32(vecs[1].v));
+  sum = vaddq_f32(sum1, sum2);
+
+  return Packet2cf(sum);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+  float32x2_t a1, a2, v1, v2, prod;
+  std::complex<float> s;
+
+  a1 = vget_low_f32(a.v);
+  a2 = vget_high_f32(a.v);
+   // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+  v1 = vdup_lane_f32(a1, 0);
+  // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
+  v2 = vdup_lane_f32(a1, 1);
+  // Multiply the real a with b
+  v1 = vmul_f32(v1, a2);
+  // Multiply the imag a with b
+  v2 = vmul_f32(v2, a2);
+  // Conjugate v2 
+  v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR));
+  // Swap real/imag elements in v2.
+  v2 = vrev64_f32(v2);
+  // Add v1, v2
+  prod = vadd_f32(v1, v2);
+
+  vst1_f32((float *)&s, prod);
+
+  return s;
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cf>
+{
+  EIGEN_STRONG_INLINE static void run(Packet2cf& first, const Packet2cf& second)
+  {
+    if (Offset==1)
+    {
+      first.v = vextq_f32(first.v, second.v, 2);
+    }
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return internal::pmul(a, pconj(b));
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return internal::pmul(pconj(a), b);
+  }
+};
+
+template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
+  {
+    return pconj(internal::pmul(a, b));
+  }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+  // 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));
+  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)));
+}
+
+} // end namespace internal
+
+#endif // EIGEN_COMPLEX_NEON_H