Fix undefined behavior in PPC load.

VSX vec_xl is Causing a bunch of test failures and failing `-fsanitize=undefined` with g++. Removing the instruction allows tests to pass and eliminates the warning.
Fix CUDA clang again with new C++11 usages
2026-04-10 11:34:33 +08:00 · 2025-03-14 07:58:36 -07:00 · 2025-03-14 07:58:29 -07:00 · 2025-03-13 15:01:33 -07:00 · 2025-03-13 21:49:24 +00:00 · 2025-03-13 11:13:35 -07:00
1812 changed files with 171713 additions and 267376 deletions
--- a/.git-blame-ignore-revs
+++ b/.git-blame-ignore-revs
@@ -1,4 +0,0 @@
 # First major clang-format MR (https://gitlab.com/libeigen/eigen/-/merge_requests/1429).
 f38e16c193d489c278c189bc06b448a94adb45fb
 # Formatting of tests, examples, benchmarks, et cetera (https://gitlab.com/libeigen/eigen/-/merge_requests/1432).
 46e9cdb7fea25d7f7aef4332b9c3ead3857e213d
--- a/.gitattributes
+++ b/.gitattributes
@@ -1,3 +0,0 @@
 *.sh                         eol=lf
 debug/msvc/*.dat             eol=crlf
 debug/msvc/*.natvis          eol=crlf
--- a/.gitignore
+++ b/.gitignore
@@ -12,7 +12,7 @@ core
 core.*
 *.bak
 *~
-*.build*
+*build*
 *.moc.*
 *.moc
 ui_*
@@ -35,7 +35,3 @@ lapack/reference
 .*project
 .settings
 Makefile
 !ci/build.gitlab-ci.yml
 !scripts/buildtests.in
 !Eigen/Core
 !Eigen/src/Core
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -7,10 +7,6 @@
 # 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/.
 default:
 # automatically cancels a job when a new pipeline for the same branch is triggered
  interruptible: true
 stages:
  - checkformat
  - build
--- a/.gitlab/issue_templates/Bug
+++ b/.gitlab/issue_templates/Bug
@@ -1,69 +0,0 @@
 <!--
 Please read this!
 Before opening a new issue, make sure to search for keywords in the issues
 filtered by "bug::confirmed" or "bug::unconfirmed" and "bugzilla" label:
 - https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bug%3A%3Aconfirmed
 - https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bug%3A%3Aunconfirmed
 - https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bugzilla
 and verify the issue you're about to submit isn't a duplicate. -->
 ### Summary
 <!-- Summarize the bug encountered concisely. -->
 ### Environment
 <!-- Please provide your development environment here -->
 - **Operating System** : Windows/Linux
 - **Architecture** : x64/Arm64/PowerPC ...
 - **Eigen Version** : 3.3.9
 - **Compiler Version** : Gcc7.0
 - **Compile Flags** : -O3 -march=native
 - **Vector Extension** : SSE/AVX/NEON ...
 ### Minimal Example
 <!-- If possible, please create a minimal example here that exhibits the problematic behavior.
 You can also link to [godbolt](https://godbolt.org). But please note that you need to click 
 the "Share" button in the top right-hand corner of the godbolt page where you reproduce the sample 
 code to get the share link instead of in your browser address bar. 
 You can read [the guidelines on stackoverflow](https://stackoverflow.com/help/minimal-reproducible-example)
 on how to create a good minimal example. -->
 ```cpp
 //show your code here
 ```
 ### Steps to reproduce
 <!-- Describe how one can reproduce the issue - this is very important. Please use an ordered list. -->
 1. first step
 2. second step
 3. ... 
 ### What is the current *bug* behavior?
 <!-- Describe what actually happens. -->
 ### What is the expected *correct* behavior?
 <!-- Describe what you should see instead. -->
 ### Relevant logs
 <!-- Add relevant code snippets or program output within blocks marked by " ``` " -->
 <!-- OPTIONAL: remove this section if you are not reporting a compilation warning issue.-->
 ### Warning Messages
 <!-- Show us the warning messages you got! -->
 <!-- OPTIONAL: remove this section if you are not reporting a performance issue. -->
 ### Benchmark scripts and results
 <!-- Please share any benchmark scripts - either standalone, or using [Google Benchmark](https://github.com/google/benchmark). -->
 ### Anything else that might help
 <!-- It will be better to provide us more information to help narrow down the cause. 
 Including but not limited to the following: 
 - lines of code that might help us diagnose the problem. 
 - potential ways to address the issue.
 - last known working/first broken version (release number or commit hash). --> 
 - [ ] Have a plan to fix this issue.
--- a/.gitlab/issue_templates/Feature
+++ b/.gitlab/issue_templates/Feature
@@ -1,7 +0,0 @@
 ### Describe the feature you would like to be implemented.
 ### Would such a feature be useful for other users? Why?
 ### Any hints on how to implement the requested feature?
 ### Additional resources
--- a/.gitlab/merge_request_templates/Merge
+++ b/.gitlab/merge_request_templates/Merge
@@ -1,26 +0,0 @@
 <!-- 
 Thanks for contributing a merge request! Please name and fully describe your MR as you would for a commit message.
 If the MR fixes an issue, please include "Fixes #issue" in the commit message and the MR description.
 In addition, we recommend that first-time contributors read our [contribution guidelines](https://eigen.tuxfamily.org/index.php?title=Contributing_to_Eigen) and [git page](https://eigen.tuxfamily.org/index.php?title=Git), which will help you submit a more standardized MR.
 Before submitting the MR, you also need to complete the following checks:
 - Make one PR per feature/bugfix (don't mix multiple changes into one PR). Avoid committing unrelated changes.
 - Rebase before committing
 - For code changes, run the test suite (at least the tests that are likely affected by the change).
  See our [test guidelines](https://eigen.tuxfamily.org/index.php?title=Tests).
 - If possible, add a test (both for bug-fixes as well as new features)
 - Make sure new features are documented
 Note that we are a team of volunteers; we appreciate your patience during the review process.
 Again, thanks for contributing! -->
 ### Reference issue
 <!-- You can link to a specific issue using the gitlab syntax #<issue number>  -->
 ### What does this implement/fix?
 <!--Please explain your changes.-->
 ### Additional information
 <!--Any additional information you think is important.-->
--- a/.hgeol
+++ b/.hgeol
@@ -0,0 +1,11 @@
 [patterns]
 *.sh = LF
 *.MINPACK = CRLF
 scripts/*.in = LF
 debug/msvc/*.dat = CRLF
 debug/msvc/*.natvis = CRLF
 unsupported/test/mpreal/*.* = CRLF
 ** = native
 [repository]
 native = LF
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,339 +1,91 @@
-cmake_minimum_required(VERSION 3.10.0)
+cmake_minimum_required(VERSION 2.8.5)
 #==============================================================================
 # CMake Policy issues.
 #==============================================================================
 # Allow overriding options in a parent project via `set` before including Eigen.
 if (POLICY CMP0077)
  cmake_policy (SET CMP0077 NEW)
 endif (POLICY CMP0077)
 # NOTE Remove setting the policy once the minimum required CMake version is
 # increased to at least 3.15. Retain enabling the export to package registry.
 if (POLICY CMP0090)
  # The export command does not populate package registry by default
  cmake_policy (SET CMP0090 NEW)
  # Unless otherwise specified, always export to package registry to ensure
  # backwards compatibility.
  if (NOT DEFINED CMAKE_EXPORT_PACKAGE_REGISTRY)
    set (CMAKE_EXPORT_PACKAGE_REGISTRY ON)
  endif (NOT DEFINED CMAKE_EXPORT_PACKAGE_REGISTRY)
 endif (POLICY CMP0090)
 # Disable warning about find_package(CUDA).
 # CUDA language support is lacking for clang as the CUDA compiler
 # until at least cmake version 3.18.  Even then, there seems to be
 # issues on Windows+Ninja in passing build flags.  Continue using
 # the "old" way for now.
 if (POLICY CMP0146)
  cmake_policy(SET CMP0146 OLD)
 endif ()
 # Normalize DESTINATION paths
 if (POLICY CMP0177)
  cmake_policy(SET CMP0177 NEW)
 endif ()
 #==============================================================================
 # CMake Project.
 #==============================================================================
 project(Eigen3)
-# Remove this block after bumping CMake to v3.21.0
+# guard against in-source builds
 # PROJECT_IS_TOP_LEVEL is defined then by default
 if(CMAKE_VERSION VERSION_LESS 3.21.0)
  if(CMAKE_SOURCE_DIR STREQUAL CMAKE_CURRENT_SOURCE_DIR)
    set(PROJECT_IS_TOP_LEVEL ON)
  else()
    set(PROJECT_IS_TOP_LEVEL OFF)
  endif()
 endif()
 #==============================================================================
 # Build ON/OFF Settings.
 #==============================================================================
 # Determine if we should build tests.
 include(CMakeDependentOption)
 cmake_dependent_option(BUILD_TESTING "Enable creation of tests." ON "PROJECT_IS_TOP_LEVEL" OFF)
 option(EIGEN_BUILD_TESTING "Enable creation of Eigen tests." ${BUILD_TESTING})
 option(EIGEN_LEAVE_TEST_IN_ALL_TARGET "Leaves tests in the all target, needed by ctest for automatic building." OFF)
 # Determine if we should build BLAS/LAPACK implementations.
 option(EIGEN_BUILD_BLAS "Toggles the building of the Eigen Blas library" ${PROJECT_IS_TOP_LEVEL})
 option(EIGEN_BUILD_LAPACK "Toggles the building of the included Eigen LAPACK library" ${PROJECT_IS_TOP_LEVEL})
 if (EIGEN_BUILD_BLAS OR EIGEN_BUILD_LAPACK)
  # Determine if we should build shared libraries for BLAS/LAPACK on this platform.
  if (NOT EIGEN_BUILD_SHARED_LIBS)
    get_cmake_property(EIGEN_BUILD_SHARED_LIBS TARGET_SUPPORTS_SHARED_LIBS)
  endif()
 endif()
 option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
 option(EIGEN_BUILD_SPBENCH "Build sparse benchmark suite" OFF)
 # Avoid building docs if included from another project.
 # Building documentation requires creating and running executables on the host
 # platform.  We shouldn't do this if cross-compiling.
 if (PROJECT_IS_TOP_LEVEL AND NOT CMAKE_CROSSCOMPILING)
  set(EIGEN_BUILD_DOC_DEFAULT ON)
 endif()
 option(EIGEN_BUILD_DOC "Enable creation of Eigen documentation" ${EIGEN_BUILD_DOC_DEFAULT})
 option(EIGEN_BUILD_DEMOS "Toggles the building of the Eigen demos" ${PROJECT_IS_TOP_LEVEL})
 # Disable pkgconfig only for native Windows builds
 if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)
  option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ${PROJECT_IS_TOP_LEVEL})
 endif()
 option(EIGEN_BUILD_CMAKE_PACKAGE "Enables the creation of EigenConfig.cmake and related files" ${PROJECT_IS_TOP_LEVEL})
 if (EIGEN_BUILD_TESTING OR EIGEN_BUILD_BLAS OR EIGEN_BUILD_LAPACK OR EIGEN_BUILT_BTL OR EIGEN_BUILD_BTL OR EIGEN_BUILD_SPBENCH OR EIGEN_BUILD_DOC OR EIGEN_BUILD_DEMOS)
  set(EIGEN_IS_BUILDING_ ON)
 endif()
 #==============================================================================
 # Version Info.
 #==============================================================================
 # If version information is not provided, automatically parse the version number
 # from header files.
 file(READ "${PROJECT_SOURCE_DIR}/Eigen/Version" _eigen_version_header)
 if (NOT DEFINED EIGEN_WORLD_VERSION)
  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}")
 endif()
 if (NOT DEFINED EIGEN_MAJOR_VERSION)
  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}")
 endif()
 if (NOT DEFINED EIGEN_MINOR_VERSION)
  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}")
 endif()
 if (NOT DEFINED EIGEN_PATCH_VERSION)
  string(REGEX MATCH "define[ \t]+EIGEN_PATCH_VERSION[ \t]+([0-9]+)" _eigen_patch_version_match "${_eigen_version_header}")
  set(EIGEN_PATCH_VERSION "${CMAKE_MATCH_1}")
 endif()
 if (NOT DEFINED EIGEN_PRERELEASE_VERSION)
  set(EIGEN_PRERELEASE_VERSION "dev")
 endif()
 # If we are in a git repo, extract a changeset.
 if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.git)
  # if the git program is absent or this will leave the EIGEN_GIT_REVNUM string empty,
  # but won't stop CMake.
  execute_process(COMMAND git ls-remote -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT)
 endif()
 # extract the git rev number from the git output...
 if(EIGEN_GIT_OUTPUT)
  string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}")
  set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}")
 endif()
 if (NOT DEFINED EIGEN_BUILD_VERSION AND DEFINED EIGEN_GIT_REVNUM)
  string(SUBSTRING "${EIGEN_GIT_REVNUM}" 0 8 EIGEN_BUILD_VERSION)
 else()
  set(EIGEN_BUILD_VERSION "")
 endif()
 # The EIGEN_VERSION_NUMBER must be of the form <major.minor.patch>.
 # The EIGEN_VERSION_STRING can contain the preprelease/build strings.
 set(EIGEN_VERSION_NUMBER "${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION}.${EIGEN_PATCH_VERSION}")
 set(EIGEN_VERSION_STRING "${EIGEN_VERSION_NUMBER}")
 if (NOT "x${EIGEN_PRERELEASE_VERSION}" STREQUAL "x")
  set(EIGEN_VERSION_STRING "${EIGEN_VERSION_STRING}-${EIGEN_PRERELEASE_VERSION}")
 endif()
 if (NOT "x${EIGEN_BUILD_VERSION}" STREQUAL "x")
  set(EIGEN_VERSION_STRING "${EIGEN_VERSION_STRING}+${EIGEN_BUILD_VERSION}")
 endif()
 # Generate version file.
 configure_file("${CMAKE_CURRENT_SOURCE_DIR}/cmake/Version.in"
               "${CMAKE_CURRENT_BINARY_DIR}/include/Eigen/Version")
 #==============================================================================
 # Install Path Configuration.
 #==============================================================================
 # Unconditionally allow install of targets to support nested dependency
 # installations.
 #
 # Note: projects that depend on Eigen should _probably_ exclude installing
 # Eigen by default (e.g. by using EXCLUDE_FROM_ALL when using
 # FetchContent_Declare or add_subdirectory) to avoid overwriting a previous
 # installation.
 include(GNUInstallDirs)
 # Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR
 if(EIGEN_INCLUDE_INSTALL_DIR)
  message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.")
 endif()
 if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)
  set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}
      CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed")
 else()
  set(INCLUDE_INSTALL_DIR
      "${CMAKE_INSTALL_INCLUDEDIR}/eigen3"
      CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed"
      )
 endif()
 set(CMAKEPACKAGE_INSTALL_DIR
    "${CMAKE_INSTALL_DATADIR}/eigen3/cmake"
    CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen3Config.cmake is installed"
    )
 set(PKGCONFIG_INSTALL_DIR
    "${CMAKE_INSTALL_DATADIR}/pkgconfig"
    CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where eigen3.pc is installed"
    )
 foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR)
  # If an absolute path is specified, make it relative to "{CMAKE_INSTALL_PREFIX}".
  if(IS_ABSOLUTE "${${var}}")
    file(RELATIVE_PATH "${var}" "${CMAKE_INSTALL_PREFIX}" "${${var}}")
  endif()
 endforeach()
 #==============================================================================
 # Eigen Library.
 #==============================================================================
 # Alias Eigen_*_DIR to Eigen3_*_DIR:
 set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
 set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
 # Imported target support
 add_library (eigen INTERFACE)
 add_library (Eigen3::Eigen ALIAS eigen)
 target_include_directories (eigen INTERFACE
  $<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
  $<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
 )
 # Eigen requires at least C++14
 target_compile_features (eigen INTERFACE cxx_std_14)
 # Export as title case Eigen
 set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
 #==============================================================================
 # Install Rule Configuration.
 #==============================================================================
 install(FILES
  signature_of_eigen3_matrix_library
  DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel
  )
 if(EIGEN_BUILD_PKGCONFIG)
    configure_file(eigen3.pc.in eigen3.pc @ONLY)
    install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
        DESTINATION ${PKGCONFIG_INSTALL_DIR})
 endif()
 install(DIRECTORY Eigen DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel)
 # Replace the "Version" header file with the generated one.
 install(FILES ${CMAKE_CURRENT_BINARY_DIR}/include/Eigen/Version
    DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/ COMPONENT Devel)
 install(TARGETS eigen EXPORT Eigen3Targets)
 if(EIGEN_BUILD_CMAKE_PACKAGE)
  include (CMakePackageConfigHelpers)
  configure_package_config_file (
    ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in
    ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
    INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
    NO_SET_AND_CHECK_MACRO # Eigen does not provide legacy style defines
    NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
  )
  set(CVF_VERSION "${EIGEN_VERSION_NUMBER}")
  configure_file("${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigVersion.cmake.in"
                 "Eigen3ConfigVersion.cmake"
                 @ONLY)
  # The Eigen target will be located in the Eigen3 namespace. Other CMake
  # targets can refer to it using Eigen3::Eigen.
  export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)
  # Export Eigen3 package to CMake registry such that it can be easily found by
  # CMake even if it has not been installed to a standard directory.
  export (PACKAGE Eigen3)
  install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
  install (FILES ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
                ${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake
          DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
  # Add uninstall target
  if(NOT TARGET uninstall AND PROJECT_IS_TOP_LEVEL)
    add_custom_target ( uninstall
        COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
  endif()
 endif()
 #==============================================================================
 # General Build Configuration.
 #==============================================================================
 # Avoid setting the standard in a parent if unset.
 if(PROJECT_IS_TOP_LEVEL)
  set(CMAKE_CXX_STANDARD 14 CACHE STRING "Default C++ standard")
  set(CMAKE_CXX_STANDARD_REQUIRED ON CACHE BOOL "Require C++ standard")
  set(CMAKE_CXX_EXTENSIONS OFF CACHE BOOL "Allow C++ extensions")
 endif()
 # Guard against in-source builds
 if(${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
+# Alias Eigen_*_DIR to Eigen3_*_DIR:
-if (PROJECT_IS_TOP_LEVEL AND NOT CMAKE_BUILD_TYPE)
+
 set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
 set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
 # guard against bad build-type strings
 if (NOT CMAKE_BUILD_TYPE)
  set(CMAKE_BUILD_TYPE "Release")
 endif()
-# Only try to figure out how to link the math library if we are building something.
+#############################################################################
-# Otherwise, let the parent project deal with dependencies.
+# retrieve version infomation                                               #
-if (EIGEN_IS_BUILDING_)
+#############################################################################
-  # Use Eigen's cmake files.
+
 # automatically parse the version number
 file(READ "${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 we are not in a mercurial clone
 if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.hg)
  # if the mercurial program is absent or 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 ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_BRANCH_OUTPUT)
 endif()
 # if this is the default (aka development) branch, extract the mercurial changeset number from the hg tip output...
 if(EIGEN_BRANCH_OUTPUT MATCHES "default")
 string(REGEX MATCH "^changeset: *[0-9]*:([0-9;a-f]+).*" EIGEN_HG_CHANGESET_MATCH "${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)
 include(GNUInstallDirs)
 set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
  set(CMAKE_INCLUDE_CURRENT_DIR OFF)
-  find_package(StandardMathLibrary)
+option(EIGEN_TEST_CXX11 "Enable testing with C++11 and C++11 features (e.g. Tensor module)." OFF)
-  set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
+
-  if(NOT STANDARD_MATH_LIBRARY_FOUND)
+
-    message(FATAL_ERROR
+macro(ei_add_cxx_compiler_flag FLAG)
-      "Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
+  string(REGEX REPLACE "-" "" SFLAG1 ${FLAG})
  string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1})
  check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
  if(COMPILER_SUPPORT_${SFLAG})
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
  endif()
 endmacro(ei_add_cxx_compiler_flag)
 check_cxx_compiler_flag("-std=c++11" EIGEN_COMPILER_SUPPORT_CPP11)
 if(EIGEN_TEST_CXX11)
  set(CMAKE_CXX_STANDARD 11)
  set(CMAKE_CXX_EXTENSIONS OFF)
  if(EIGEN_COMPILER_SUPPORT_CPP11)
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
  endif()
 else()
-    if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+  #set(CMAKE_CXX_STANDARD 03)
-      set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}")
+  #set(CMAKE_CXX_EXTENSIONS OFF)
-    else()
+  ei_add_cxx_compiler_flag("-std=c++03")
      set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}")
    endif()
  endif()
  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
    message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}")
  else()
    message(STATUS "Standard libraries to link to explicitly: none")
 endif()
  # Default tests/examples/libraries to row-major.
  option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF)
  if(EIGEN_DEFAULT_TO_ROW_MAJOR)
    add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR")
  endif()
 endif()
 #==============================================================================
 # Test Configuration.
 #==============================================================================
 if (EIGEN_BUILD_TESTING)
 function(ei_maybe_separate_arguments variable mode args)
  # Use separate_arguments if the input is a single string containing a space.
  # Otherwise, if it is already a list or doesn't have a space, just propagate
@@ -348,26 +100,61 @@ if (EIGEN_BUILD_TESTING)
  set(${variable} ${args} PARENT_SCOPE)
 endfunction(ei_maybe_separate_arguments)
-  include(CheckCXXCompilerFlag)
+#############################################################################
-  macro(ei_add_cxx_compiler_flag FLAG)
+# find how to link to the standard libraries                                #
-    string(REGEX REPLACE "-" "" SFLAG1 ${FLAG})
+#############################################################################
-    string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1})
+
-    check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
+find_package(StandardMathLibrary)
-    if(COMPILER_SUPPORT_${SFLAG})
+
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
    endif()
  endmacro()
 set(EIGEN_TEST_CUSTOM_LINKER_FLAGS  "" CACHE STRING "Additional linker flags when linking unit tests.")
 set(EIGEN_TEST_CUSTOM_CXX_FLAGS     "" CACHE STRING "Additional compiler flags when compiling unit tests.")
 # Convert space-separated arguments into CMake lists for downstream consumption.
 ei_maybe_separate_arguments(EIGEN_TEST_CUSTOM_LINKER_FLAGS NATIVE_COMMAND "${EIGEN_TEST_CUSTOM_LINKER_FLAGS}")
 ei_maybe_separate_arguments(EIGEN_TEST_CUSTOM_CXX_FLAGS NATIVE_COMMAND "${EIGEN_TEST_CUSTOM_CXX_FLAGS}")
 set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
 if(NOT STANDARD_MATH_LIBRARY_FOUND)
  message(FATAL_ERROR
    "Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
 else()
  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
    set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${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)
 # Disable pkgconfig only for native Windows builds
 if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)
  option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON)
 endif()
 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()
 set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320")
  # Flags for tests.
 if(NOT MSVC)
  # We assume that other compilers are partly compatible with GNUCC
@@ -381,6 +168,7 @@ if (EIGEN_BUILD_TESTING)
  ei_add_cxx_compiler_flag("-Wall")
  ei_add_cxx_compiler_flag("-Wextra")
  #ei_add_cxx_compiler_flag("-Weverything")              # clang
  ei_add_cxx_compiler_flag("-Wundef")
  ei_add_cxx_compiler_flag("-Wcast-align")
  ei_add_cxx_compiler_flag("-Wchar-subscripts")
@@ -395,20 +183,34 @@ if (EIGEN_BUILD_TESTING)
  ei_add_cxx_compiler_flag("-Wc++11-extensions")
  ei_add_cxx_compiler_flag("-Wdouble-promotion")
 #  ei_add_cxx_compiler_flag("-Wconversion")
  # -Wshadow is insanely too strict with gcc, hopefully it will become usable with gcc 6
  # if(NOT CMAKE_COMPILER_IS_GNUCXX OR (CMAKE_CXX_COMPILER_VERSION VERSION_GREATER "5.0.0"))
  if(NOT CMAKE_COMPILER_IS_GNUCXX)
    ei_add_cxx_compiler_flag("-Wshadow")
  endif()
  ei_add_cxx_compiler_flag("-Wno-psabi")
  ei_add_cxx_compiler_flag("-Wno-variadic-macros")
  ei_add_cxx_compiler_flag("-Wno-long-long")
  ei_add_cxx_compiler_flag("-fno-check-new")
  ei_add_cxx_compiler_flag("-fno-common")
  ei_add_cxx_compiler_flag("-fstrict-aliasing")
  ei_add_cxx_compiler_flag("-wd981")                    # disable ICC's "operands are evaluated in unspecified order" remark
  ei_add_cxx_compiler_flag("-wd2304")                   # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
    # Clang emits warnings about unused flag.
    if (NOT CMAKE_CXX_COMPILER_ID MATCHES "Clang")
      ei_add_cxx_compiler_flag("-fno-check-new")
    endif()
  # The -ansi flag must be added last, otherwise it is also used as a linker flag by check_cxx_compiler_flag making it fails
  # Moreover we should not set both -strict-ansi and -ansi
  check_cxx_compiler_flag("-strict-ansi" COMPILER_SUPPORT_STRICTANSI)
  ei_add_cxx_compiler_flag("-Qunused-arguments")        # disable clang warning: argument unused during compilation: '-ansi'
  if(COMPILER_SUPPORT_STRICTANSI)
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -strict-ansi")
  else()
    ei_add_cxx_compiler_flag("-ansi")
  endif()
  if(ANDROID_NDK)
    ei_add_cxx_compiler_flag("-pie")
@@ -459,30 +261,12 @@ if (EIGEN_BUILD_TESTING)
    message(STATUS "Enabling FMA in tests/examples")
  endif()
    option(EIGEN_TEST_AVX2 "Enable/Disable AVX2 in tests/examples" OFF)
    if(EIGEN_TEST_AVX2)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx2 -mfma")
      message(STATUS "Enabling AVX2 in tests/examples")
    endif()
  option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
  if(EIGEN_TEST_AVX512)
-      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma")
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -fabi-version=6 -DEIGEN_ENABLE_AVX512")
    message(STATUS "Enabling AVX512 in tests/examples")
  endif()
    option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF)
    if(EIGEN_TEST_AVX512DQ)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512dq -mfma")
      message(STATUS "Enabling AVX512DQ in tests/examples")
    endif()
    option(EIGEN_TEST_AVX512FP16 "Enable/Disable AVX512-FP16 in tests/examples" OFF)
    if(EIGEN_TEST_AVX512FP16)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma -mavx512vl -mavx512fp16")
    message(STATUS "Enabling AVX512-FP16 in tests/examples")
    endif()
  option(EIGEN_TEST_F16C "Enable/Disable F16C in tests/examples" OFF)
  if(EIGEN_TEST_F16C)
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mf16c")
@@ -501,18 +285,6 @@ if (EIGEN_BUILD_TESTING)
    message(STATUS "Enabling VSX in tests/examples")
  endif()
    option(EIGEN_TEST_MSA "Enable/Disable MSA in tests/examples" OFF)
    if(EIGEN_TEST_MSA)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mmsa")
      message(STATUS "Enabling MSA in tests/examples")
    endif()
   option(EIGEN_TEST_LSX "Enable/Disable LSX in tests/examples" OFF)
   if(EIGEN_TEST_LSX)
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mlsx")
     message(STATUS "Enabling LSX in tests/examples")
   endif()
  option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
  if(EIGEN_TEST_NEON)
    if(EIGEN_TEST_FMA)
@@ -530,18 +302,12 @@ if (EIGEN_BUILD_TESTING)
    message(STATUS "Enabling NEON in tests/examples")
  endif()
-    option(EIGEN_TEST_Z13 "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
+  option(EIGEN_TEST_ZVECTOR "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
-    if(EIGEN_TEST_Z13)
+  if(EIGEN_TEST_ZVECTOR)
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector")
    message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
  endif()
    option(EIGEN_TEST_Z14 "Enable/Disable S390X(zEC14) ZVECTOR in tests/examples" OFF)
    if(EIGEN_TEST_Z14)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z14 -mzvector")
      message(STATUS "Enabling S390X(zEC13) ZVECTOR 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)
@@ -551,14 +317,15 @@ if (EIGEN_BUILD_TESTING)
    endif()
  endif()
-  else()
+else(NOT 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 deactivate selectively)
+  # C4505 - unreferenced local function has been removed (impossible to deactive selectively)
  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714")
  # replace all /Wx by /W4
@@ -578,30 +345,9 @@ if (EIGEN_BUILD_TESTING)
    if(NOT CMAKE_CL_64)
      # arch is not supported on 64 bit systems, SSE is enabled automatically.
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
-      endif()
+    endif(NOT CMAKE_CL_64)
    message(STATUS "Enabling SSE2 in tests/examples")
-    endif()
+  endif(EIGEN_TEST_SSE2)
    option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
    if(EIGEN_TEST_AVX)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX")
      message(STATUS "Enabling AVX in tests/examples")
    endif()
    option(EIGEN_TEST_FMA "Enable/Disable FMA/AVX2 in tests/examples" OFF)
    option(EIGEN_TEST_AVX2 "Enable/Disable FMA/AVX2 in tests/examples" OFF)
    if((EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON) OR EIGEN_TEST_AVX2)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX2")
      message(STATUS "Enabling FMA/AVX2 in tests/examples")
    endif()
    option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
    option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF)
    if(EIGEN_TEST_AVX512 OR EIGEN_TEST_AVX512DQ)
      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX512")
      message(STATUS "Enabling AVX512 in tests/examples")
    endif()
 endif(NOT MSVC)
 option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
@@ -645,130 +391,132 @@ if (EIGEN_BUILD_TESTING)
 endif()
 set(EIGEN_CUDA_CXX_FLAGS "" CACHE STRING "Additional flags to pass to the cuda compiler.")
-  set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture(s) to target when compiling CUDA code")
+set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture level to target when compiling CUDA code")
-  option(EIGEN_TEST_SYCL "Add Sycl support." OFF)
+include_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})
  if(EIGEN_TEST_SYCL)
    option(EIGEN_SYCL_DPCPP "Use the DPCPP Sycl implementation (DPCPP is default SYCL-Compiler)." ON)
    option(EIGEN_SYCL_TRISYCL "Use the triSYCL Sycl implementation." OFF)
    option(EIGEN_SYCL_ComputeCpp "Use the ComputeCPP Sycl implementation." OFF)
-    # Building options
+# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR
-    # https://developer.codeplay.com/products/computecpp/ce/2.11.0/guides/eigen-overview/options-for-building-eigen-sycl
+if(EIGEN_INCLUDE_INSTALL_DIR)
-    option(EIGEN_SYCL_USE_DEFAULT_SELECTOR "Use sycl default selector to select the preferred device." OFF)
+  message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.")
    option(EIGEN_SYCL_NO_LOCAL_MEM "Build for devices without dedicated shared memory." OFF)
    option(EIGEN_SYCL_LOCAL_MEM "Allow the use of local memory (enabled by default)." ON)
    option(EIGEN_SYCL_LOCAL_THREAD_DIM0 "Set work group size for dimension 0." 16)
    option(EIGEN_SYCL_LOCAL_THREAD_DIM1 "Set work group size for dimension 1." 16)
    option(EIGEN_SYCL_ASYNC_EXECUTION "Allow asynchronous execution (enabled by default)." ON)
    option(EIGEN_SYCL_DISABLE_SKINNY "Disable optimization for tall/skinny matrices." OFF)
    option(EIGEN_SYCL_DISABLE_DOUBLE_BUFFER "Disable double buffer." OFF)
    option(EIGEN_SYCL_DISABLE_SCALAR "Disable scalar contraction." OFF)
    option(EIGEN_SYCL_DISABLE_GEMV "Disable GEMV and create a single kernel to calculate contraction instead." OFF)
    set(EIGEN_SYCL ON)
    set(CMAKE_CXX_STANDARD 17)
    set(CMAKE_CXX_FLAGS  "${CMAKE_CXX_FLAGS} -Wno-deprecated-declarations -Wno-shorten-64-to-32 -Wno-cast-align")
    set(CMAKE_CXX_FLAGS  "${CMAKE_CXX_FLAGS} -Wno-deprecated-copy-with-user-provided-copy -Wno-unused-variable")
    set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}")
    find_package(Threads REQUIRED)
    if(EIGEN_SYCL_TRISYCL)
      message(STATUS "Using triSYCL")
      include(FindTriSYCL)
    elseif(EIGEN_SYCL_ComputeCpp)
      message(STATUS "Using ComputeCPP SYCL")
      include(FindComputeCpp)
      set(COMPUTECPP_DRIVER_DEFAULT_VALUE OFF)
      if (NOT MSVC)
        set(COMPUTECPP_DRIVER_DEFAULT_VALUE ON)
 endif()
-      option(COMPUTECPP_USE_COMPILER_DRIVER
+
-              "Use ComputeCpp driver instead of a 2 steps compilation"
+if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)
-              ${COMPUTECPP_DRIVER_DEFAULT_VALUE}
+  set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}
      CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed")
 else()
  set(INCLUDE_INSTALL_DIR
      "${CMAKE_INSTALL_INCLUDEDIR}/eigen3"
      CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed"
      )
    else() #Default SYCL compiler is DPCPP (EIGEN_SYCL_DPCPP)
      set(DPCPP_SYCL_TARGET "spir64" CACHE STRING "Default target for Intel CPU/GPU")
      message(STATUS "Using DPCPP")
      find_package(DPCPP)
      add_definitions(-DSYCL_COMPILER_IS_DPCPP)
    endif(EIGEN_SYCL_TRISYCL)
    if(EIGEN_DONT_VECTORIZE_SYCL)
      message(STATUS "Disabling SYCL vectorization in tests/examples")
      # When disabling SYCL vectorization, also disable Eigen default vectorization
      add_definitions(-DEIGEN_DONT_VECTORIZE=1)
      add_definitions(-DEIGEN_DONT_VECTORIZE_SYCL=1)
 endif()
 set(CMAKEPACKAGE_INSTALL_DIR
    "${CMAKE_INSTALL_DATADIR}/eigen3/cmake"
    CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen3Config.cmake is installed"
    )
 set(PKGCONFIG_INSTALL_DIR
    "${CMAKE_INSTALL_DATADIR}/pkgconfig"
    CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where eigen3.pc is installed"
    )
 foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR)
  if(IS_ABSOLUTE "${${var}}")
    message(FATAL_ERROR "${var} must be relative to CMAKE_PREFIX_PATH. Got: ${${var}}")
  endif()
 endforeach()
 # 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)
    configure_file(eigen3.pc.in eigen3.pc @ONLY)
    install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
        DESTINATION ${PKGCONFIG_INSTALL_DIR}
        )
 endif()
 add_subdirectory(Eigen)
 add_subdirectory(doc EXCLUDE_FROM_ALL)
 option(BUILD_TESTING "Enable creation of Eigen tests." ON)
 if(BUILD_TESTING)
  include(EigenConfigureTesting)
  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
-    # CTest automatic test building relies on the "all" target.
+    add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
    add_subdirectory(test)
    add_subdirectory(failtest)
  else()
    add_subdirectory(test EXCLUDE_FROM_ALL)
-    add_subdirectory(failtest EXCLUDE_FROM_ALL)
+  endif()
 endif()
-  ei_testing_print_summary()
+if (NOT CMAKE_CROSSCOMPILING)
-
+  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
-  if (EIGEN_SPLIT_TESTSUITE)
+    add_subdirectory(blas)
-    ei_split_testsuite("${EIGEN_SPLIT_TESTSUITE}")
+    add_subdirectory(lapack)
  else()
    add_subdirectory(blas EXCLUDE_FROM_ALL)
    add_subdirectory(lapack EXCLUDE_FROM_ALL)
  endif()
 endif(NOT CMAKE_CROSSCOMPILING)
 # add SYCL
 option(EIGEN_TEST_SYCL "Add Sycl support." OFF)
 if(EIGEN_TEST_SYCL)
  set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}")
  include(FindComputeCpp)
 endif()
 endif(EIGEN_BUILD_TESTING)
 #==============================================================================
 # Other Build Configurations.
 #==============================================================================
 add_subdirectory(unsupported)
-if(EIGEN_BUILD_BLAS)
+add_subdirectory(demos EXCLUDE_FROM_ALL)
  add_subdirectory(blas)
 endif()
-if (EIGEN_BUILD_LAPACK)
+# must be after test and unsupported, for configuring buildtests.in
-  add_subdirectory(lapack)
+add_subdirectory(scripts EXCLUDE_FROM_ALL)
 endif()
 if(EIGEN_BUILD_DOC)
  add_subdirectory(doc EXCLUDE_FROM_ALL)
 endif()
 # 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()
+endif(EIGEN_BUILD_BTL)
-if(NOT WIN32 AND EIGEN_BUILD_SPBENCH)
+if(NOT WIN32)
  add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)
-endif()
+endif(NOT WIN32)
 if (EIGEN_BUILD_DEMOS)
  add_subdirectory(demos EXCLUDE_FROM_ALL)
 endif()
 if (PROJECT_IS_TOP_LEVEL)
  # must be after test and unsupported, for configuring buildtests.in
  add_subdirectory(scripts EXCLUDE_FROM_ALL)
 configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)
 if(BUILD_TESTING)
  ei_testing_print_summary()
 endif()
-#==============================================================================
+message(STATUS "")
-# Summary.
+message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
-#==============================================================================
+message(STATUS "")
 option(EIGEN_FAILTEST "Enable failtests." OFF)
 if(EIGEN_FAILTEST)
  add_subdirectory(failtest)
 endif()
 if(PROJECT_IS_TOP_LEVEL)
 string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower)
 if(cmake_generator_tolower MATCHES "makefile")
-    message(STATUS "Available targets (use: make TARGET):")
+  message(STATUS "Some things you can do now:")
-  else()
+  message(STATUS "--------------+--------------------------------------------------------------")
-    message(STATUS "Available targets (use: cmake --build . --target TARGET):")
+  message(STATUS "Command       |   Description")
-  endif()
+  message(STATUS "--------------+--------------------------------------------------------------")
-  message(STATUS "------------+--------------------------------------------------------------")
+  message(STATUS "make install  | Install Eigen. Headers will be installed to:")
  message(STATUS "Target      |   Description")
  message(STATUS "------------+--------------------------------------------------------------")
  message(STATUS "install     | Install Eigen. Headers will be installed to:")
  message(STATUS "              |     <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
  message(STATUS "              |   Using the following values:")
  message(STATUS "              |     CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
@@ -777,25 +525,111 @@ if(PROJECT_IS_TOP_LEVEL)
  message(STATUS "              |     cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
  message(STATUS "              |   Or:")
  message(STATUS "              |     cmake . -DINCLUDE_INSTALL_DIR=yourdir")
-  message(STATUS "uninstall   | Remove files installed by the install target")
+  message(STATUS "make doc      | Generate the API documentation, requires Doxygen & LaTeX")
-  if (EIGEN_BUILD_DOC)
+  message(STATUS "make check    | Build and run the unit-tests. Read this page:")
    message(STATUS "doc         | Generate the API documentation, requires Doxygen & LaTeX")
    message(STATUS "install-doc | Install the API documentation")
  endif()
  if(EIGEN_BUILD_TESTING)
    message(STATUS "check       | Build and run the unit-tests. Read this page:")
  message(STATUS "              |   http://eigen.tuxfamily.org/index.php?title=Tests")
-  endif()
+  message(STATUS "make blas     | Build BLAS library (not the same thing as Eigen)")
-  if (EIGEN_BUILD_BLAS)
+  message(STATUS "make uninstall| Removes files installed by make install")
-    message(STATUS "blas        | Build BLAS library (not the same thing as Eigen)")
+  message(STATUS "--------------+--------------------------------------------------------------")
-  endif()
+else()
-  if (EIGEN_BUILD_LAPACK)
+  message(STATUS "To build/run the unit tests, read this page:")
-    message(STATUS "lapack      | Build LAPACK subset library (not the same thing as Eigen)")
+  message(STATUS "  http://eigen.tuxfamily.org/index.php?title=Tests")
  endif()
  message(STATUS "------------+--------------------------------------------------------------")
  message(STATUS "")
 endif()
 message(STATUS "")
-message(STATUS "Configured Eigen ${EIGEN_VERSION_STRING}")
+
-message(STATUS "")
+
 set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )
 set ( EIGEN_VERSION_MAJOR  ${EIGEN_WORLD_VERSION} )
 set ( EIGEN_VERSION_MINOR  ${EIGEN_MAJOR_VERSION} )
 set ( EIGEN_VERSION_PATCH  ${EIGEN_MINOR_VERSION} )
 set ( EIGEN_DEFINITIONS "")
 set ( EIGEN_INCLUDE_DIR "${CMAKE_INSTALL_PREFIX}/${INCLUDE_INSTALL_DIR}" )
 set ( EIGEN_ROOT_DIR ${CMAKE_INSTALL_PREFIX} )
 # Interface libraries require at least CMake 3.0
 if (NOT CMAKE_VERSION VERSION_LESS 3.0)
  include (CMakePackageConfigHelpers)
  # Imported target support
  add_library (eigen INTERFACE)
  add_library (Eigen3::Eigen ALIAS eigen)
  target_compile_definitions (eigen INTERFACE ${EIGEN_DEFINITIONS})
  target_include_directories (eigen INTERFACE
    $<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
    $<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
  )
  # Export as title case Eigen
  set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
  install (TARGETS eigen EXPORT Eigen3Targets)
  configure_package_config_file (
    ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in
    ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
    PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR
    INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
    NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
  )
  # Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does
  # not depend on architecture specific settings or libraries. More
  # specifically, an Eigen3Config.cmake generated from a 64 bit target can be
  # used for 32 bit targets as well (and vice versa).
  set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})
  unset (CMAKE_SIZEOF_VOID_P)
  write_basic_package_version_file (Eigen3ConfigVersion.cmake
                                    VERSION ${EIGEN_VERSION_NUMBER}
                                    COMPATIBILITY SameMajorVersion)
  set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})
  # The Eigen target will be located in the Eigen3 namespace. Other CMake
  # targets can refer to it using Eigen3::Eigen.
  export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)
  # Export Eigen3 package to CMake registry such that it can be easily found by
  # CMake even if it has not been installed to a standard directory.
  export (PACKAGE Eigen3)
  install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
 else (NOT CMAKE_VERSION VERSION_LESS 3.0)
  # Fallback to legacy Eigen3Config.cmake without the imported target
  # If CMakePackageConfigHelpers module is available (CMake >= 2.8.8)
  # create a relocatable Config file, otherwise leave the hardcoded paths
  include(CMakePackageConfigHelpers OPTIONAL RESULT_VARIABLE CPCH_PATH)
  if(CPCH_PATH)
    configure_package_config_file (
      ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in
      ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
      PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR
      INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
      NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
    )
  else()
    # The PACKAGE_* variables are defined by the configure_package_config_file
    # but without it we define them manually to the hardcoded paths
    set(PACKAGE_INIT "")
    set(PACKAGE_EIGEN_INCLUDE_DIR ${EIGEN_INCLUDE_DIR})
    set(PACKAGE_EIGEN_ROOT_DIR ${EIGEN_ROOT_DIR})
    configure_file ( ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in
                     ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
                     @ONLY ESCAPE_QUOTES )
  endif()
  write_basic_package_version_file( Eigen3ConfigVersion.cmake
                                    VERSION ${EIGEN_VERSION_NUMBER}
                                    COMPATIBILITY SameMajorVersion )
 endif (NOT CMAKE_VERSION VERSION_LESS 3.0)
 install ( FILES ${CMAKE_CURRENT_SOURCE_DIR}/cmake/UseEigen3.cmake
                ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
                ${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake
          DESTINATION ${CMAKEPACKAGE_INSTALL_DIR} )
 # Add uninstall target
 add_custom_target ( uninstall
    COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
--- a/COPYING.APACHE
+++ b/COPYING.APACHE
@@ -1,203 +0,0 @@
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--- a/COPYING.GPL
+++ b/COPYING.GPL
@@ -0,0 +1,674 @@
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--- a/COPYING.LGPL
+++ b/COPYING.LGPL
@@ -0,0 +1,502 @@
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 original copyright holder who places the Library under this License may add
 an explicit geographical distribution limitation excluding those countries,
 so that distribution is permitted only in or among countries not thus
 excluded.  In such case, this License incorporates the limitation as if
 written in the body of this License.
  13. The Free Software Foundation may publish revised and/or new
 versions of the 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
 specifies a version number of this License which applies to it and
 "any later version", you have the option of following the terms and
 conditions either of that version or of any later version published by
 the Free Software Foundation.  If the Library does not specify a
 license version number, you may choose any version ever published by
 the Free Software Foundation.
  14. If you wish to incorporate parts of the Library into other free
 programs whose distribution conditions are incompatible with these,
 write to the author to ask for permission.  For software which is
 copyrighted by the Free Software Foundation, write to the Free
 Software Foundation; we sometimes make exceptions for this.  Our
 decision will be guided by the two goals of preserving the free status
 of all derivatives of our free software and of promoting the sharing
 and reuse of software generally.
                            NO WARRANTY
  15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
 WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
 EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR
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 IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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 LIBRARY IS WITH YOU.  SHOULD THE LIBRARY PROVE DEFECTIVE, YOU ASSUME
 THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
  16. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN
 WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY
 AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU
 FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR
 CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE
 LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING
 RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A
 FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
 SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
 DAMAGES.
                     END OF TERMS AND CONDITIONS
           How to Apply These Terms to Your New Libraries
  If you develop a new library, and you want it to be of the greatest
 possible use to the public, we recommend making it free software that
 everyone can redistribute and change.  You can do so by permitting
 redistribution under these terms (or, alternatively, under the terms of the
 ordinary General Public License).
  To apply these terms, attach the following notices to the library.  It is
 safest to attach them to the start of each source file to most effectively
 convey the exclusion of warranty; and each file should have at least the
 "copyright" line and a pointer to where the full notice is found.
    <one line to give the library's name and a brief idea of what it does.>
    Copyright (C) <year>  <name of author>
    This library 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 2.1 of the License, or (at your option) any later version.
    This library 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 for more details.
    You should have received a copy of the GNU Lesser General Public
    License along with this library; if not, write to the Free Software
    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 Also add information on how to contact you by electronic and paper mail.
 You should also get your employer (if you work as a programmer) or your
 school, if any, to sign a "copyright disclaimer" for the library, if
 necessary.  Here is a sample; alter the names:
  Yoyodyne, Inc., hereby disclaims all copyright interest in the
  library `Frob' (a library for tweaking knobs) written by James Random Hacker.
  <signature of Ty Coon>, 1 April 1990
  Ty Coon, President of Vice
 That's all there is to it!
--- a/COPYING.MINPACK
+++ b/COPYING.MINPACK
@@ -49,3 +49,4 @@ SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
 (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
 EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
 POSSIBILITY OF SUCH LOSS OR DAMAGES.
--- a/COPYING.MPL2
+++ b/COPYING.MPL2
@@ -357,7 +357,7 @@ Exhibit A - Source Code Form License Notice
  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 https://mozilla.org/MPL/2.0/.
+  file, You can obtain one at http://mozilla.org/MPL/2.0/.
 If it is not possible or desirable to put the notice in a particular
 file, then You may include the notice in a location (such as a LICENSE
--- a/COPYING.README
+++ b/COPYING.README
@@ -2,5 +2,17 @@ Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:
  http://www.mozilla.org/MPL/2.0/
  http://www.mozilla.org/MPL/2.0/FAQ.html
-Some files contain third-party code under BSD or other MPL2-compatible licenses,
+Some files contain third-party code under BSD or LGPL licenses, whence the other
-whence the other COPYING.* files here.
+COPYING.* files here.
 All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later.
 For this reason, the COPYING.LGPL file contains the LGPL 2.1 text.
 If you want to guarantee that the Eigen code that you are #including is licensed
 under the MPL2 and possibly more permissive licenses (like BSD), #define this
 preprocessor symbol:
  EIGEN_MPL2_ONLY
 For example, with most compilers, you could add this to your project CXXFLAGS:
  -DEIGEN_MPL2_ONLY
 This will cause a compilation error to be generated if you #include any code that is
 LGPL licensed.
--- a/CTestConfig.cmake
+++ b/CTestConfig.cmake
@@ -2,8 +2,8 @@
 ## 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()
+##   ENABLE_TESTING()
-##   include(CTest)
+##   INCLUDE(CTest)
 set(CTEST_PROJECT_NAME "Eigen")
 set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC")
@@ -11,7 +11,3 @@ set(CTEST_DROP_METHOD "http")
 set(CTEST_DROP_SITE "my.cdash.org")
 set(CTEST_DROP_LOCATION "/submit.php?project=Eigen")
 set(CTEST_DROP_SITE_CDASH TRUE)
 #set(CTEST_PROJECT_SUBPROJECTS
 #Official
 #Unsupported
 #)
--- a/Eigen/AccelerateSupport
+++ b/Eigen/AccelerateSupport
@@ -1,52 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
 #define EIGEN_ACCELERATESUPPORT_MODULE_H
 #include "SparseCore"
 #include "src/Core/util/DisableStupidWarnings.h"
 /** \ingroup Support_modules
 * \defgroup AccelerateSupport_Module AccelerateSupport module
 *
 * This module provides an interface to the Apple Accelerate library.
 * It provides the seven following main factorization classes:
 * - class AccelerateLLT: a Cholesky (LL^T) factorization.
 * - class AccelerateLDLT: the default LDL^T factorization.
 * - class AccelerateLDLTUnpivoted: a Cholesky-like LDL^T factorization with only 1x1 pivots and no pivoting
 * - class AccelerateLDLTSBK: an LDL^T factorization with Supernode Bunch-Kaufman and static pivoting
 * - class AccelerateLDLTTPP: an LDL^T factorization with full threshold partial pivoting
 * - class AccelerateQR: a QR factorization
 * - class AccelerateCholeskyAtA: a QR factorization without storing Q (equivalent to A^TA = R^T R)
 *
 * \code
 * #include <Eigen/AccelerateSupport>
 * \endcode
 *
 * In order to use this module, the Accelerate headers must be accessible from
 * the include paths, and your binary must be linked to the Accelerate framework.
 * The Accelerate library is only available on Apple hardware.
 *
 * Note that many of the algorithms can be influenced by the UpLo template
 * argument. All matrices are assumed to be symmetric. For example, the following
 * creates an LDLT factorization where your matrix is symmetric (implicit) and
 * uses the lower triangle:
 *
 * \code
 * AccelerateLDLT<SparseMatrix<float>, Lower> ldlt;
 * \endcode
 */
 // IWYU pragma: begin_exports
 #include "src/AccelerateSupport/AccelerateSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif  // EIGEN_ACCELERATESUPPORT_MODULE_H
--- a/Eigen/CMakeLists.txt
+++ b/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
  )
 install(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel FILES_MATCHING PATTERN "*.h")
--- a/Eigen/Cholesky
+++ b/Eigen/Cholesky
@@ -29,15 +29,18 @@
  * \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/Cholesky/LLT.h"
 #include "src/Cholesky/LDLT.h"
 #ifdef EIGEN_USE_LAPACKE
-#include "src/misc/lapacke_helpers.h"
+#ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
 #include "src/Cholesky/LLT_LAPACKE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_CHOLESKY_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/CholmodSupport
+++ b/Eigen/CholmodSupport
@@ -12,16 +12,17 @@
 #include "src/Core/util/DisableStupidWarnings.h"
 extern "C" {
  #include <cholmod.h>
 }
 /** \ingroup Support_modules
  * \defgroup CholmodSupport_Module CholmodSupport module
  *
- * This module provides an interface to the Cholmod library which is part of the <a
+  * This module provides an interface to the Cholmod library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
- * href="http://www.suitesparse.com">suitesparse</a> package. It provides the two following main factorization classes:
+  * It provides the two following main factorization classes:
  * - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
- * - class CholmodDecomposition: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of
+  * - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).
 * the underlying factorization method (supernodal or simplicial).
  *
  * For the sake of completeness, this module also propose the two following classes:
  * - class CholmodSimplicialLLT
@@ -33,16 +34,15 @@
  * #include <Eigen/CholmodSupport>
  * \endcode
  *
- * In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.
- * linked to the cholmod library and its dependencies. The dependencies depend on how cholmod has been compiled. For a
+  * The dependencies depend on how cholmod has been compiled.
- * cmake based project, you can use our FindCholmod.cmake module to help you in this task.
+  * For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.
  *
  */
 // IWYU pragma: begin_exports
 #include "src/CholmodSupport/CholmodSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_CHOLMODSUPPORT_MODULE_H
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -8,58 +8,267 @@
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-#ifndef EIGEN_CORE_MODULE_H
+#ifndef EIGEN_CORE_H
-#define EIGEN_CORE_MODULE_H
+#define EIGEN_CORE_H
-// Eigen version information.
+// first thing Eigen does: stop the compiler from committing suicide
 #include "Version"
 // first thing Eigen does: stop the compiler from reporting useless warnings.
 #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
+#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
-// it's where we do all the compiler/OS/arch detections and define most defaults.
+  #define EIGEN_CUDACC __CUDACC__
-#include "src/Core/util/Macros.h"
+#endif
-// This detects SSE/AVX/NEON/etc. and configure alignment settings
+#if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA)
-#include "src/Core/util/ConfigureVectorization.h"
+  #define EIGEN_CUDA_ARCH __CUDA_ARCH__
 #endif
-// We need cuda_runtime.h/hip_runtime.h to ensure that
+#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)
-// the EIGEN_USING_STD macro works properly on the device side
+#define EIGEN_CUDACC_VER  ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))
-#if defined(EIGEN_CUDACC)
+#elif defined(__CUDACC_VER__)
 #define EIGEN_CUDACC_VER __CUDACC_VER__
 #else
 #define EIGEN_CUDACC_VER 0
 #endif
 // Handle NVCC/CUDA/SYCL
 #if defined(EIGEN_CUDACC) || defined(__SYCL_DEVICE_ONLY__)
  // Do not try asserts on CUDA and SYCL!
  #ifndef EIGEN_NO_DEBUG
  #define EIGEN_NO_DEBUG
  #endif
  #ifdef EIGEN_INTERNAL_DEBUGGING
  #undef EIGEN_INTERNAL_DEBUGGING
  #endif
  #ifdef EIGEN_EXCEPTIONS
  #undef EIGEN_EXCEPTIONS
  #endif
  // All functions callable from CUDA code must be qualified with __device__
  #ifdef EIGEN_CUDACC
    // Do not try to vectorize on CUDA and SYCL!
    #ifndef EIGEN_DONT_VECTORIZE
    #define EIGEN_DONT_VECTORIZE
    #endif
    #define EIGEN_DEVICE_FUNC __host__ __device__
    // We need cuda_runtime.h to ensure that that EIGEN_USING_STD_MATH macro
    // works properly on the device side
    #include <cuda_runtime.h>
-#elif defined(EIGEN_HIPCC)
+  #else
-#include <hip/hip_runtime.h>
+    #define EIGEN_DEVICE_FUNC
  #endif
 #else
  #define EIGEN_DEVICE_FUNC
 #endif
 #if defined(EIGEN_CUDACC)
  #include <cuda.h>
  #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
 #else
  #define EIGEN_CUDA_SDK_VER 0
 #endif
 // When compiling CUDA device code with NVCC, pull in math functions from the
 // global namespace.  In host mode, and when device doee with clang, use the
 // std versions.
 #if defined(__CUDA_ARCH__) && defined(__NVCC__)
  #define EIGEN_USING_STD_MATH(FUNC) using ::FUNC;
 #else
  #define EIGEN_USING_STD_MATH(FUNC) using std::FUNC;
 #endif
 #if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL)
  #define EIGEN_EXCEPTIONS
 #endif
 #ifdef EIGEN_EXCEPTIONS
  #include <new>
 #endif
-// Disable the ipa-cp-clone optimization flag with MinGW 6.x or older (enabled by default with -O3)
+// 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"
 // Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3)
 // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.
-#if EIGEN_COMP_MINGW && EIGEN_GNUC_STRICT_LESS_THAN(6, 0, 0)
+#if EIGEN_COMP_MINGW && EIGEN_GNUC_AT_LEAST(4,6)
  #pragma GCC optimize ("-fno-ipa-cp-clone")
 #endif
 // Prevent ICC from specializing std::complex operators that silently fail
 // on device. This allows us to use our own device-compatible specializations
 // instead.
 #if EIGEN_COMP_ICC && defined(EIGEN_GPU_COMPILE_PHASE) && !defined(_OVERRIDE_COMPLEX_SPECIALIZATION_)
 #define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
 #endif
 #include <complex>
 // this include file manages BLAS and MKL related macros
 // and inclusion of their respective header files
 #include "src/Core/util/MKL_support.h"
-#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
+// if alignment is disabled, then disable vectorization. Note: EIGEN_MAX_ALIGN_BYTES is the proper check, it takes into
-#define EIGEN_HAS_GPU_FP16
+// account both the user's will (EIGEN_MAX_ALIGN_BYTES,EIGEN_DONT_ALIGN) and our own platform checks
 #if EIGEN_MAX_ALIGN_BYTES==0
  #ifndef EIGEN_DONT_VECTORIZE
    #define EIGEN_DONT_VECTORIZE
  #endif
 #endif
-#if defined(EIGEN_HAS_CUDA_BF16) || defined(EIGEN_HAS_HIP_BF16)
+#if EIGEN_COMP_MSVC
-#define EIGEN_HAS_GPU_BF16
+  #include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled
  #if (EIGEN_COMP_MSVC >= 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)) || EIGEN_ARCH_x86_64
      #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__) && ( (!EIGEN_COMP_GNUC) || EIGEN_COMP_ICC || EIGEN_GNUC_AT_LEAST(4,2) )
    #define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC
  #endif
 #endif
 #if !defined(EIGEN_DONT_VECTORIZE) && !defined(EIGEN_CUDACC)
  #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
    #ifdef __AVX__
      #define EIGEN_VECTORIZE_AVX
      #define EIGEN_VECTORIZE_SSE3
      #define EIGEN_VECTORIZE_SSSE3
      #define EIGEN_VECTORIZE_SSE4_1
      #define EIGEN_VECTORIZE_SSE4_2
    #endif
    #ifdef __AVX2__
      #define EIGEN_VECTORIZE_AVX2
    #endif
    #ifdef __FMA__
      #define EIGEN_VECTORIZE_FMA
    #endif
    #if defined(__AVX512F__) && defined(EIGEN_ENABLE_AVX512)
      #define EIGEN_VECTORIZE_AVX512
      #define EIGEN_VECTORIZE_AVX2
      #define EIGEN_VECTORIZE_AVX
      #define EIGEN_VECTORIZE_FMA
      #ifdef __AVX512DQ__
        #define EIGEN_VECTORIZE_AVX512DQ
      #endif
      #ifdef __AVX512ER__
        #define EIGEN_VECTORIZE_AVX512ER
      #endif
    #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" {
      // In theory we should only include immintrin.h and not the other *mmintrin.h header files directly.
      // Doing so triggers some issues with ICC. However old gcc versions seems to not have this file, thus:
      #if EIGEN_COMP_ICC >= 1110
        #include <immintrin.h>
      #else
        #include <mmintrin.h>
        #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
        #if defined(EIGEN_VECTORIZE_AVX) || defined(EIGEN_VECTORIZE_AVX512)
        #include <immintrin.h>
        #endif
      #endif
    } // end extern "C"
  #elif defined __VSX__
    #define EIGEN_VECTORIZE
    #define EIGEN_VECTORIZE_FMA
    #define EIGEN_VECTORIZE_VSX
    #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 __ALTIVEC__
    #define EIGEN_VECTORIZE
    #define EIGEN_VECTORIZE_FMA
    #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) || (defined __ARM_NEON__)
    #define EIGEN_VECTORIZE
    #define EIGEN_VECTORIZE_NEON
    #include <arm_neon.h>
    // Enable FMA for ARM.
    #if defined(__ARM_FEATURE_FMA)
      #define EIGEN_VECTORIZE_FMA
    #endif
  #elif (defined __s390x__ && defined __VEC__)
    #define EIGEN_VECTORIZE
    #define EIGEN_VECTORIZE_ZVECTOR
    #include <vecintrin.h>
  #endif
 #endif
 #if defined(__F16C__) && !defined(EIGEN_COMP_CLANG)
  // We can use the optimized fp16 to float and float to fp16 conversion routines
  #define EIGEN_HAS_FP16_C
 #endif
 #if defined EIGEN_CUDACC
  #define EIGEN_VECTORIZE_CUDA
  #include <vector_types.h>
  #if EIGEN_CUDA_SDK_VER >= 70500
    #define EIGEN_HAS_CUDA_FP16
  #endif
 #endif
 #if defined EIGEN_HAS_CUDA_FP16
  #include <cuda_runtime_api.h>
  #include <cuda_fp16.h>
 #endif
 #if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
@@ -67,7 +276,6 @@
 #endif
 #ifdef EIGEN_HAS_OPENMP
 #include <atomic>
 #include <omp.h>
 #endif
@@ -82,9 +290,10 @@
 #include <cstddef>
 #include <cstdlib>
 #include <cmath>
 #include <cassert>
 #include <functional>
 #ifndef EIGEN_NO_IO
 #include <sstream>
 #ifndef EIGEN_NO_IO
  #include <iosfwd>
 #endif
 #include <cstring>
@@ -94,26 +303,9 @@
 // for min/max:
 #include <algorithm>
 #include <array>
 #include <memory>
 #include <vector>
 // for std::is_nothrow_move_assignable
 #ifdef EIGEN_INCLUDE_TYPE_TRAITS
 #include <type_traits>
 // for std::this_thread::yield().
 #if !defined(EIGEN_USE_BLAS) && (defined(EIGEN_HAS_OPENMP) || defined(EIGEN_GEMM_THREADPOOL))
 #include <thread>
 #endif
 // for __cpp_lib feature test macros
 #if defined(__has_include) && __has_include(<version>)
 #include <version>
 #endif
 // for std::bit_cast()
 #if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
 #include <bit>
 #endif
 // for outputting debug info
@@ -122,32 +314,44 @@
 #endif
 // required for __cpuid, needs to be included after cmath
-// also required for _BitScanReverse on Windows on ARM
+#if EIGEN_COMP_MSVC && EIGEN_ARCH_i386_OR_x86_64 && !EIGEN_OS_WINCE
 #if EIGEN_COMP_MSVC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM64) && !EIGEN_OS_WINCE
  #include <intrin.h>
 #endif
-#if defined(EIGEN_USE_SYCL)
+/** \brief Namespace containing all symbols from the %Eigen library. */
-#undef min
+namespace Eigen {
 #undef max
 #undef isnan
 #undef isinf
 #undef isfinite
 #include <CL/sycl.hpp>
 #include <map>
 #include <thread>
 #include <utility>
 #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0
 #define EIGEN_SYCL_LOCAL_THREAD_DIM0 16
 #endif
 #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM1
 #define EIGEN_SYCL_LOCAL_THREAD_DIM1 16
 #endif
 #endif
-#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || \
+inline static const char *SimdInstructionSetsInUse(void) {
-    defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API ||  \
+#if defined(EIGEN_VECTORIZE_AVX512)
-    defined EIGEN2_SUPPORT
+  return "AVX512, FMA, AVX2, AVX, SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
 #elif defined(EIGEN_VECTORIZE_AVX)
  return "AVX SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
 #elif 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_VSX)
  return "VSX";
 #elif defined(EIGEN_VECTORIZE_NEON)
  return "ARM NEON";
 #elif defined(EIGEN_VECTORIZE_ZVECTOR)
  return "S390X ZVECTOR";
 #else
  return "None";
 #endif
 }
 } // end namespace Eigen
 #if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || defined EIGEN2_SUPPORT
 // This will generate an error message:
 #error Eigen2-support is only available up to version 3.2. Please go to "http://eigen.tuxfamily.org/index.php?title=Eigen2" for further information
 #endif
@@ -160,7 +364,7 @@ using std::size_t;
 // gcc 4.6.0 wants std:: for ptrdiff_t
 using std::ptrdiff_t;
-}  // namespace Eigen
+}
 /** \defgroup Core_Module Core module
  * This is the main module of Eigen providing dense matrix and vector support
@@ -172,134 +376,66 @@ using std::ptrdiff_t;
  * \endcode
  */
 #ifdef EIGEN_USE_LAPACKE
 #ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
 #endif
 // IWYU pragma: begin_exports
 #include "src/Core/util/Constants.h"
 #include "src/Core/util/Meta.h"
 #include "src/Core/util/Assert.h"
 #include "src/Core/util/ForwardDeclarations.h"
 #include "src/Core/util/StaticAssert.h"
 #include "src/Core/util/XprHelper.h"
 #include "src/Core/util/Memory.h"
 #include "src/Core/util/IntegralConstant.h"
 #include "src/Core/util/Serializer.h"
 #include "src/Core/util/SymbolicIndex.h"
 #include "src/Core/util/EmulateArray.h"
 #include "src/Core/util/MoreMeta.h"
 #include "src/Core/NumTraits.h"
 #include "src/Core/MathFunctions.h"
 #include "src/Core/RandomImpl.h"
 #include "src/Core/GenericPacketMath.h"
 #include "src/Core/MathFunctionsImpl.h"
 #include "src/Core/arch/Default/ConjHelper.h"
 // Generic half float support
 #include "src/Core/arch/Default/Half.h"
 #include "src/Core/arch/Default/BFloat16.h"
 #include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
 #if defined EIGEN_VECTORIZE_AVX512
  #include "src/Core/arch/SSE/PacketMath.h"
 #include "src/Core/arch/SSE/Reductions.h"
 #include "src/Core/arch/AVX/PacketMath.h"
 #include "src/Core/arch/AVX/Reductions.h"
 #include "src/Core/arch/AVX512/PacketMath.h"
 #include "src/Core/arch/AVX512/Reductions.h"
 #if defined EIGEN_VECTORIZE_AVX512FP16
 #include "src/Core/arch/AVX512/PacketMathFP16.h"
 #endif
 #include "src/Core/arch/SSE/TypeCasting.h"
 #include "src/Core/arch/AVX/TypeCasting.h"
 #include "src/Core/arch/AVX512/TypeCasting.h"
 #if defined EIGEN_VECTORIZE_AVX512FP16
 #include "src/Core/arch/AVX512/TypeCastingFP16.h"
 #endif
 #include "src/Core/arch/SSE/Complex.h"
 #include "src/Core/arch/AVX/Complex.h"
 #include "src/Core/arch/AVX512/Complex.h"
  #include "src/Core/arch/SSE/MathFunctions.h"
  #include "src/Core/arch/AVX/PacketMath.h"
  #include "src/Core/arch/AVX/MathFunctions.h"
  #include "src/Core/arch/AVX512/PacketMath.h"
  #include "src/Core/arch/AVX512/MathFunctions.h"
 #if defined EIGEN_VECTORIZE_AVX512FP16
 #include "src/Core/arch/AVX512/MathFunctionsFP16.h"
 #endif
 #include "src/Core/arch/AVX512/TrsmKernel.h"
 #elif defined EIGEN_VECTORIZE_AVX
  // Use AVX for floats and doubles, SSE for integers
  #include "src/Core/arch/SSE/PacketMath.h"
 #include "src/Core/arch/SSE/Reductions.h"
 #include "src/Core/arch/SSE/TypeCasting.h"
  #include "src/Core/arch/SSE/Complex.h"
 #include "src/Core/arch/AVX/PacketMath.h"
 #include "src/Core/arch/AVX/Reductions.h"
 #include "src/Core/arch/AVX/TypeCasting.h"
 #include "src/Core/arch/AVX/Complex.h"
  #include "src/Core/arch/SSE/MathFunctions.h"
  #include "src/Core/arch/AVX/PacketMath.h"
  #include "src/Core/arch/AVX/MathFunctions.h"
  #include "src/Core/arch/AVX/Complex.h"
  #include "src/Core/arch/AVX/TypeCasting.h"
  #include "src/Core/arch/SSE/TypeCasting.h"
 #elif defined EIGEN_VECTORIZE_SSE
  #include "src/Core/arch/SSE/PacketMath.h"
 #include "src/Core/arch/SSE/Reductions.h"
 #include "src/Core/arch/SSE/TypeCasting.h"
  #include "src/Core/arch/SSE/MathFunctions.h"
  #include "src/Core/arch/SSE/Complex.h"
-#endif
+  #include "src/Core/arch/SSE/TypeCasting.h"
-
+#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
 #if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
  #include "src/Core/arch/AltiVec/PacketMath.h"
 #include "src/Core/arch/AltiVec/TypeCasting.h"
  #include "src/Core/arch/AltiVec/MathFunctions.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/TypeCasting.h"
  #include "src/Core/arch/NEON/MathFunctions.h"
  #include "src/Core/arch/NEON/Complex.h"
 #elif defined EIGEN_VECTORIZE_LSX
 #include "src/Core/arch/LSX/PacketMath.h"
 #include "src/Core/arch/LSX/TypeCasting.h"
 #include "src/Core/arch/LSX/MathFunctions.h"
 #include "src/Core/arch/LSX/Complex.h"
 #elif defined EIGEN_VECTORIZE_SVE
 #include "src/Core/arch/SVE/PacketMath.h"
 #include "src/Core/arch/SVE/TypeCasting.h"
 #include "src/Core/arch/SVE/MathFunctions.h"
 #elif defined EIGEN_VECTORIZE_ZVECTOR
  #include "src/Core/arch/ZVector/PacketMath.h"
  #include "src/Core/arch/ZVector/MathFunctions.h"
  #include "src/Core/arch/ZVector/Complex.h"
 #elif defined EIGEN_VECTORIZE_MSA
 #include "src/Core/arch/MSA/PacketMath.h"
 #include "src/Core/arch/MSA/MathFunctions.h"
 #include "src/Core/arch/MSA/Complex.h"
 #elif defined EIGEN_VECTORIZE_HVX
 #include "src/Core/arch/HVX/PacketMath.h"
 #endif
-#if defined EIGEN_VECTORIZE_GPU
+// Half float support
-#include "src/Core/arch/GPU/PacketMath.h"
+#include "src/Core/arch/CUDA/Half.h"
-#include "src/Core/arch/GPU/MathFunctions.h"
+#include "src/Core/arch/CUDA/PacketMathHalf.h"
-#include "src/Core/arch/GPU/TypeCasting.h"
+#include "src/Core/arch/CUDA/TypeCasting.h"
 #endif
-#if defined(EIGEN_USE_SYCL)
+#if defined EIGEN_VECTORIZE_CUDA
-#include "src/Core/arch/SYCL/InteropHeaders.h"
+  #include "src/Core/arch/CUDA/PacketMath.h"
-#if !defined(EIGEN_DONT_VECTORIZE_SYCL)
+  #include "src/Core/arch/CUDA/MathFunctions.h"
 #include "src/Core/arch/SYCL/PacketMath.h"
 #include "src/Core/arch/SYCL/MathFunctions.h"
 #include "src/Core/arch/SYCL/TypeCasting.h"
 #endif
 #endif
 #include "src/Core/arch/Default/Settings.h"
 // This file provides generic implementations valid for scalar as well
 #include "src/Core/arch/Default/GenericPacketMathFunctions.h"
 #include "src/Core/functors/TernaryFunctors.h"
 #include "src/Core/functors/BinaryFunctors.h"
@@ -308,22 +444,11 @@ using std::ptrdiff_t;
 #include "src/Core/functors/StlFunctors.h"
 #include "src/Core/functors/AssignmentFunctors.h"
-// Specialized functors for GPU.
+// Specialized functors to enable the processing of complex numbers
-#ifdef EIGEN_GPUCC
+// on CUDA devices
-#include "src/Core/arch/GPU/Complex.h"
+#include "src/Core/arch/CUDA/Complex.h"
 #endif
 // Specializations of vectorized activation functions for NEON.
 #ifdef EIGEN_VECTORIZE_NEON
 #include "src/Core/arch/NEON/UnaryFunctors.h"
 #endif
 #include "src/Core/util/IndexedViewHelper.h"
 #include "src/Core/util/ReshapedHelper.h"
 #include "src/Core/ArithmeticSequence.h"
 #ifndef EIGEN_NO_IO
 #include "src/Core/IO.h"
 #endif
 #include "src/Core/DenseCoeffsBase.h"
 #include "src/Core/DenseBase.h"
 #include "src/Core/MatrixBase.h"
@@ -332,8 +457,11 @@ using std::ptrdiff_t;
 #include "src/Core/Product.h"
 #include "src/Core/CoreEvaluators.h"
 #include "src/Core/AssignEvaluator.h"
-#include "src/Core/RealView.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/ArrayBase.h"
 #include "src/Core/util/BlasUtil.h"
@@ -347,14 +475,12 @@ using std::ptrdiff_t;
 #include "src/Core/PlainObjectBase.h"
 #include "src/Core/Matrix.h"
 #include "src/Core/Array.h"
 #include "src/Core/Fill.h"
 #include "src/Core/CwiseTernaryOp.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/InnerProduct.h"
 #include "src/Core/Dot.h"
 #include "src/Core/StableNorm.h"
 #include "src/Core/Stride.h"
@@ -363,16 +489,12 @@ using std::ptrdiff_t;
 #include "src/Core/Ref.h"
 #include "src/Core/Block.h"
 #include "src/Core/VectorBlock.h"
 #include "src/Core/IndexedView.h"
 #include "src/Core/Reshaped.h"
 #include "src/Core/Transpose.h"
 #include "src/Core/DiagonalMatrix.h"
 #include "src/Core/Diagonal.h"
 #include "src/Core/DiagonalProduct.h"
 #include "src/Core/SkewSymmetricMatrix3.h"
 #include "src/Core/Redux.h"
 #include "src/Core/Visitor.h"
 #include "src/Core/FindCoeff.h"
 #include "src/Core/Fuzzy.h"
 #include "src/Core/Swap.h"
 #include "src/Core/CommaInitializer.h"
@@ -385,10 +507,6 @@ using std::ptrdiff_t;
 #include "src/Core/TriangularMatrix.h"
 #include "src/Core/SelfAdjointView.h"
 #include "src/Core/products/GeneralBlockPanelKernel.h"
 #include "src/Core/DeviceWrapper.h"
 #ifdef EIGEN_GEMM_THREADPOOL
 #include "ThreadPool"
 #endif
 #include "src/Core/products/Parallelizer.h"
 #include "src/Core/ProductEvaluators.h"
 #include "src/Core/products/GeneralMatrixVector.h"
@@ -407,26 +525,13 @@ using std::ptrdiff_t;
 #include "src/Core/CoreIterators.h"
 #include "src/Core/ConditionEstimator.h"
-#if defined(EIGEN_VECTORIZE_VSX)
+#include "src/Core/BooleanRedux.h"
 #include "src/Core/arch/AltiVec/MatrixProduct.h"
 #elif defined EIGEN_VECTORIZE_NEON
 #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
 #elif defined EIGEN_VECTORIZE_LSX
 #include "src/Core/arch/LSX/GeneralBlockPanelKernel.h"
 #endif
 #if defined(EIGEN_VECTORIZE_AVX512)
 #include "src/Core/arch/AVX512/GemmKernel.h"
 #endif
 #include "src/Core/Select.h"
 #include "src/Core/VectorwiseOp.h"
 #include "src/Core/PartialReduxEvaluator.h"
 #include "src/Core/Random.h"
 #include "src/Core/Replicate.h"
 #include "src/Core/Reverse.h"
 #include "src/Core/ArrayWrapper.h"
 #include "src/Core/StlIterators.h"
 #ifdef EIGEN_USE_BLAS
 #include "src/Core/products/GeneralMatrixMatrix_BLAS.h"
@@ -444,8 +549,7 @@ using std::ptrdiff_t;
 #endif
 #include "src/Core/GlobalFunctions.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
-#endif  // EIGEN_CORE_MODULE_H
+#endif // EIGEN_CORE_H
--- a/Eigen/Eigenvalues
+++ b/Eigen/Eigenvalues
@@ -33,8 +33,6 @@
  */
 #include "src/misc/RealSvd2x2.h"
 // IWYU pragma: begin_exports
 #include "src/Eigenvalues/Tridiagonalization.h"
 #include "src/Eigenvalues/RealSchur.h"
 #include "src/Eigenvalues/EigenSolver.h"
@@ -56,8 +54,8 @@
 #include "src/Eigenvalues/ComplexSchur_LAPACKE.h"
 #include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_EIGENVALUES_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/Geometry
+++ b/Eigen/Geometry
@@ -22,19 +22,20 @@
  *  - fixed-size homogeneous transformations
  *  - translation, scaling, 2D and 3D rotations
  *  - \link Quaternion quaternions \endlink
- *  - cross products (\ref MatrixBase::cross(), \ref MatrixBase::cross3())
+  *  - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
- *  - orthogonal vector generation (MatrixBase::unitOrthogonal)
+  *  - orthognal vector generation (\ref MatrixBase::unitOrthogonal)
  *  - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
  *  - \link AlignedBox axis aligned bounding boxes \endlink
- *  - \link umeyama() least-square transformation fitting \endlink
+  *  - \link umeyama least-square transformation fitting \endlink
  *
  * \code
  * #include <Eigen/Geometry>
  * \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/Geometry/OrthoMethods.h"
 #include "src/Geometry/EulerAngles.h"
 #include "src/Geometry/Homogeneous.h"
 #include "src/Geometry/RotationBase.h"
 #include "src/Geometry/Rotation2D.h"
@@ -48,12 +49,14 @@
 #include "src/Geometry/AlignedBox.h"
 #include "src/Geometry/Umeyama.h"
-// Use the SSE optimized version whenever possible.
+// Use the SSE optimized version whenever possible. At the moment the
-#if (defined EIGEN_VECTORIZE_SSE) || (defined EIGEN_VECTORIZE_NEON)
+// SSE version doesn't compile when AVX is enabled
-#include "src/Geometry/arch/Geometry_SIMD.h"
+#if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX
 #include "src/Geometry/arch/Geometry_SSE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_GEOMETRY_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/Householder
+++ b/Eigen/Householder
@@ -20,12 +20,11 @@
  * \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/Householder/Householder.h"
 #include "src/Householder/HouseholderSequence.h"
 #include "src/Householder/BlockHouseholder.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_HOUSEHOLDER_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/IterativeLinearSolvers
+++ b/Eigen/IterativeLinearSolvers
@@ -16,8 +16,7 @@
 /** 
  * \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
  *
-  * This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a
+  * This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse.
  squared matrix, usually very large and sparse.
  * Those solvers are accessible via the following classes:
  *  - ConjugateGradient for selfadjoint (hermitian) matrices,
  *  - LeastSquaresConjugateGradient for rectangular least-square problems,
@@ -28,15 +27,13 @@
  *  - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
  *  - IncompleteLUT - incomplete LU factorization with dual thresholding
  *
-  * Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport,
+  * Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport.
  UmfPackSupport, SuperLUSupport, AccelerateSupport.
  *
    \code
    #include <Eigen/IterativeLinearSolvers>
    \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/IterativeLinearSolvers/SolveWithGuess.h"
 #include "src/IterativeLinearSolvers/IterativeSolverBase.h"
 #include "src/IterativeLinearSolvers/BasicPreconditioners.h"
@@ -45,7 +42,6 @@
 #include "src/IterativeLinearSolvers/BiCGSTAB.h"
 #include "src/IterativeLinearSolvers/IncompleteLUT.h"
 #include "src/IterativeLinearSolvers/IncompleteCholesky.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/Jacobi
+++ b/Eigen/Jacobi
@@ -24,10 +24,10 @@
  *  - MatrixBase::applyOnTheRight().
  */
 // IWYU pragma: begin_exports
 #include "src/Jacobi/Jacobi.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_JACOBI_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/KLUSupport
+++ b/Eigen/KLUSupport
@@ -1,43 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_KLUSUPPORT_MODULE_H
 #define EIGEN_KLUSUPPORT_MODULE_H
 #include "SparseCore"
 #include "src/Core/util/DisableStupidWarnings.h"
 extern "C" {
 #include <btf.h>
 #include <klu.h>
 }
 /** \ingroup Support_modules
 * \defgroup KLUSupport_Module KLUSupport module
 *
 * This module provides an interface to the KLU library which is part of the <a
 * href="http://www.suitesparse.com">suitesparse</a> package. It provides the following factorization class:
 * - class KLU: a sparse LU factorization, well-suited for circuit simulation.
 *
 * \code
 * #include <Eigen/KLUSupport>
 * \endcode
 *
 * In order to use this module, the klu and btf headers must be accessible from the include paths, and your binary must
 * be linked to the klu library and its dependencies. The dependencies depend on how umfpack has been compiled. For a
 * cmake based project, you can use our FindKLU.cmake module to help you in this task.
 *
 */
 // IWYU pragma: begin_exports
 #include "src/KLUSupport/KLUSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif  // EIGEN_KLUSUPPORT_MODULE_H
--- a/Eigen/LU
+++ b/Eigen/LU
@@ -25,22 +25,26 @@
 #include "src/misc/Kernel.h"
 #include "src/misc/Image.h"
 // IWYU pragma: begin_exports
 #include "src/LU/FullPivLU.h"
 #include "src/LU/PartialPivLU.h"
 #ifdef EIGEN_USE_LAPACKE
-#include "src/misc/lapacke_helpers.h"
+#ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
 #include "src/LU/PartialPivLU_LAPACKE.h"
 #endif
 #include "src/LU/Determinant.h"
 #include "src/LU/InverseImpl.h"
-#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_NEON
+// Use the SSE optimized version whenever possible. At the moment the
-#include "src/LU/arch/InverseSize4.h"
+// SSE version doesn't compile when AVX is enabled
 #if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX
  #include "src/LU/arch/Inverse_SSE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_LU_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/MetisSupport
+++ b/Eigen/MetisSupport
@@ -16,6 +16,7 @@ extern "C" {
 #include <metis.h>
 }
 /** \ingroup Support_modules
  * \defgroup MetisSupport_Module MetisSupport module
  *
@@ -26,9 +27,8 @@ extern "C" {
  * It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink
  */
-// IWYU pragma: begin_exports
+
 #include "src/MetisSupport/MetisSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/OrderingMethods
+++ b/Eigen/OrderingMethods
@@ -54,7 +54,7 @@
  * \note Some of these methods (like AMD or METIS), need the sparsity pattern 
  * of the input matrix to be symmetric. When the matrix is structurally unsymmetric, 
  * Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
- * If your matrix is already symmetric (at least in structure), you can avoid that
+  * If your matrix is already symmetric (at leat in structure), you can avoid that
  * by calling the method with a SelfAdjointView type.
  * 
  * \code
@@ -63,11 +63,11 @@
  * \endcode
  */
-// IWYU pragma: begin_exports
+#ifndef EIGEN_MPL2_ONLY
 #include "src/OrderingMethods/Amd.h"
-#include "src/OrderingMethods/Ordering.h"
+#endif
 // IWYU pragma: end_exports
 #include "src/OrderingMethods/Ordering.h"
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_ORDERINGMETHODS_MODULE_H
--- a/Eigen/PaStiXSupport
+++ b/Eigen/PaStiXSupport
@@ -35,16 +35,13 @@ extern "C" {
  * #include <Eigen/PaStiXSupport>
  * \endcode
  *
- * In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.
- * linked to the PaSTiX library and its dependencies. This wrapper resuires PaStiX version 5.x compiled without MPI
+  * The dependencies depend on how PaSTiX has been compiled.
- * support. The dependencies depend on how PaSTiX has been compiled. For a cmake based project, you can use our
+  * For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.
 * FindPaSTiX.cmake module to help you in this task.
  *
  */
 // IWYU pragma: begin_exports
 #include "src/PaStiXSupport/PaStiXSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/PardisoSupport
+++ b/Eigen/PardisoSupport
@@ -23,15 +23,12 @@
  * #include <Eigen/PardisoSupport>
  * \endcode
  *
- * In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.
- * linked to the MKL library and its dependencies. See this \ref TopicUsingIntelMKL "page" for more information on
+  * See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration.
 * MKL-Eigen integration.
  * 
  */
 // IWYU pragma: begin_exports
 #include "src/PardisoSupport/PardisoSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/QR
+++ b/Eigen/QR
@@ -31,18 +31,21 @@
  * \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/QR/HouseholderQR.h"
 #include "src/QR/FullPivHouseholderQR.h"
 #include "src/QR/ColPivHouseholderQR.h"
 #include "src/QR/CompleteOrthogonalDecomposition.h"
 #ifdef EIGEN_USE_LAPACKE
-#include "src/misc/lapacke_helpers.h"
+#ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
 #include "src/QR/HouseholderQR_LAPACKE.h"
 #include "src/QR/ColPivHouseholderQR_LAPACKE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_QR_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/QtAlignedMalloc
+++ b/Eigen/QtAlignedMalloc
@@ -14,11 +14,18 @@
 #include "src/Core/util/DisableStupidWarnings.h"
-void *qMalloc(std::size_t size) { return Eigen::internal::aligned_malloc(size); }
+void *qMalloc(std::size_t size)
 {
  return Eigen::internal::aligned_malloc(size);
 }
-void qFree(void *ptr) { Eigen::internal::aligned_free(ptr); }
+void qFree(void *ptr)
 {
  Eigen::internal::aligned_free(ptr);
 }
-void *qRealloc(void *ptr, std::size_t size) {
+void *qRealloc(void *ptr, std::size_t size)
 {
  void* newPtr = Eigen::internal::aligned_malloc(size);
  std::memcpy(newPtr, ptr, size);
  Eigen::internal::aligned_free(ptr);
@@ -30,3 +37,4 @@ void *qRealloc(void *ptr, std::size_t size) {
 #endif
 #endif // EIGEN_QTMALLOC_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/SPQRSupport
+++ b/Eigen/SPQRSupport
@@ -17,25 +17,18 @@
 /** \ingroup Support_modules
  * \defgroup SPQRSupport_Module SuiteSparseQR module
  * 
- * This module provides an interface to the SPQR library, which is part of the <a
+  * This module provides an interface to the SPQR library, which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
 * href="http://www.suitesparse.com">suitesparse</a> package.
  *
  * \code
  * #include <Eigen/SPQRSupport>
  * \endcode
  *
- * In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...).
- * linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...). For a cmake based project, you can use
+  * For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules
 * our FindSPQR.cmake and FindCholmod.Cmake modules
  *
  */
-#include "CholmodSupport"
+#include "src/CholmodSupport/CholmodSupport.h"
 // IWYU pragma: begin_exports
 #include "src/SPQRSupport/SuiteSparseQRSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif
--- a/Eigen/SVD
+++ b/Eigen/SVD
@@ -20,10 +20,9 @@
  *
  * This module provides SVD decomposition for matrices (both real and complex).
  * Two decomposition algorithms are provided:
- *  - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very
+  *  - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.
- * slow for larger ones.
+  *  - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.
- *  - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast
+  * These decompositions are accessible via the respective classes and following MatrixBase methods:
 * for large problems. These decompositions are accessible via the respective classes and following MatrixBase methods:
  *  - MatrixBase::jacobiSvd()
  *  - MatrixBase::bdcSvd()
  *
@@ -32,25 +31,21 @@
  * \endcode
  */
 // IWYU pragma: begin_exports
 #include "src/misc/RealSvd2x2.h"
 #include "src/SVD/UpperBidiagonalization.h"
 #include "src/SVD/SVDBase.h"
 #include "src/SVD/JacobiSVD.h"
 #include "src/SVD/BDCSVD.h"
-#ifdef EIGEN_USE_LAPACKE
+#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
 #ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
 #ifndef EIGEN_USE_LAPACKE_STRICT
 #include "src/SVD/JacobiSVD_LAPACKE.h"
 #endif
 #include "src/SVD/BDCSVD_LAPACKE.h"
 #endif
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_SVD_MODULE_H
 /* vim: set filetype=cpp et sw=2 ts=2 ai: */
--- a/Eigen/Sparse
+++ b/Eigen/Sparse
@@ -25,9 +25,12 @@
 #include "SparseCore"
 #include "OrderingMethods"
 #ifndef EIGEN_MPL2_ONLY
 #include "SparseCholesky"
 #endif
 #include "SparseLU"
 #include "SparseQR"
 #include "IterativeLinearSolvers"
 #endif // EIGEN_SPARSE_MODULE_H
--- a/Eigen/SparseCholesky
+++ b/Eigen/SparseCholesky
@@ -18,8 +18,8 @@
 /** 
  * \defgroup SparseCholesky_Module SparseCholesky module
  *
- * This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian)
+  * This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.
- * matrices. Those decompositions are accessible via the following classes:
+  * Those decompositions are accessible via the following classes:
  *  - SimplicialLLt,
  *  - SimplicialLDLt
  *
@@ -30,10 +30,15 @@
  * \endcode
  */
-// IWYU pragma: begin_exports
+#ifdef EIGEN_MPL2_ONLY
 #error The SparseCholesky module has nothing to offer in MPL2 only mode
 #endif
 #include "src/SparseCholesky/SimplicialCholesky.h"
 #ifndef EIGEN_MPL2_ONLY
 #include "src/SparseCholesky/SimplicialCholesky_impl.h"
-// IWYU pragma: end_exports
+#endif
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/SparseCore
+++ b/Eigen/SparseCore
@@ -17,7 +17,6 @@
 #include <cstdlib>
 #include <cstring>
 #include <algorithm>
 #include <numeric>
 /** 
  * \defgroup SparseCore_Module SparseCore module
@@ -34,7 +33,6 @@
  * This module depends on: Core.
  */
 // IWYU pragma: begin_exports
 #include "src/SparseCore/SparseUtil.h"
 #include "src/SparseCore/SparseMatrixBase.h"
 #include "src/SparseCore/SparseAssign.h"
@@ -43,6 +41,7 @@
 #include "src/SparseCore/SparseCompressedBase.h"
 #include "src/SparseCore/SparseMatrix.h"
 #include "src/SparseCore/SparseMap.h"
 #include "src/SparseCore/MappedSparseMatrix.h"
 #include "src/SparseCore/SparseVector.h"
 #include "src/SparseCore/SparseRef.h"
 #include "src/SparseCore/SparseCwiseUnaryOp.h"
@@ -63,8 +62,8 @@
 #include "src/SparseCore/SparsePermutation.h"
 #include "src/SparseCore/SparseFuzzy.h"
 #include "src/SparseCore/SparseSolverBase.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_SPARSECORE_MODULE_H
--- a/Eigen/SparseLU
+++ b/Eigen/SparseLU
@@ -23,9 +23,8 @@
 // Ordering interface
 #include "OrderingMethods"
-#include "src/Core/util/DisableStupidWarnings.h"
+#include "src/SparseLU/SparseLU_gemm_kernel.h"
 // IWYU pragma: begin_exports
 #include "src/SparseLU/SparseLU_Structs.h"
 #include "src/SparseLU/SparseLU_SupernodalMatrix.h"
 #include "src/SparseLU/SparseLUImpl.h"
@@ -43,8 +42,5 @@
 #include "src/SparseLU/SparseLU_pruneL.h"
 #include "src/SparseLU/SparseLU_Utils.h"
 #include "src/SparseLU/SparseLU.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif // EIGEN_SPARSELU_MODULE_H
--- a/Eigen/SparseQR
+++ b/Eigen/SparseQR
@@ -28,10 +28,8 @@
  * 
  */
 // IWYU pragma: begin_exports
 #include "src/SparseCore/SparseColEtree.h"
 #include "src/SparseQR/SparseQR.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/StdDeque
+++ b/Eigen/StdDeque
@@ -14,16 +14,13 @@
 #include "Core"
 #include <deque>
-#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
    (EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
 #define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
 #else
 // IWYU pragma: begin_exports
 #include "src/StlSupport/StdDeque.h"
 // IWYU pragma: end_exports
 #endif
--- a/Eigen/StdList
+++ b/Eigen/StdList
@@ -13,16 +13,13 @@
 #include "Core"
 #include <list>
-#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
    (EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
 #define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
 #else
 // IWYU pragma: begin_exports
 #include "src/StlSupport/StdList.h"
 // IWYU pragma: end_exports
 #endif
--- a/Eigen/StdVector
+++ b/Eigen/StdVector
@@ -14,16 +14,13 @@
 #include "Core"
 #include <vector>
-#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
    (EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
 #define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
 #else
 // IWYU pragma: begin_exports
 #include "src/StlSupport/StdVector.h"
 // IWYU pragma: end_exports
 #endif
--- a/Eigen/SuperLUSupport
+++ b/Eigen/SuperLUSupport
@@ -33,9 +33,7 @@ typedef int int_t;
 #define SUPERLU_EMPTY (-1)
-namespace Eigen {
+namespace Eigen { struct SluMatrix; }
 struct SluMatrix;
 }
 /** \ingroup Support_modules
  * \defgroup SuperLUSupport_Module SuperLUSupport module
@@ -43,27 +41,23 @@ struct SluMatrix;
  * This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
  * It provides the following factorization class:
  * - class SuperLU: a supernodal sequential LU factorization.
- * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative
+  * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
 * methods).
  *
  * \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.
  *
- * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined
+  * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
 * because it is too polluting.
  *
  * \code
  * #include <Eigen/SuperLUSupport>
  * \endcode
  *
- * In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.
- * linked to the superlu library and its dependencies. The dependencies depend on how superlu has been compiled. For a
+  * The dependencies depend on how superlu has been compiled.
- * cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
+  * For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
  *
  */
 // IWYU pragma: begin_exports
 #include "src/SuperLUSupport/SuperLUSupport.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/ThreadPool
+++ b/Eigen/ThreadPool
@@ -1,80 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_THREADPOOL_MODULE_H
 #define EIGEN_THREADPOOL_MODULE_H
 #include "Core"
 #include "src/Core/util/DisableStupidWarnings.h"
 /** \defgroup ThreadPool_Module ThreadPool Module
 *
 * This module provides 2 threadpool implementations
 *  - a simple reference implementation
 *  - a faster non blocking implementation
 *
 * \code
 * #include <Eigen/ThreadPool>
 * \endcode
 */
 #include <cstddef>
 #include <cstring>
 #include <time.h>
 #include <vector>
 #include <atomic>
 #include <condition_variable>
 #include <deque>
 #include <mutex>
 #include <thread>
 #include <functional>
 #include <memory>
 #include <utility>
 // There are non-parenthesized calls to "max" in the  <unordered_map> header,
 // which trigger a check in test/main.h causing compilation to fail.
 // We work around the check here by removing the check for max in
 // the case where we have to emulate thread_local.
 #ifdef max
 #undef max
 #endif
 #include <unordered_map>
 #include "src/Core/util/Meta.h"
 #include "src/Core/util/MaxSizeVector.h"
 #ifndef EIGEN_MUTEX
 #define EIGEN_MUTEX std::mutex
 #endif
 #ifndef EIGEN_MUTEX_LOCK
 #define EIGEN_MUTEX_LOCK std::unique_lock<std::mutex>
 #endif
 #ifndef EIGEN_CONDVAR
 #define EIGEN_CONDVAR std::condition_variable
 #endif
 // IWYU pragma: begin_exports
 #include "src/ThreadPool/ThreadLocal.h"
 #include "src/ThreadPool/ThreadYield.h"
 #include "src/ThreadPool/ThreadCancel.h"
 #include "src/ThreadPool/EventCount.h"
 #include "src/ThreadPool/RunQueue.h"
 #include "src/ThreadPool/ThreadPoolInterface.h"
 #include "src/ThreadPool/ThreadEnvironment.h"
 #include "src/ThreadPool/Barrier.h"
 #include "src/ThreadPool/NonBlockingThreadPool.h"
 #include "src/ThreadPool/CoreThreadPoolDevice.h"
 #include "src/ThreadPool/ForkJoin.h"
 // IWYU pragma: end_exports
 #include "src/Core/util/ReenableStupidWarnings.h"
 #endif  // EIGEN_CXX11_THREADPOOL_MODULE_H
--- a/Eigen/UmfPackSupport
+++ b/Eigen/UmfPackSupport
@@ -19,23 +19,21 @@ extern "C" {
 /** \ingroup Support_modules
  * \defgroup UmfPackSupport_Module UmfPackSupport module
  *
- * This module provides an interface to the UmfPack library which is part of the <a
+  * This module provides an interface to the UmfPack library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
- * href="http://www.suitesparse.com">suitesparse</a> package. It provides the following factorization class:
+  * It provides the following factorization class:
  * - class UmfPackLU: a multifrontal sequential LU factorization.
  *
  * \code
  * #include <Eigen/UmfPackSupport>
  * \endcode
  *
- * In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be
+  * In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.
- * linked to the umfpack library and its dependencies. The dependencies depend on how umfpack has been compiled. For a
+  * The dependencies depend on how umfpack has been compiled.
- * cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
+  * For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
  *
  */
 // IWYU pragma: begin_exports
 #include "src/UmfPackSupport/UmfPackSupport.h"
 // IWYU pragma: endexports
 #include "src/Core/util/ReenableStupidWarnings.h"
--- a/Eigen/Version
+++ b/Eigen/Version
@@ -1,14 +0,0 @@
 #ifndef EIGEN_VERSION_H
 #define EIGEN_VERSION_H
 // The "WORLD" version will forever remain "3" for the "Eigen3" library.
 #define EIGEN_WORLD_VERSION 3
 // As of Eigen3 5.0.0, we have moved to Semantic Versioning (semver.org).
 #define EIGEN_MAJOR_VERSION 5
 #define EIGEN_MINOR_VERSION 0
 #define EIGEN_PATCH_VERSION 1
 #define EIGEN_PRERELEASE_VERSION ""
 #define EIGEN_BUILD_VERSION ""
 #define EIGEN_VERSION_STRING "5.0.1"
 #endif  // EIGEN_VERSION_H
--- a/Eigen/src/AccelerateSupport/AccelerateSupport.h
+++ b/Eigen/src/AccelerateSupport/AccelerateSupport.h
@@ -1,423 +0,0 @@
 #ifndef EIGEN_ACCELERATESUPPORT_H
 #define EIGEN_ACCELERATESUPPORT_H
 #include <Accelerate/Accelerate.h>
 #include <Eigen/Sparse>
 namespace Eigen {
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 class AccelerateImpl;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateLLT
 * \brief A direct Cholesky (LLT) factorization and solver based on Accelerate
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateLLT
 */
 template <typename MatrixType, int UpLo = Lower>
 using AccelerateLLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationCholesky, true>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateLDLT
 * \brief The default Cholesky (LDLT) factorization and solver based on Accelerate
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLT
 */
 template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLT, true>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateLDLTUnpivoted
 * \brief A direct Cholesky-like LDL^T factorization and solver based on Accelerate with only 1x1 pivots and no pivoting
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTUnpivoted
 */
 template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTUnpivoted = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTUnpivoted, true>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateLDLTSBK
 * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with Supernode Bunch-Kaufman and static
 * pivoting
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTSBK
 */
 template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTSBK = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTSBK, true>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateLDLTTPP
 * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with full threshold partial pivoting
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTTPP
 */
 template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTTPP = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTTPP, true>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateQR
 * \brief A QR factorization and solver based on Accelerate
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateQR
 */
 template <typename MatrixType>
 using AccelerateQR = AccelerateImpl<MatrixType, 0, SparseFactorizationQR, false>;
 /** \ingroup AccelerateSupport_Module
 * \typedef AccelerateCholeskyAtA
 * \brief A QR factorization and solver based on Accelerate without storing Q (equivalent to A^TA = R^T R)
 *
 * \warning Only single and double precision real scalar types are supported by Accelerate
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 *
 * \sa \ref TutorialSparseSolverConcept, class AccelerateCholeskyAtA
 */
 template <typename MatrixType>
 using AccelerateCholeskyAtA = AccelerateImpl<MatrixType, 0, SparseFactorizationCholeskyAtA, false>;
 namespace internal {
 template <typename T>
 struct AccelFactorizationDeleter {
  void operator()(T* sym) {
    if (sym) {
      SparseCleanup(*sym);
      delete sym;
      sym = nullptr;
    }
  }
 };
 template <typename DenseVecT, typename DenseMatT, typename SparseMatT, typename NumFactT>
 struct SparseTypesTraitBase {
  typedef DenseVecT AccelDenseVector;
  typedef DenseMatT AccelDenseMatrix;
  typedef SparseMatT AccelSparseMatrix;
  typedef SparseOpaqueSymbolicFactorization SymbolicFactorization;
  typedef NumFactT NumericFactorization;
  typedef AccelFactorizationDeleter<SymbolicFactorization> SymbolicFactorizationDeleter;
  typedef AccelFactorizationDeleter<NumericFactorization> NumericFactorizationDeleter;
 };
 template <typename Scalar>
 struct SparseTypesTrait {};
 template <>
 struct SparseTypesTrait<double> : SparseTypesTraitBase<DenseVector_Double, DenseMatrix_Double, SparseMatrix_Double,
                                                       SparseOpaqueFactorization_Double> {};
 template <>
 struct SparseTypesTrait<float>
    : SparseTypesTraitBase<DenseVector_Float, DenseMatrix_Float, SparseMatrix_Float, SparseOpaqueFactorization_Float> {
 };
 }  // end namespace internal
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 class AccelerateImpl : public SparseSolverBase<AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_> > {
 protected:
  using Base = SparseSolverBase<AccelerateImpl>;
  using Base::derived;
  using Base::m_isInitialized;
 public:
  using Base::_solve_impl;
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  enum { ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic };
  enum { UpLo = UpLo_ };
  using AccelDenseVector = typename internal::SparseTypesTrait<Scalar>::AccelDenseVector;
  using AccelDenseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelDenseMatrix;
  using AccelSparseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelSparseMatrix;
  using SymbolicFactorization = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorization;
  using NumericFactorization = typename internal::SparseTypesTrait<Scalar>::NumericFactorization;
  using SymbolicFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorizationDeleter;
  using NumericFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::NumericFactorizationDeleter;
  AccelerateImpl() {
    m_isInitialized = false;
    auto check_flag_set = [](int value, int flag) { return ((value & flag) == flag); };
    if (check_flag_set(UpLo_, Symmetric)) {
      m_sparseKind = SparseSymmetric;
      m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
    } else if (check_flag_set(UpLo_, UnitLower)) {
      m_sparseKind = SparseUnitTriangular;
      m_triType = SparseLowerTriangle;
    } else if (check_flag_set(UpLo_, UnitUpper)) {
      m_sparseKind = SparseUnitTriangular;
      m_triType = SparseUpperTriangle;
    } else if (check_flag_set(UpLo_, StrictlyLower)) {
      m_sparseKind = SparseTriangular;
      m_triType = SparseLowerTriangle;
    } else if (check_flag_set(UpLo_, StrictlyUpper)) {
      m_sparseKind = SparseTriangular;
      m_triType = SparseUpperTriangle;
    } else if (check_flag_set(UpLo_, Lower)) {
      m_sparseKind = SparseTriangular;
      m_triType = SparseLowerTriangle;
    } else if (check_flag_set(UpLo_, Upper)) {
      m_sparseKind = SparseTriangular;
      m_triType = SparseUpperTriangle;
    } else {
      m_sparseKind = SparseOrdinary;
      m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
    }
    m_order = SparseOrderDefault;
  }
  explicit AccelerateImpl(const MatrixType& matrix) : AccelerateImpl() { compute(matrix); }
  ~AccelerateImpl() {}
  inline Index cols() const { return m_nCols; }
  inline Index rows() const { return m_nRows; }
  ComputationInfo info() const {
    eigen_assert(m_isInitialized && "Decomposition is not initialized.");
    return m_info;
  }
  void analyzePattern(const MatrixType& matrix);
  void factorize(const MatrixType& matrix);
  void compute(const MatrixType& matrix);
  template <typename Rhs, typename Dest>
  void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const;
  /** Sets the ordering algorithm to use. */
  void setOrder(SparseOrder_t order) { m_order = order; }
 private:
  template <typename T>
  void buildAccelSparseMatrix(const SparseMatrix<T>& a, AccelSparseMatrix& A, std::vector<long>& columnStarts) {
    const Index nColumnsStarts = a.cols() + 1;
    columnStarts.resize(nColumnsStarts);
    for (Index i = 0; i < nColumnsStarts; i++) columnStarts[i] = a.outerIndexPtr()[i];
    SparseAttributes_t attributes{};
    attributes.transpose = false;
    attributes.triangle = m_triType;
    attributes.kind = m_sparseKind;
    SparseMatrixStructure structure{};
    structure.attributes = attributes;
    structure.rowCount = static_cast<int>(a.rows());
    structure.columnCount = static_cast<int>(a.cols());
    structure.blockSize = 1;
    structure.columnStarts = columnStarts.data();
    structure.rowIndices = const_cast<int*>(a.innerIndexPtr());
    A.structure = structure;
    A.data = const_cast<T*>(a.valuePtr());
  }
  void doAnalysis(AccelSparseMatrix& A) {
    m_numericFactorization.reset(nullptr);
    SparseSymbolicFactorOptions opts{};
    opts.control = SparseDefaultControl;
    opts.orderMethod = m_order;
    opts.order = nullptr;
    opts.ignoreRowsAndColumns = nullptr;
    opts.malloc = malloc;
    opts.free = free;
    opts.reportError = nullptr;
    m_symbolicFactorization.reset(new SymbolicFactorization(SparseFactor(Solver_, A.structure, opts)));
    SparseStatus_t status = m_symbolicFactorization->status;
    updateInfoStatus(status);
    if (status != SparseStatusOK) m_symbolicFactorization.reset(nullptr);
  }
  void doFactorization(AccelSparseMatrix& A) {
    SparseStatus_t status = SparseStatusReleased;
    if (m_symbolicFactorization) {
      m_numericFactorization.reset(new NumericFactorization(SparseFactor(*m_symbolicFactorization, A)));
      status = m_numericFactorization->status;
      if (status != SparseStatusOK) m_numericFactorization.reset(nullptr);
    }
    updateInfoStatus(status);
  }
 protected:
  void updateInfoStatus(SparseStatus_t status) const {
    switch (status) {
      case SparseStatusOK:
        m_info = Success;
        break;
      case SparseFactorizationFailed:
      case SparseMatrixIsSingular:
        m_info = NumericalIssue;
        break;
      case SparseInternalError:
      case SparseParameterError:
      case SparseStatusReleased:
      default:
        m_info = InvalidInput;
        break;
    }
  }
  mutable ComputationInfo m_info;
  Index m_nRows, m_nCols;
  std::unique_ptr<SymbolicFactorization, SymbolicFactorizationDeleter> m_symbolicFactorization;
  std::unique_ptr<NumericFactorization, NumericFactorizationDeleter> m_numericFactorization;
  SparseKind_t m_sparseKind;
  SparseTriangle_t m_triType;
  SparseOrder_t m_order;
 };
 /** Computes the symbolic and numeric decomposition of matrix \a a */
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::compute(const MatrixType& a) {
  if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
  m_nRows = a.rows();
  m_nCols = a.cols();
  AccelSparseMatrix A{};
  std::vector<long> columnStarts;
  buildAccelSparseMatrix(a, A, columnStarts);
  doAnalysis(A);
  if (m_symbolicFactorization) doFactorization(A);
  m_isInitialized = true;
 }
 /** Performs a symbolic decomposition on the sparsity pattern of matrix \a a.
 *
 * This function is particularly useful when solving for several problems having the same structure.
 *
 * \sa factorize()
 */
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::analyzePattern(const MatrixType& a) {
  if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
  m_nRows = a.rows();
  m_nCols = a.cols();
  AccelSparseMatrix A{};
  std::vector<long> columnStarts;
  buildAccelSparseMatrix(a, A, columnStarts);
  doAnalysis(A);
  m_isInitialized = true;
 }
 /** Performs a numeric decomposition of matrix \a a.
 *
 * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been
 * performed.
 *
 * \sa analyzePattern()
 */
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::factorize(const MatrixType& a) {
  eigen_assert(m_symbolicFactorization && "You must first call analyzePattern()");
  eigen_assert(m_nRows == a.rows() && m_nCols == a.cols());
  if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
  AccelSparseMatrix A{};
  std::vector<long> columnStarts;
  buildAccelSparseMatrix(a, A, columnStarts);
  doFactorization(A);
 }
 template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
 template <typename Rhs, typename Dest>
 void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::_solve_impl(const MatrixBase<Rhs>& b,
                                                                              MatrixBase<Dest>& x) const {
  if (!m_numericFactorization) {
    m_info = InvalidInput;
    return;
  }
  eigen_assert(m_nRows == b.rows());
  eigen_assert(((b.cols() == 1) || b.outerStride() == b.rows()));
  SparseStatus_t status = SparseStatusOK;
  Scalar* b_ptr = const_cast<Scalar*>(b.derived().data());
  Scalar* x_ptr = const_cast<Scalar*>(x.derived().data());
  AccelDenseMatrix xmat{};
  xmat.attributes = SparseAttributes_t();
  xmat.columnCount = static_cast<int>(x.cols());
  xmat.rowCount = static_cast<int>(x.rows());
  xmat.columnStride = xmat.rowCount;
  xmat.data = x_ptr;
  AccelDenseMatrix bmat{};
  bmat.attributes = SparseAttributes_t();
  bmat.columnCount = static_cast<int>(b.cols());
  bmat.rowCount = static_cast<int>(b.rows());
  bmat.columnStride = bmat.rowCount;
  bmat.data = b_ptr;
  SparseSolve(*m_numericFactorization, bmat, xmat);
  updateInfoStatus(status);
 }
 }  // end namespace Eigen
 #endif  // EIGEN_ACCELERATESUPPORT_H
--- a/Eigen/src/AccelerateSupport/InternalHeaderCheck.h
+++ b/Eigen/src/AccelerateSupport/InternalHeaderCheck.h
@@ -1,3 +0,0 @@
 #ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
 #error "Please include Eigen/AccelerateSupport instead of including headers inside the src directory directly."
 #endif
--- a/Eigen/src/Cholesky/InternalHeaderCheck.h
+++ b/Eigen/src/Cholesky/InternalHeaderCheck.h
@@ -1,3 +0,0 @@
 #ifndef EIGEN_CHOLESKY_MODULE_H
 #error "Please include Eigen/Cholesky instead of including headers inside the src directory directly."
 #endif
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -13,26 +13,14 @@
 #ifndef EIGEN_LDLT_H
 #define EIGEN_LDLT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
-template <typename MatrixType_, int UpLo_>
+  template<typename MatrixType, int UpLo> struct LDLT_Traits;
 struct traits<LDLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
  typedef MatrixXpr XprKind;
  typedef SolverStorage StorageKind;
  typedef int StorageIndex;
  enum { Flags = 0 };
 };
 template <typename MatrixType, int UpLo>
 struct LDLT_Traits;
  // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
  enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
-}  // namespace internal
+}
 /** \ingroup Cholesky_Module
  *
@@ -40,15 +28,15 @@ enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
  *
  * \brief Robust Cholesky decomposition of a matrix with pivoting
  *
- * \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition
+  * \tparam _MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
- * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
+  * \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
  *             The other triangular part won't be read.
  *
  * 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 D will have
+  * 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.
  *
@@ -59,19 +47,21 @@ enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
  *
  * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
  */
-template <typename MatrixType_, int UpLo_>
+template<typename _MatrixType, int _UpLo> class LDLT
-class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
+{
  public:
-  typedef MatrixType_ MatrixType;
+    typedef _MatrixType MatrixType;
  typedef SolverBase<LDLT> Base;
  friend class SolverBase<LDLT>;
  EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
    enum {
      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    UpLo = UpLo_
+      UpLo = _UpLo
    };
    typedef typename MatrixType::Scalar Scalar;
    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
    typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
    typedef typename MatrixType::StorageIndex StorageIndex;
    typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
    typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
@@ -84,7 +74,12 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
      * 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_sign(internal::ZeroSign), m_isInitialized(false) {}
+    LDLT()
      : m_matrix(),
        m_transpositions(),
        m_sign(internal::ZeroSign),
        m_isInitialized(false)
    {}
    /** \brief Default Constructor with memory preallocation
      *
@@ -97,7 +92,8 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
        m_transpositions(size),
        m_temporary(size),
        m_sign(internal::ZeroSign),
-        m_isInitialized(false) {}
+        m_isInitialized(false)
    {}
    /** \brief Constructor with decomposition
      *
@@ -111,14 +107,14 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
        m_transpositions(matrix.rows()),
        m_temporary(matrix.rows()),
        m_sign(internal::ZeroSign),
-        m_isInitialized(false) {
+        m_isInitialized(false)
    {
      compute(matrix.derived());
    }
    /** \brief Constructs a LDLT factorization from a given matrix
      *
-   * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c
+      * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
   * MatrixType is a Eigen::Ref.
      *
      * \sa LDLT(const EigenBase&)
      */
@@ -128,53 +124,62 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
        m_transpositions(matrix.rows()),
        m_temporary(matrix.rows()),
        m_sign(internal::ZeroSign),
-        m_isInitialized(false) {
+        m_isInitialized(false)
    {
      compute(matrix.derived());
    }
    /** Clear any existing decomposition
     * \sa rankUpdate(w,sigma)
     */
-  void setZero() { m_isInitialized = false; }
+    void setZero()
    {
      m_isInitialized = false;
    }
    /** \returns a view of the upper triangular matrix U */
-  inline typename Traits::MatrixU matrixU() const {
+    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 {
+    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 {
+    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() const {
+    inline Diagonal<const MatrixType> vectorD() const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return m_matrix.diagonal();
    }
    /** \returns true if the matrix is positive (semidefinite) */
-  inline bool isPositive() const {
+    inline bool isPositive() const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
    }
    /** \returns true if the matrix is negative (semidefinite) */
-  inline bool isNegative(void) const {
+    inline bool isNegative(void) const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
    }
 #ifdef EIGEN_PARSED_BY_DOXYGEN
    /** \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> .
@@ -186,13 +191,19 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
      * \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$ if \f$ A \f$ is singular.
+      * computes the least-square solution of \f$ A x = b \f$ is \f$ A \f$ is singular.
      *
      * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
      */
    template<typename Rhs>
-  inline const Solve<LDLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
+    inline const Solve<LDLT, Rhs>
-#endif
+    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 Solve<LDLT, Rhs>(*this, b.derived());
    }
    template<typename Derived>
    bool solveInPlace(MatrixBase<Derived> &bAndX) const;
@@ -203,7 +214,8 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
    /** \returns an estimate of the reciprocal condition number of the matrix of
     *  which \c *this is the LDLT decomposition.
     */
-  RealScalar rcond() const {
+    RealScalar rcond() const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return internal::rcond_estimate_helper(m_l1_norm, *this);
    }
@@ -215,44 +227,47 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
      *
      * TODO: document the storage layout
      */
-  inline const MatrixType& matrixLDLT() const {
+    inline const MatrixType& matrixLDLT() const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return m_matrix;
    }
    MatrixType reconstructedMatrix() const;
-  /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
+    /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
   * is self-adjoint.
      *
      * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
      * \code x = decomposition.adjoint().solve(b) \endcode
      */
-  const LDLT& adjoint() const { return *this; }
+    const LDLT& adjoint() const { return *this; };
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
+    inline Index rows() const { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
+    inline Index cols() const { return m_matrix.cols(); }
    /** \brief Reports whether previous computation was successful.
      *
-   * \returns \c Success if computation was successful,
+      * \returns \c Success if computation was succesful,
      *          \c NumericalIssue if the factorization failed because of a zero pivot.
      */
-  ComputationInfo info() const {
+    ComputationInfo info() const
    {
      eigen_assert(m_isInitialized && "LDLT is not initialized.");
      return m_info;
    }
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    template<typename RhsType, typename DstType>
    EIGEN_DEVICE_FUNC
    void _solve_impl(const RhsType &rhs, DstType &dst) const;
  template <bool Conjugate, typename RhsType, typename DstType>
  void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
    #endif
  protected:
-  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
    static void check_template_parameters()
    {
      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
    }
    /** \internal
      * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
@@ -271,13 +286,13 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
 namespace internal {
-template <int UpLo>
+template<int UpLo> struct ldlt_inplace;
 struct ldlt_inplace;
-template <>
+template<> struct ldlt_inplace<Lower>
-struct ldlt_inplace<Lower> {
+{
  template<typename MatrixType, typename TranspositionType, typename Workspace>
-  static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign) {
+  static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
  {
    using std::abs;
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::RealScalar RealScalar;
@@ -287,34 +302,34 @@ struct ldlt_inplace<Lower> {
    bool found_zero_pivot = false;
    bool ret = true;
-    if (size <= 1) {
+    if (size <= 1)
    {
      transpositions.setIdentity();
-      if (size == 0)
+      if(size==0) sign = ZeroSign;
-        sign = ZeroSign;
+      else if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
-      else if (numext::real(mat.coeff(0, 0)) > static_cast<RealScalar>(0))
+      else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
-        sign = PositiveSemiDef;
+      else sign = ZeroSign;
      else if (numext::real(mat.coeff(0, 0)) < static_cast<RealScalar>(0))
        sign = NegativeSemiDef;
      else
        sign = ZeroSign;
      return true;
    }
-    for (Index k = 0; k < size; ++k) {
+    for (Index k = 0; k < size; ++k)
    {
      // Find largest diagonal element
      Index index_of_biggest_in_corner;
      mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
      index_of_biggest_in_corner += k;
      transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
-      if (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 (Index i = k + 1; i < index_of_biggest_in_corner; ++i) {
+        for(Index i=k+1;i<index_of_biggest_in_corner;++i)
        {
          Scalar tmp = mat.coeffRef(i,k);
          mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
          mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
@@ -332,10 +347,12 @@ struct ldlt_inplace<Lower> {
      Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
      Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
-      if (k > 0) {
+      if(k>0)
      {
        temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
        mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
-        if (rs > 0) A21.noalias() -= A20 * temp.head(k);
+        if(rs>0)
          A21.noalias() -= A20 * temp.head(k);
      }
      // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
@@ -345,11 +362,13 @@ struct ldlt_inplace<Lower> {
      RealScalar realAkk = numext::real(mat.coeffRef(k,k));
      bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
-      if (k == 0 && !pivot_is_valid) {
+      if(k==0 && !pivot_is_valid)
      {
        // The entire diagonal is zero, there is nothing more to do
        // except filling the transpositions, and checking whether the matrix is zero.
        sign = ZeroSign;
-        for (Index j = 0; j < size; ++j) {
+        for(Index j = 0; j<size; ++j)
        {
          transpositions.coeffRef(j) = IndexType(j);
          ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();
        }
@@ -361,20 +380,16 @@ struct ldlt_inplace<Lower> {
      else if(rs>0)
        ret = ret && (A21.array()==Scalar(0)).all();
-      if (found_zero_pivot && pivot_is_valid)
+      if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed
-        ret = false;  // factorization failed
+      else if(!pivot_is_valid) found_zero_pivot = true;
      else if (!pivot_is_valid)
        found_zero_pivot = true;
      if (sign == PositiveSemiDef) {
        if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
      } else if (sign == NegativeSemiDef) {
        if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
      } else if (sign == ZeroSign) {
-        if (realAkk > static_cast<RealScalar>(0))
+        if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
-          sign = PositiveSemiDef;
+        else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
        else if (realAkk < static_cast<RealScalar>(0))
          sign = NegativeSemiDef;
      }
    }
@@ -389,8 +404,8 @@ struct ldlt_inplace<Lower> {
  // Here only rank-1 updates are implemented, to reduce the
  // requirement for intermediate storage and improve accuracy
  template<typename MatrixType, typename WDerived>
-  static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w,
+  static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
-                            const typename MatrixType::RealScalar& sigma = 1) {
+  {
    using numext::isfinite;
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::RealScalar RealScalar;
@@ -401,9 +416,11 @@ struct ldlt_inplace<Lower> {
    RealScalar alpha = 1;
    // Apply the update
-    for (Index j = 0; j < size; j++) {
+    for (Index j = 0; j < size; j++)
    {
      // Check for termination due to an original decomposition of low-rank
-      if (!(isfinite)(alpha)) break;
+      if (!(isfinite)(alpha))
        break;
      // Update the diagonal terms
      RealScalar dj = numext::real(mat.coeff(j,j));
@@ -414,17 +431,19 @@ struct ldlt_inplace<Lower> {
      mat.coeffRef(j,j) += swj2/alpha;
      alpha += swj2/dj;
      // Update the terms of L
      Index rs = size-j-1;
      w.tail(rs) -= wj * mat.col(j).tail(rs);
-      if (!numext::is_exactly_zero(gamma)) mat.col(j).tail(rs) += (sigma * numext::conj(wj) / gamma) * w.tail(rs);
+      if(gamma != 0)
        mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
    }
    return true;
  }
  template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
-  static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w,
+  static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
-                     const typename MatrixType::RealScalar& sigma = 1) {
+  {
    // Apply the permutation to the input w
    tmp = transpositions * w;
@@ -432,33 +451,33 @@ struct ldlt_inplace<Lower> {
  }
 };
-template <>
+template<> struct ldlt_inplace<Upper>
-struct ldlt_inplace<Upper> {
+{
  template<typename MatrixType, typename TranspositionType, typename Workspace>
-  static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp,
+  static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
-                                            SignMatrix& sign) {
+  {
    Transpose<MatrixType> matt(mat);
    return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
  }
  template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
-  static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w,
+  static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
-                                         const typename MatrixType::RealScalar& sigma = 1) {
+  {
    Transpose<MatrixType> matt(mat);
    return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
  }
 };
-template <typename MatrixType>
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
-struct LDLT_Traits<MatrixType, Lower> {
+{
  typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
 };
-template <typename MatrixType>
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
-struct LDLT_Traits<MatrixType, Upper> {
+{
  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
  typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
@@ -469,9 +488,12 @@ struct LDLT_Traits<MatrixType, Upper> {
 /** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
  */
-template <typename MatrixType, int UpLo_>
+template<typename MatrixType, int _UpLo>
 template<typename InputType>
-LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
 {
  check_template_parameters();
  eigen_assert(a.rows()==a.cols());
  const Index size = a.rows();
@@ -482,13 +504,12 @@ LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputT
  // TODO move this code to SelfAdjointView
  for (Index col = 0; col < size; ++col) {
    RealScalar abs_col_sum;
-    if (UpLo_ == Lower)
+    if (_UpLo == Lower)
-      abs_col_sum =
+      abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
          m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
    else
-      abs_col_sum =
+      abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
-          m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
+    if (abs_col_sum > m_l1_norm)
-    if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
+      m_l1_norm = abs_col_sum;
  }
  m_transpositions.resize(size);
@@ -496,8 +517,7 @@ LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputT
  m_temporary.resize(size);
  m_sign = internal::ZeroSign;
-  m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success
+  m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;
                                                                                                    : NumericalIssue;
  m_isInitialized = true;
  return *this;
@@ -505,22 +525,26 @@ LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputT
 /** Update the LDLT decomposition:  given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
 * \param w a vector to be incorporated into the decomposition.
- * \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column
+ * \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
- * vectors. Optional; default value is +1. \sa setZero()
+ * \sa setZero()
  */
-template <typename MatrixType, int UpLo_>
+template<typename MatrixType, int _UpLo>
 template<typename Derived>
-LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::rankUpdate(
+LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma)
-    const MatrixBase<Derived>& w, const typename LDLT<MatrixType, UpLo_>::RealScalar& sigma) {
+{
  typedef typename TranspositionType::StorageIndex IndexType;
  const Index size = w.rows();
-  if (m_isInitialized) {
+  if (m_isInitialized)
  {
    eigen_assert(m_matrix.rows()==size);
-  } else {
+  }
  else
  {
    m_matrix.resize(size,size);
    m_matrix.setZero();
    m_transpositions.resize(size);
-    for (Index i = 0; i < size; i++) m_transpositions.coeffRef(i) = IndexType(i);
+    for (Index i = 0; i < size; i++)
      m_transpositions.coeffRef(i) = IndexType(i);
    m_temporary.resize(size);
    m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
    m_isInitialized = true;
@@ -532,47 +556,42 @@ LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::rankUpdate(
 }
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-template <typename MatrixType_, int UpLo_>
+template<typename _MatrixType, int _UpLo>
 template<typename RhsType, typename DstType>
-void LDLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
+EIGEN_DEVICE_FUNC void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
-  _solve_impl_transposed<true>(rhs, dst);
+{
-}
+  eigen_assert(rhs.rows() == rows());
 template <typename MatrixType_, int UpLo_>
 template <bool Conjugate, typename RhsType, typename DstType>
 void LDLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
  // dst = P b
  dst = m_transpositions * rhs;
  // dst = L^-1 (P b)
-  // dst = L^-*T (P b)
+  matrixL().solveInPlace(dst);
  matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
-  // dst = D^-* (L^-1 P b)
+  // dst = D^-1 (L^-1 P b)
  // dst = D^-1 (L^-*T P b)
  // more precisely, use pseudo-inverse of D (see bug 241)
  using std::abs;
  const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
  // In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
  // and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
-  // RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1)
+  // RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
-  // / NumTraits<RealScalar>::highest()); However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the
+  // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
-  // highest diagonal element is not well justified and leads to numerical issues in some cases. Moreover, Lapack's
+  // diagonal element is not well justified and leads to numerical issues in some cases.
-  // xSYTRS routines use 0 for the tolerance. Using numeric_limits::min() gives us more robustness to denormals.
+  // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
  // Using numeric_limits::min() gives us more robustness to denormals.
  RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
-  for (Index i = 0; i < vecD.size(); ++i) {
+
  for (Index i = 0; i < vecD.size(); ++i)
  {
    if(abs(vecD(i)) > tolerance)
      dst.row(i) /= vecD(i);
    else
      dst.row(i).setZero();
  }
-  // dst = L^-* (D^-* L^-1 P b)
+  // dst = L^-T (D^-1 L^-1 P b)
-  // dst = L^-T (D^-1 L^-*T P b)
+  matrixU().solveInPlace(dst);
  matrixL().transpose().template conjugateIf<Conjugate>().solveInPlace(dst);
-  // dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b
+  // dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b
  // dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b
  dst = m_transpositions.transpose() * dst;
 }
 #endif
@@ -590,9 +609,10 @@ void LDLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstTyp
  *
  * \sa LDLT::solve(), MatrixBase::ldlt()
  */
-template <typename MatrixType, int UpLo_>
+template<typename MatrixType,int _UpLo>
 template<typename Derived>
-bool LDLT<MatrixType, UpLo_>::solveInPlace(MatrixBase<Derived>& bAndX) const {
+bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
 {
  eigen_assert(m_isInitialized && "LDLT is not initialized.");
  eigen_assert(m_matrix.rows() == bAndX.rows());
@@ -604,8 +624,9 @@ bool LDLT<MatrixType, UpLo_>::solveInPlace(MatrixBase<Derived>& bAndX) const {
 /** \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_>
+template<typename MatrixType, int _UpLo>
-MatrixType LDLT<MatrixType, UpLo_>::reconstructedMatrix() const {
+MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
 {
  eigen_assert(m_isInitialized && "LDLT is not initialized.");
  const Index size = m_matrix.rows();
  MatrixType res(size,size);
@@ -631,7 +652,8 @@ MatrixType LDLT<MatrixType, UpLo_>::reconstructedMatrix() const {
  */
 template<typename MatrixType, unsigned int UpLo>
 inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
-SelfAdjointView<MatrixType, UpLo>::ldlt() const {
+SelfAdjointView<MatrixType, UpLo>::ldlt() const
 {
  return LDLT<PlainObject,UpLo>(m_matrix);
 }
@@ -640,7 +662,9 @@ SelfAdjointView<MatrixType, UpLo>::ldlt() const {
  * \sa SelfAdjointView::ldlt()
  */
 template<typename Derived>
-inline const LDLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::ldlt() const {
+inline const LDLT<typename MatrixBase<Derived>::PlainObject>
 MatrixBase<Derived>::ldlt() const
 {
  return LDLT<PlainObject>(derived());
 }
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -10,24 +10,11 @@
 #ifndef EIGEN_LLT_H
 #define EIGEN_LLT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal{
-
+template<typename MatrixType, int UpLo> struct LLT_Traits;
-template <typename MatrixType_, int UpLo_>
+}
 struct traits<LLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
  typedef MatrixXpr XprKind;
  typedef SolverStorage StorageKind;
  typedef int StorageIndex;
  enum { Flags = 0 };
 };
 template <typename MatrixType, int UpLo>
 struct LLT_Traits;
 }  // namespace internal
 /** \ingroup Cholesky_Module
  *
@@ -35,8 +22,8 @@ struct LLT_Traits;
  *
  * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
  *
- * \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition
+  * \tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
- * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
+  * \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
  *               The other triangular part won't be read.
  *
  * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
@@ -47,9 +34,9 @@ struct LLT_Traits;
  * 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
+  * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
- * definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine
+  * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
- * whether a system of equations has a solution.
+  * has a solution.
  *
  * Example: \include LLT_example.cpp
  * Output: \verbinclude LLT_example.out
@@ -61,22 +48,30 @@ struct LLT_Traits;
  *
  * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
  *
- * Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is
+  * Note that during the decomposition, only the lower (or upper, as defined by _UpLo) triangular part of A is considered.
- * considered. Therefore, the strict lower part does not have to store correct values.
+  * Therefore, the strict lower part does not have to store correct values.
  *
  * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
  */
-template <typename MatrixType_, int UpLo_>
+template<typename _MatrixType, int _UpLo> class LLT
-class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
+{
  public:
-  typedef MatrixType_ MatrixType;
+    typedef _MatrixType MatrixType;
-  typedef SolverBase<LLT> Base;
+    enum {
-  friend class SolverBase<LLT>;
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
    };
    typedef typename MatrixType::Scalar Scalar;
    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
    typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
    typedef typename MatrixType::StorageIndex StorageIndex;
-  EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
+    enum {
-  enum { MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
+      PacketSize = internal::packet_traits<Scalar>::size,
-
+      AlignmentMask = int(PacketSize)-1,
-  enum { PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize) - 1, UpLo = UpLo_ };
+      UpLo = _UpLo
    };
    typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
@@ -94,14 +89,18 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
      * according to the specified problem \a size.
      * \sa LLT()
      */
-  explicit LLT(Index size) : m_matrix(size, size), m_isInitialized(false) {}
+    explicit LLT(Index size) : m_matrix(size, size),
                    m_isInitialized(false) {}
    template<typename InputType>
-  explicit LLT(const EigenBase<InputType>& matrix) : m_matrix(matrix.rows(), matrix.cols()), m_isInitialized(false) {
+    explicit LLT(const EigenBase<InputType>& matrix)
      : m_matrix(matrix.rows(), matrix.cols()),
        m_isInitialized(false)
    {
      compute(matrix.derived());
    }
-  /** \brief Constructs a LLT factorization from a given matrix
+    /** \brief Constructs a LDLT factorization from a given matrix
      *
      * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
      * \c MatrixType is a Eigen::Ref.
@@ -109,23 +108,27 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
      * \sa LLT(const EigenBase&)
      */
    template<typename InputType>
-  explicit LLT(EigenBase<InputType>& matrix) : m_matrix(matrix.derived()), m_isInitialized(false) {
+    explicit LLT(EigenBase<InputType>& matrix)
      : m_matrix(matrix.derived()),
        m_isInitialized(false)
    {
      compute(matrix.derived());
    }
    /** \returns a view of the upper triangular matrix U */
-  inline typename Traits::MatrixU matrixU() const {
+    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 {
+    inline typename Traits::MatrixL matrixL() const
    {
      eigen_assert(m_isInitialized && "LLT is not initialized.");
      return Traits::getL(m_matrix);
    }
 #ifdef EIGEN_PARSED_BY_DOXYGEN
    /** \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
@@ -137,8 +140,14 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
      * \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
      */
    template<typename Rhs>
-  inline const Solve<LLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
+    inline const Solve<LLT, Rhs>
-#endif
+    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 Solve<LLT, Rhs>(*this, b.derived());
    }
    template<typename Derived>
    void solveInPlace(const MatrixBase<Derived> &bAndX) const;
@@ -149,7 +158,8 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
    /** \returns an estimate of the reciprocal condition number of the matrix of
      *  which \c *this is the Cholesky decomposition.
      */
-  RealScalar rcond() const {
+    RealScalar rcond() const
    {
      eigen_assert(m_isInitialized && "LLT is not initialized.");
      eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
      return internal::rcond_estimate_helper(m_l1_norm, *this);
@@ -159,47 +169,51 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
      *
      * TODO: document the storage layout
      */
-  inline const MatrixType& matrixLLT() const {
+    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 successful,
+      * \returns \c Success if computation was succesful,
      *          \c NumericalIssue if the matrix.appears not to be positive definite.
      */
-  ComputationInfo info() const {
+    ComputationInfo info() const
    {
      eigen_assert(m_isInitialized && "LLT is not initialized.");
      return m_info;
    }
-  /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
+    /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
   * is self-adjoint.
      *
      * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
      * \code x = decomposition.adjoint().solve(b) \endcode
      */
-  const LLT& adjoint() const noexcept { return *this; }
+    const LLT& adjoint() const { return *this; };
-  constexpr Index rows() const noexcept { return m_matrix.rows(); }
+    inline Index rows() const { return m_matrix.rows(); }
-  constexpr Index cols() const noexcept { return m_matrix.cols(); }
+    inline Index cols() const { return m_matrix.cols(); }
    template<typename VectorType>
-  LLT& rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
+    LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    template<typename RhsType, typename DstType>
    EIGEN_DEVICE_FUNC
    void _solve_impl(const RhsType &rhs, DstType &dst) const;
  template <bool Conjugate, typename RhsType, typename DstType>
  void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
    #endif
  protected:
-  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
    static void check_template_parameters()
    {
      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
    }
    /** \internal
      * Used to compute and store L
@@ -213,17 +227,16 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
 namespace internal {
-template <typename Scalar, int UpLo>
+template<typename Scalar, int UpLo> struct llt_inplace;
 struct llt_inplace;
 template<typename MatrixType, typename VectorType>
-static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec,
+static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
-                                   const typename MatrixType::RealScalar& sigma) {
+{
  using std::sqrt;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::ColXpr ColXpr;
-  typedef internal::remove_all_t<ColXpr> ColXprCleaned;
+  typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
  typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
  typedef Matrix<Scalar,Dynamic,1> TempVectorType;
  typedef typename TempVectorType::SegmentReturnType TempVecSegment;
@@ -233,27 +246,33 @@ static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec,
  TempVectorType temp;
-  if (sigma > 0) {
+  if(sigma>0)
  {
    // This version is based on Givens rotations.
    // It is faster than the other one below, but only works for updates,
    // i.e., for sigma > 0
    temp = sqrt(sigma) * vec;
-    for (Index i = 0; i < n; ++i) {
+    for(Index i=0; i<n; ++i)
    {
      JacobiRotation<Scalar> g;
      g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
      Index rs = n-i-1;
-      if (rs > 0) {
+      if(rs>0)
      {
        ColXprSegment x(mat.col(i).tail(rs));
        TempVecSegment y(temp.tail(rs));
        apply_rotation_in_the_plane(x, y, g);
      }
    }
-  } else {
+  }
  else
  {
    temp = vec;
    RealScalar beta = 1;
-    for (Index j = 0; j < n; ++j) {
+    for(Index j=0; j<n; ++j)
    {
      RealScalar Ljj = numext::real(mat.coeff(j,j));
      RealScalar dj = numext::abs2(Ljj);
      Scalar wj = temp.coeff(j);
@@ -261,34 +280,37 @@ static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec,
      RealScalar gamma = dj*beta + swj2;
      RealScalar x = dj + swj2/beta;
-      if (x <= RealScalar(0)) return j;
+      if (x<=RealScalar(0))
        return j;
      RealScalar nLjj = sqrt(x);
      mat.coeffRef(j,j) = nLjj;
      beta += swj2/dj;
      // Update the terms of L
      Index rs = n-j-1;
-      if (rs) {
+      if(rs)
      {
        temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
-        if (!numext::is_exactly_zero(gamma))
+        if(gamma != 0)
-          mat.col(j).tail(rs) =
+          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
              (nLjj / Ljj) * mat.col(j).tail(rs) + (nLjj * sigma * numext::conj(wj) / gamma) * temp.tail(rs);
      }
    }
  }
  return -1;
 }
-template <typename Scalar>
+template<typename Scalar> struct llt_inplace<Scalar, Lower>
-struct llt_inplace<Scalar, Lower> {
+{
  typedef typename NumTraits<Scalar>::Real RealScalar;
  template<typename MatrixType>
-  static Index unblocked(MatrixType& mat) {
+  static Index unblocked(MatrixType& mat)
  {
    using std::sqrt;
    eigen_assert(mat.rows()==mat.cols());
    const Index size = mat.rows();
-    for (Index k = 0; k < size; ++k) {
+    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);
@@ -297,7 +319,8 @@ struct llt_inplace<Scalar, Lower> {
      RealScalar x = numext::real(mat.coeff(k,k));
      if (k>0) x -= A10.squaredNorm();
-      if (x <= RealScalar(0)) return k;
+      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 /= x;
@@ -306,16 +329,19 @@ struct llt_inplace<Scalar, Lower> {
  }
  template<typename MatrixType>
-  static Index blocked(MatrixType& m) {
+  static Index blocked(MatrixType& m)
  {
    eigen_assert(m.rows()==m.cols());
    Index size = m.rows();
-    if (size < 32) return unblocked(m);
+    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) {
+    for (Index k=0; k<size; k+=blockSize)
    {
      // partition the matrix:
      //       A00 |  -  |  -
      // lu  = A10 | A11 |  -
@@ -329,60 +355,60 @@ struct llt_inplace<Scalar, Lower> {
      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)
+      if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
        A22.template selfadjointView<Lower>().rankUpdate(A21,
                                                         typename NumTraits<RealScalar>::Literal(-1));  // bottleneck
    }
    return -1;
  }
  template<typename MatrixType, typename VectorType>
-  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
+  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
  {
    return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
  }
 };
-template <typename Scalar>
+template<typename Scalar> struct llt_inplace<Scalar, Upper>
-struct llt_inplace<Scalar, Upper> {
+{
  typedef typename NumTraits<Scalar>::Real RealScalar;
  template<typename MatrixType>
-  static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat) {
+  static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)
  {
    Transpose<MatrixType> matt(mat);
    return llt_inplace<Scalar, Lower>::unblocked(matt);
  }
  template<typename MatrixType>
-  static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat) {
+  static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)
  {
    Transpose<MatrixType> matt(mat);
    return llt_inplace<Scalar, Lower>::blocked(matt);
  }
  template<typename MatrixType, typename VectorType>
-  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
+  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
  {
    Transpose<MatrixType> matt(mat);
    return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
  }
 };
-template <typename MatrixType>
+template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
-struct LLT_Traits<MatrixType, Lower> {
+{
  typedef const TriangularView<const MatrixType, Lower> MatrixL;
  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
-  static bool inplace_decomposition(MatrixType& m) {
+  static bool inplace_decomposition(MatrixType& m)
-    return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m) == -1;
+  { return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
  }
 };
-template <typename MatrixType>
+template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
-struct LLT_Traits<MatrixType, Upper> {
+{
  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
  typedef const TriangularView<const MatrixType, Upper> MatrixU;
  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
-  static bool inplace_decomposition(MatrixType& m) {
+  static bool inplace_decomposition(MatrixType& m)
-    return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m) == -1;
+  { return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
  }
 };
 } // end namespace internal
@@ -394,26 +420,29 @@ struct LLT_Traits<MatrixType, Upper> {
  * Example: \include TutorialLinAlgComputeTwice.cpp
  * Output: \verbinclude TutorialLinAlgComputeTwice.out
  */
-template <typename MatrixType, int UpLo_>
+template<typename MatrixType, int _UpLo>
 template<typename InputType>
-LLT<MatrixType, UpLo_>& LLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
+LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
 {
  check_template_parameters();
  eigen_assert(a.rows()==a.cols());
  const Index size = a.rows();
  m_matrix.resize(size, size);
-  if (!internal::is_same_dense(m_matrix, a.derived())) m_matrix = a.derived();
+  if (!internal::is_same_dense(m_matrix, a.derived()))
    m_matrix = a.derived();
  // Compute matrix L1 norm = max abs column sum.
  m_l1_norm = RealScalar(0);
  // TODO move this code to SelfAdjointView
  for (Index col = 0; col < size; ++col) {
    RealScalar abs_col_sum;
-    if (UpLo_ == Lower)
+    if (_UpLo == Lower)
-      abs_col_sum =
+      abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
          m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
    else
-      abs_col_sum =
+      abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
-          m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
+    if (abs_col_sum > m_l1_norm)
-    if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
+      m_l1_norm = abs_col_sum;
  }
  m_isInitialized = true;
@@ -428,9 +457,10 @@ LLT<MatrixType, UpLo_>& LLT<MatrixType, UpLo_>::compute(const EigenBase<InputTyp
  * then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
  * of same dimension.
  */
-template <typename MatrixType_, int UpLo_>
+template<typename _MatrixType, int _UpLo>
 template<typename VectorType>
-LLT<MatrixType_, UpLo_>& LLT<MatrixType_, UpLo_>::rankUpdate(const VectorType& v, const RealScalar& sigma) {
+LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)
 {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
  eigen_assert(v.size()==m_matrix.cols());
  eigen_assert(m_isInitialized);
@@ -443,19 +473,12 @@ LLT<MatrixType_, UpLo_>& LLT<MatrixType_, UpLo_>::rankUpdate(const VectorType& v
 }
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-template <typename MatrixType_, int UpLo_>
+template<typename _MatrixType,int _UpLo>
 template<typename RhsType, typename DstType>
-void LLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
+EIGEN_DEVICE_FUNC void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
-  _solve_impl_transposed<true>(rhs, dst);
+{
 }
 template <typename MatrixType_, int UpLo_>
 template <bool Conjugate, typename RhsType, typename DstType>
 void LLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
  dst = rhs;
-
+  solveInPlace(dst);
  matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
  matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
 }
 #endif
@@ -472,9 +495,10 @@ void LLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType
  *
  * \sa LLT::solve(), MatrixBase::llt()
  */
-template <typename MatrixType, int UpLo_>
+template<typename MatrixType, int _UpLo>
 template<typename Derived>
-void LLT<MatrixType, UpLo_>::solveInPlace(const MatrixBase<Derived>& bAndX) const {
+void LLT<MatrixType,_UpLo>::solveInPlace(const MatrixBase<Derived> &bAndX) const
 {
  eigen_assert(m_isInitialized && "LLT is not initialized.");
  eigen_assert(m_matrix.rows()==bAndX.rows());
  matrixL().solveInPlace(bAndX);
@@ -484,8 +508,9 @@ void LLT<MatrixType, UpLo_>::solveInPlace(const MatrixBase<Derived>& bAndX) cons
 /** \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_>
+template<typename MatrixType, int _UpLo>
-MatrixType LLT<MatrixType, UpLo_>::reconstructedMatrix() const {
+MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
 {
  eigen_assert(m_isInitialized && "LLT is not initialized.");
  return matrixL() * matrixL().adjoint().toDenseMatrix();
 }
@@ -495,7 +520,9 @@ MatrixType LLT<MatrixType, UpLo_>::reconstructedMatrix() const {
  * \sa SelfAdjointView::llt()
  */
 template<typename Derived>
-inline const LLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::llt() const {
+inline const LLT<typename MatrixBase<Derived>::PlainObject>
 MatrixBase<Derived>::llt() const
 {
  return LLT<PlainObject>(derived());
 }
@@ -504,8 +531,9 @@ inline const LLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>:
  * \sa SelfAdjointView::llt()
  */
 template<typename MatrixType, unsigned int UpLo>
-inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo> SelfAdjointView<MatrixType, UpLo>::llt()
+inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
-    const {
+SelfAdjointView<MatrixType, UpLo>::llt() const
 {
  return LLT<PlainObject,UpLo>(m_matrix);
 }
--- a/Eigen/src/Cholesky/LLT_LAPACKE.h
+++ b/Eigen/src/Cholesky/LLT_LAPACKE.h
@@ -33,89 +33,64 @@
 #ifndef EIGEN_LLT_LAPACKE_H
 #define EIGEN_LLT_LAPACKE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
-namespace lapacke_helpers {
+template<typename Scalar> struct lapacke_llt;
 // -------------------------------------------------------------------------------------------------------------------
 //        Dispatch for rank update handling upper and lower parts
 // -------------------------------------------------------------------------------------------------------------------
-template <UpLoType Mode>
+#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \
-struct rank_update {};
+template<> struct lapacke_llt<EIGTYPE> \
-
+{ \
-template <>
+  template<typename MatrixType> \
-struct rank_update<Lower> {
+  static inline Index potrf(MatrixType& m, char uplo) \
-  template <typename MatrixType, typename VectorType>
+  { \
-  static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
+    lapack_int matrix_order; \
-    return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
+    lapack_int size, lda, info, StorageOrder; \
-  }
+    EIGTYPE* a; \
    eigen_assert(m.rows()==m.cols()); \
    /* Set up parameters for ?potrf */ \
    size = convert_index<lapack_int>(m.rows()); \
    StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \
    matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
    a = &(m.coeffRef(0,0)); \
    lda = convert_index<lapack_int>(m.outerStride()); \
 \
    info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \
    info = (info==0) ? -1 : info>0 ? info-1 : size; \
    return info; \
  } \
 }; \
 template<> struct llt_inplace<EIGTYPE, Lower> \
 { \
  template<typename MatrixType> \
  static Index blocked(MatrixType& m) \
  { \
    return lapacke_llt<EIGTYPE>::potrf(m, 'L'); \
  } \
  template<typename MatrixType, typename VectorType> \
  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
  { return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \
 }; \
 template<> struct llt_inplace<EIGTYPE, Upper> \
 { \
  template<typename MatrixType> \
  static Index blocked(MatrixType& m) \
  { \
    return lapacke_llt<EIGTYPE>::potrf(m, 'U'); \
  } \
  template<typename MatrixType, typename VectorType> \
  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
  { \
    Transpose<MatrixType> matt(mat); \
    return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \
  } \
 };
-template <>
+EIGEN_LAPACKE_LLT(double, double, d)
-struct rank_update<Upper> {
+EIGEN_LAPACKE_LLT(float, float, s)
-  template <typename MatrixType, typename VectorType>
+EIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z)
-  static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
+EIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c)
    Transpose<MatrixType> matt(mat);
    return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
  }
 };
 // -------------------------------------------------------------------------------------------------------------------
 //        Generic lapacke llt implementation that hands of to the dispatches
 // -------------------------------------------------------------------------------------------------------------------
 template <typename Scalar, UpLoType Mode>
 struct lapacke_llt {
  EIGEN_STATIC_ASSERT(((Mode == Lower) || (Mode == Upper)), MODE_MUST_BE_UPPER_OR_LOWER)
  template <typename MatrixType>
  static Index blocked(MatrixType &m) {
    eigen_assert(m.rows() == m.cols());
    if (m.rows() == 0) {
      return -1;
    }
    /* Set up parameters for ?potrf */
    lapack_int size = to_lapack(m.rows());
    lapack_int matrix_order = lapack_storage_of(m);
    constexpr char uplo = Mode == Upper ? 'U' : 'L';
    Scalar *a = &(m.coeffRef(0, 0));
    lapack_int lda = to_lapack(m.outerStride());
    lapack_int info = potrf(matrix_order, uplo, size, to_lapack(a), lda);
    info = (info == 0) ? -1 : info > 0 ? info - 1 : size;
    return info;
  }
  template <typename MatrixType, typename VectorType>
  static Index rankUpdate(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
    return rank_update<Mode>::run(mat, vec, sigma);
  }
 };
 }  // namespace lapacke_helpers
 // end namespace lapacke_helpers
 /*
 * Here, we just put the generic implementation from lapacke_llt into a full specialization of the llt_inplace
 * type. By being a full specialization, the versions defined here thus get precedence over the generic implementation
 * in LLT.h for double, float and complex double, complex float types.
 */
 #define EIGEN_LAPACKE_LLT(EIGTYPE)                                                             \
  template <>                                                                                  \
  struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
  template <>                                                                                  \
  struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
 EIGEN_LAPACKE_LLT(double)
 EIGEN_LAPACKE_LLT(float)
 EIGEN_LAPACKE_LLT(std::complex<double>)
 EIGEN_LAPACKE_LLT(std::complex<float>)
 #undef EIGEN_LAPACKE_LLT
 } // end namespace internal
--- a/Eigen/src/CholmodSupport/CholmodSupport.h
+++ b/Eigen/src/CholmodSupport/CholmodSupport.h
@@ -10,18 +10,13 @@
 #ifndef EIGEN_CHOLMODSUPPORT_H
 #define EIGEN_CHOLMODSUPPORT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
-template <typename Scalar>
+template<typename Scalar> struct cholmod_configure_matrix;
 struct cholmod_configure_matrix;
-template <>
+template<> struct cholmod_configure_matrix<double> {
 struct cholmod_configure_matrix<double> {
  template<typename CholmodType>
  static void run(CholmodType& mat) {
    mat.xtype = CHOLMOD_REAL;
@@ -29,8 +24,7 @@ struct cholmod_configure_matrix<double> {
  }
 };
-template <>
+template<> struct cholmod_configure_matrix<std::complex<double> > {
 struct cholmod_configure_matrix<std::complex<double> > {
  template<typename CholmodType>
  static void run(CholmodType& mat) {
    mat.xtype = CHOLMOD_COMPLEX;
@@ -38,7 +32,7 @@ struct cholmod_configure_matrix<std::complex<double> > {
  }
 };
-// Other scalar types are not yet supported by Cholmod
+// Other scalar types are not yet suppotred by Cholmod
 // template<> struct cholmod_configure_matrix<float> {
 //   template<typename CholmodType>
 //   static void run(CholmodType& mat) {
@@ -60,8 +54,9 @@ struct cholmod_configure_matrix<std::complex<double> > {
 /** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
  * Note that the data are shared.
  */
-template <typename Scalar_, int Options_, typename StorageIndex_>
+template<typename _Scalar, int _Options, typename _StorageIndex>
-cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, StorageIndex_> > mat) {
+cholmod_sparse viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_StorageIndex> > mat)
 {
  cholmod_sparse res;
  res.nzmax   = mat.nonZeros();
  res.nrow    = mat.rows();
@@ -71,10 +66,13 @@ cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, StorageIndex_>
  res.x       = mat.valuePtr();
  res.z       = 0;
  res.sorted  = 1;
-  if (mat.isCompressed()) {
+  if(mat.isCompressed())
  {
    res.packed  = 1;
    res.nz = 0;
-  } else {
+  }
  else
  {
    res.packed  = 0;
    res.nz = mat.innerNonZeroPtr();
  }
@@ -82,46 +80,50 @@ cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, StorageIndex_>
  res.dtype   = 0;
  res.stype   = -1;
-  if (internal::is_same<StorageIndex_, int>::value) {
+  if (internal::is_same<_StorageIndex,int>::value)
  {
    res.itype = CHOLMOD_INT;
-  } else if (internal::is_same<StorageIndex_, SuiteSparse_long>::value) {
+  }
  else if (internal::is_same<_StorageIndex,long>::value)
  {
    res.itype = CHOLMOD_LONG;
-  } else {
+  }
  else
  {
    eigen_assert(false && "Index type not supported yet");
  }
  // setup res.xtype
-  internal::cholmod_configure_matrix<Scalar_>::run(res);
+  internal::cholmod_configure_matrix<_Scalar>::run(res);
  res.stype = 0;
  return res;
 }
-template <typename Scalar_, int Options_, typename Index_>
+template<typename _Scalar, int _Options, typename _Index>
-const cholmod_sparse viewAsCholmod(const SparseMatrix<Scalar_, Options_, Index_>& mat) {
+const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
-  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
+{
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
  return res;
 }
-template <typename Scalar_, int Options_, typename Index_>
+template<typename _Scalar, int _Options, typename _Index>
-const cholmod_sparse viewAsCholmod(const SparseVector<Scalar_, Options_, Index_>& mat) {
+const cholmod_sparse viewAsCholmod(const SparseVector<_Scalar,_Options,_Index>& mat)
-  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
+{
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
  return res;
 }
 /** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
  * The data are not copied but shared. */
-template <typename Scalar_, int Options_, typename Index_, unsigned int UpLo>
+template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
-cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<Scalar_, Options_, Index_>, UpLo>& mat) {
+cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
-  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.matrix().const_cast_derived()));
+{
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.matrix().const_cast_derived()));
  if(UpLo==Upper) res.stype =  1;
  if(UpLo==Lower) res.stype = -1;
  // swap stype for rowmajor matrices (only works for real matrices)
  EIGEN_STATIC_ASSERT((Options_ & RowMajorBit) == 0 || NumTraits<Scalar_>::IsComplex == 0,
                      THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
  if (Options_ & RowMajorBit) res.stype *= -1;
  return res;
 }
@@ -129,9 +131,9 @@ cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<Scal
 /** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
  * The data are not copied but shared. */
 template<typename Derived>
-cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat) {
+cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
-  EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags & RowMajorBit) == 0,
+{
-                      THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+  EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
  typedef typename Derived::Scalar Scalar;
  cholmod_dense res;
@@ -149,132 +151,67 @@ cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat) {
 /** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
  * The data are not copied but shared. */
-template <typename Scalar, typename StorageIndex>
+template<typename Scalar, int Flags, typename StorageIndex>
-Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_sparse& cm) {
+MappedSparseMatrix<Scalar,Flags,StorageIndex> viewAsEigen(cholmod_sparse& cm)
-  return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
+{
-      cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol], static_cast<StorageIndex*>(cm.p),
+  return MappedSparseMatrix<Scalar,Flags,StorageIndex>
-      static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
+         (cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],
          static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );
 }
-/** Returns a view of the Cholmod sparse matrix factor \a cm as an Eigen sparse matrix.
+enum CholmodMode {
- * The data are not copied but shared. */
+  CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
-template <typename Scalar, typename StorageIndex>
+};
 Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_factor& cm) {
  return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
      cm.n, cm.n, static_cast<StorageIndex*>(cm.p)[cm.n], static_cast<StorageIndex*>(cm.p),
      static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
 }
 namespace internal {
 // template specializations for int and long that call the correct cholmod method
 #define EIGEN_CHOLMOD_SPECIALIZE0(ret, name)                        \
  template <typename StorageIndex_>                                 \
  inline ret cm_##name(cholmod_common& Common) {                    \
    return cholmod_##name(&Common);                                 \
  }                                                                 \
  template <>                                                       \
  inline ret cm_##name<SuiteSparse_long>(cholmod_common & Common) { \
    return cholmod_l_##name(&Common);                               \
  }
 #define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1)                         \
  template <typename StorageIndex_>                                          \
  inline ret cm_##name(t1& a1, cholmod_common& Common) {                     \
    return cholmod_##name(&a1, &Common);                                     \
  }                                                                          \
  template <>                                                                \
  inline ret cm_##name<SuiteSparse_long>(t1 & a1, cholmod_common & Common) { \
    return cholmod_l_##name(&a1, &Common);                                   \
  }
 EIGEN_CHOLMOD_SPECIALIZE0(int, start)
 EIGEN_CHOLMOD_SPECIALIZE0(int, finish)
 EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
 EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
 EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)
 EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
 EIGEN_CHOLMOD_SPECIALIZE1(cholmod_sparse*, factor_to_sparse, cholmod_factor, L)
 template <typename StorageIndex_>
 inline cholmod_dense* cm_solve(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
  return cholmod_solve(sys, &L, &B, &Common);
 }
 template <>
 inline cholmod_dense* cm_solve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
  return cholmod_l_solve(sys, &L, &B, &Common);
 }
 template <typename StorageIndex_>
 inline cholmod_sparse* cm_spsolve(int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common& Common) {
  return cholmod_spsolve(sys, &L, &B, &Common);
 }
 template <>
 inline cholmod_sparse* cm_spsolve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_sparse& B,
                                                    cholmod_common& Common) {
  return cholmod_l_spsolve(sys, &L, &B, &Common);
 }
 template <typename StorageIndex_>
 inline int cm_factorize_p(cholmod_sparse* A, double beta[2], StorageIndex_* fset, std::size_t fsize, cholmod_factor* L,
                          cholmod_common& Common) {
  return cholmod_factorize_p(A, beta, fset, fsize, L, &Common);
 }
 template <>
 inline int cm_factorize_p<SuiteSparse_long>(cholmod_sparse* A, double beta[2], SuiteSparse_long* fset,
                                            std::size_t fsize, cholmod_factor* L, cholmod_common& Common) {
  return cholmod_l_factorize_p(A, beta, fset, fsize, L, &Common);
 }
 #undef EIGEN_CHOLMOD_SPECIALIZE0
 #undef EIGEN_CHOLMOD_SPECIALIZE1
 }  // namespace internal
 enum CholmodMode { CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt };
 /** \ingroup CholmodSupport_Module
  * \class CholmodBase
  * \brief The base class for the direct Cholesky factorization of Cholmod
  * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
  */
-template <typename MatrixType_, int UpLo_, typename Derived>
+template<typename _MatrixType, int _UpLo, typename Derived>
-class CholmodBase : public SparseSolverBase<Derived> {
+class CholmodBase : public SparseSolverBase<Derived>
 {
  protected:
    typedef SparseSolverBase<Derived> Base;
    using Base::derived;
    using Base::m_isInitialized;
  public:
-  typedef MatrixType_ MatrixType;
+    typedef _MatrixType MatrixType;
-  enum { UpLo = UpLo_ };
+    enum { UpLo = _UpLo };
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::RealScalar RealScalar;
    typedef MatrixType CholMatrixType;
    typedef typename MatrixType::StorageIndex StorageIndex;
-  enum { ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
+    enum {
      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
    };
  public:
-  CholmodBase() : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
+
    CholmodBase()
      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
    {
      EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
      m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
-    internal::cm_start<StorageIndex>(m_cholmod);
+      cholmod_start(&m_cholmod);
    }
    explicit CholmodBase(const MatrixType& matrix)
-      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
+      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
    {
      EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
      m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
-    internal::cm_start<StorageIndex>(m_cholmod);
+      cholmod_start(&m_cholmod);
      compute(matrix);
    }
-  ~CholmodBase() {
+    ~CholmodBase()
-    if (m_cholmodFactor) internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
+    {
-    internal::cm_finish<StorageIndex>(m_cholmod);
+      if(m_cholmodFactor)
        cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
      cholmod_finish(&m_cholmod);
    }
    inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
@@ -282,16 +219,18 @@ class CholmodBase : public SparseSolverBase<Derived> {
    /** \brief Reports whether previous computation was successful.
      *
-   * \returns \c Success if computation was successful,
+      * \returns \c Success if computation was succesful,
      *          \c NumericalIssue if the matrix.appears to be negative.
      */
-  ComputationInfo info() const {
+    ComputationInfo info() const
    {
      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
      return m_info;
    }
    /** Computes the sparse Cholesky decomposition of \a matrix */
-  Derived& compute(const MatrixType& matrix) {
+    Derived& compute(const MatrixType& matrix)
    {
      analyzePattern(matrix);
      factorize(matrix);
      return derived();
@@ -303,13 +242,15 @@ class CholmodBase : public SparseSolverBase<Derived> {
      * 
      * \sa factorize()
      */
-  void analyzePattern(const MatrixType& matrix) {
+    void analyzePattern(const MatrixType& matrix)
-    if (m_cholmodFactor) {
+    {
-      internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
+      if(m_cholmodFactor)
      {
        cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
        m_cholmodFactor = 0;
      }
      cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
-    m_cholmodFactor = internal::cm_analyze<StorageIndex>(A, m_cholmod);
+      m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);
      this->m_isInitialized = true;
      this->m_info = Success;
@@ -319,20 +260,18 @@ class CholmodBase : public SparseSolverBase<Derived> {
    /** Performs a numeric decomposition of \a matrix
      *
-   * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been
+      * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
   * performed.
      *
      * \sa analyzePattern()
      */
-  void factorize(const MatrixType& matrix) {
+    void factorize(const MatrixType& matrix)
    {
      eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
      cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
-    internal::cm_factorize_p<StorageIndex>(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod);
+      cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod);
-    // If the factorization failed, either the input matrix was zero (so m_cholmodFactor == nullptr), or minor is the
+      // If the factorization failed, minor is the column at which it did. On success minor == n.
-    // column at which it failed. On success minor == n.
+      this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
    this->m_info =
        (m_cholmodFactor != nullptr && m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
      m_factorizationIsOk = true;
    }
@@ -343,57 +282,53 @@ class CholmodBase : public SparseSolverBase<Derived> {
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** \internal */
    template<typename Rhs,typename Dest>
-  void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const {
+    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
-    eigen_assert(m_factorizationIsOk &&
+    {
-                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
+      eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
                 "symbolic()/numeric()");
      const Index size = m_cholmodFactor->n;
      EIGEN_UNUSED_VARIABLE(size);
      eigen_assert(size==b.rows());
-    // Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
+      // Cholmod needs column-major stoarge without inner-stride, which corresponds to the default behavior of Ref.
      Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
      cholmod_dense b_cd = viewAsCholmod(b_ref);
-    cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod);
+      cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
-    if (!x_cd) {
+      if(!x_cd)
      {
        this->m_info = NumericalIssue;
        return;
      }
      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
-    // NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
+      dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
-    dest = Matrix<Scalar, Dest::RowsAtCompileTime, Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),
+      cholmod_free_dense(&x_cd, &m_cholmod);
                                                                                 b.rows(), b.cols());
    internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
    }
    /** \internal */
    template<typename RhsDerived, typename DestDerived>
-  void _solve_impl(const SparseMatrixBase<RhsDerived>& b, SparseMatrixBase<DestDerived>& dest) const {
+    void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &dest) const
-    eigen_assert(m_factorizationIsOk &&
+    {
-                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
+      eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
                 "symbolic()/numeric()");
      const Index size = m_cholmodFactor->n;
      EIGEN_UNUSED_VARIABLE(size);
      eigen_assert(size==b.rows());
      // note: cs stands for Cholmod Sparse
-    Ref<SparseMatrix<typename RhsDerived::Scalar, ColMajor, typename RhsDerived::StorageIndex> > b_ref(
+      Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());
        b.const_cast_derived());
      cholmod_sparse b_cs = viewAsCholmod(b_ref);
-    cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod);
+      cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);
-    if (!x_cs) {
+      if(!x_cs)
      {
        this->m_info = NumericalIssue;
        return;
      }
      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
-    // NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's
+      dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);
-    // sparse solver)
+      cholmod_free_sparse(&x_cs, &m_cholmod);
    dest.derived() = viewAsEigen<typename DestDerived::Scalar, typename DestDerived::StorageIndex>(*x_cs);
    internal::cm_free_sparse<StorageIndex>(x_cs, m_cholmod);
    }
    #endif // EIGEN_PARSED_BY_DOXYGEN
    /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
      *
      * During the numerical factorization, an offset term is added to the diagonal coefficients:\n
@@ -403,29 +338,31 @@ class CholmodBase : public SparseSolverBase<Derived> {
      *
      * \returns a reference to \c *this.
      */
-  Derived& setShift(const RealScalar& offset) {
+    Derived& setShift(const RealScalar& offset)
    {
      m_shiftOffset[0] = double(offset);
      return derived();
    }
    /** \returns the determinant of the underlying matrix from the current factorization */
-  Scalar determinant() const {
+    Scalar determinant() const
    {
      using std::exp;
      return exp(logDeterminant());
    }
    /** \returns the log determinant of the underlying matrix from the current factorization */
-  Scalar logDeterminant() const {
+    Scalar logDeterminant() const
-    using numext::real;
+    {
      using std::log;
-    eigen_assert(m_factorizationIsOk &&
+      using numext::real;
-                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
+      eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
                 "symbolic()/numeric()");
      RealScalar logDet = 0;
      Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
-    if (m_cholmodFactor->is_super) {
+      if (m_cholmodFactor->is_super)
-      // Supernodal factorization stored as a packed list of dense column-major blocks,
+      {
        // Supernodal factorization stored as a packed list of dense column-major blocs,
        // as described by the following structure:
        // super[k] == index of the first column of the j-th super node
@@ -436,25 +373,31 @@ class CholmodBase : public SparseSolverBase<Derived> {
        StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
        Index nb_super_nodes = m_cholmodFactor->nsuper;
-      for (Index k = 0; k < nb_super_nodes; ++k) {
+        for (Index k=0; k < nb_super_nodes; ++k)
        {
          StorageIndex ncols = super[k + 1] - super[k];
          StorageIndex nrows = pi[k + 1] - pi[k];
          Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
          logDet += sk.real().log().sum();
        }
-    } else {
+      }
      else
      {
        // Simplicial factorization stored as standard CSC matrix.
        StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
        Index size = m_cholmodFactor->n;
-      for (Index k = 0; k < size; ++k) logDet += log(real(x[p[k]]));
+        for (Index k=0; k<size; ++k)
          logDet += log(real( x[p[k]] ));
      }
-    if (m_cholmodFactor->is_ll) logDet *= 2.0;
+      if (m_cholmodFactor->is_ll)
        logDet *= 2.0;
      return logDet;
-  }
+    };
    template<typename Stream>
-  void dumpMemory(Stream& /*s*/) {}
+    void dumpMemory(Stream& /*s*/)
    {}
  protected:
    mutable cholmod_common m_cholmod;
@@ -471,127 +414,95 @@ class CholmodBase : public SparseSolverBase<Derived> {
  *
  * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
  * using the Cholmod library.
- * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
- * interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
+  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
- * either dense or sparse.
+  * X and B can be either dense or sparse.
  *
- * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
- * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
  *               or Upper. Default is Lower.
  *
  * \implsparsesolverconcept
  *
- * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
+  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
 * compressed.
  *
  * \warning Only double precision real and complex scalar types are supported by Cholmod.
  *
  * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
  */
-template <typename MatrixType_, int UpLo_ = Lower>
+template<typename _MatrixType, int _UpLo = Lower>
-class CholmodSimplicialLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT<MatrixType_, UpLo_> > {
+class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
-  typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT> Base;
+{
    typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
    using Base::m_cholmod;
  public:
-  typedef MatrixType_ MatrixType;
+    
-  typedef typename MatrixType::Scalar Scalar;
+    typedef _MatrixType MatrixType;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef TriangularView<const MatrixType, Eigen::Lower> MatrixL;
  typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::Upper> MatrixU;
    CholmodSimplicialLLT() : Base() { init(); }
-  CholmodSimplicialLLT(const MatrixType& matrix) : Base() {
+    CholmodSimplicialLLT(const MatrixType& matrix) : Base()
    {
      init();
      this->compute(matrix);
    }
    ~CholmodSimplicialLLT() {}
  /** \returns an expression of the factor L */
  inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }
  /** \returns an expression of the factor U (= L^*) */
  inline MatrixU matrixU() const { return matrixL().adjoint(); }
  protected:
-  void init() {
+    void init()
    {
      m_cholmod.final_asis = 0;
      m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
      m_cholmod.final_ll = 1;
    }
 };
 /** \ingroup CholmodSupport_Module
  * \class CholmodSimplicialLDLT
  * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
  *
  * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
  * using the Cholmod library.
- * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical
+  * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
- * interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
+  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
- * either dense or sparse.
+  * X and B can be either dense or sparse.
  *
- * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
- * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
  *               or Upper. Default is Lower.
  *
  * \implsparsesolverconcept
  *
- * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
+  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
 * compressed.
  *
  * \warning Only double precision real and complex scalar types are supported by Cholmod.
  *
  * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
  */
-template <typename MatrixType_, int UpLo_ = Lower>
+template<typename _MatrixType, int _UpLo = Lower>
-class CholmodSimplicialLDLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT<MatrixType_, UpLo_> > {
+class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
-  typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT> Base;
+{
    typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
    using Base::m_cholmod;
  public:
-  typedef MatrixType_ MatrixType;
+    
-  typedef typename MatrixType::Scalar Scalar;
+    typedef _MatrixType MatrixType;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef Matrix<Scalar, Dynamic, 1> VectorType;
  typedef TriangularView<const MatrixType, Eigen::UnitLower> MatrixL;
  typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;
    CholmodSimplicialLDLT() : Base() { init(); }
-  CholmodSimplicialLDLT(const MatrixType& matrix) : Base() {
+    CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
    {
      init();
      this->compute(matrix);
    }
    ~CholmodSimplicialLDLT() {}
  /** \returns a vector expression of the diagonal D */
  inline VectorType vectorD() const {
    auto cholmodL = viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor);
    VectorType D{cholmodL.rows()};
    for (Index k = 0; k < cholmodL.outerSize(); ++k) {
      typename decltype(cholmodL)::InnerIterator it{cholmodL, k};
      D(k) = it.value();
    }
    return D;
  }
  /** \returns an expression of the factor L */
  inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }
  /** \returns an expression of the factor U (= L^*) */
  inline MatrixU matrixU() const { return matrixL().adjoint(); }
  protected:
-  void init() {
+    void init()
    {
      m_cholmod.final_asis = 1;
      m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
    }
@@ -607,54 +518,40 @@ class CholmodSimplicialLDLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimp
  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
  * X and B can be either dense or sparse.
  *
- * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
- * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
  *               or Upper. Default is Lower.
  *
  * \implsparsesolverconcept
  *
- * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
+  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
 * compressed.
  *
  * \warning Only double precision real and complex scalar types are supported by Cholmod.
  *
  * \sa \ref TutorialSparseSolverConcept
  */
-template <typename MatrixType_, int UpLo_ = Lower>
+template<typename _MatrixType, int _UpLo = Lower>
-class CholmodSupernodalLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT<MatrixType_, UpLo_> > {
+class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
-  typedef CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT> Base;
+{
    typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
    using Base::m_cholmod;
  public:
-  typedef MatrixType_ MatrixType;
+    
-  typedef typename MatrixType::Scalar Scalar;
+    typedef _MatrixType MatrixType;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
    CholmodSupernodalLLT() : Base() { init(); }
-  CholmodSupernodalLLT(const MatrixType& matrix) : Base() {
+    CholmodSupernodalLLT(const MatrixType& matrix) : Base()
    {
      init();
      this->compute(matrix);
    }
    ~CholmodSupernodalLLT() {}
  /** \returns an expression of the factor L */
  inline MatrixType matrixL() const {
    // Convert Cholmod factor's supernodal storage format to Eigen's CSC storage format
    cholmod_sparse* cholmodL = internal::cm_factor_to_sparse(*Base::m_cholmodFactor, m_cholmod);
    MatrixType L = viewAsEigen<Scalar, StorageIndex>(*cholmodL);
    internal::cm_free_sparse<StorageIndex>(cholmodL, m_cholmod);
    return L;
  }
  /** \returns an expression of the factor U (= L^*) */
  inline MatrixType matrixU() const { return matrixL().adjoint(); }
  protected:
-  void init() {
+    void init()
    {
      m_cholmod.final_asis = 1;
      m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
    }
@@ -672,38 +569,42 @@ class CholmodSupernodalLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSuper
  * On the other hand, it does not provide access to the result of the factorization.
  * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
  *
- * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
- * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+  * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
  *               or Upper. Default is Lower.
  *
  * \implsparsesolverconcept
  *
- * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
+  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
 * compressed.
  *
  * \warning Only double precision real and complex scalar types are supported by Cholmod.
  *
  * \sa \ref TutorialSparseSolverConcept
  */
-template <typename MatrixType_, int UpLo_ = Lower>
+template<typename _MatrixType, int _UpLo = Lower>
-class CholmodDecomposition : public CholmodBase<MatrixType_, UpLo_, CholmodDecomposition<MatrixType_, UpLo_> > {
+class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
-  typedef CholmodBase<MatrixType_, UpLo_, CholmodDecomposition> Base;
+{
    typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
    using Base::m_cholmod;
  public:
-  typedef MatrixType_ MatrixType;
+    
    typedef _MatrixType MatrixType;
    CholmodDecomposition() : Base() { init(); }
-  CholmodDecomposition(const MatrixType& matrix) : Base() {
+    CholmodDecomposition(const MatrixType& matrix) : Base()
    {
      init();
      this->compute(matrix);
    }
    ~CholmodDecomposition() {}
-  void setMode(CholmodMode mode) {
+    void setMode(CholmodMode mode)
-    switch (mode) {
+    {
      switch(mode)
      {
        case CholmodAuto:
          m_cholmod.final_asis = 1;
          m_cholmod.supernodal = CHOLMOD_AUTO;
@@ -725,9 +626,9 @@ class CholmodDecomposition : public CholmodBase<MatrixType_, UpLo_, CholmodDecom
          break;
      }
    }
  protected:
-  void init() {
+    void init()
    {
      m_cholmod.final_asis = 1;
      m_cholmod.supernodal = CHOLMOD_AUTO;
    }
--- a/Eigen/src/CholmodSupport/InternalHeaderCheck.h
+++ b/Eigen/src/CholmodSupport/InternalHeaderCheck.h
@@ -1,3 +0,0 @@
 #ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
 #error "Please include Eigen/CholmodSupport instead of including headers inside the src directory directly."
 #endif
--- a/Eigen/src/Core/ArithmeticSequence.h
+++ b/Eigen/src/Core/ArithmeticSequence.h
@@ -1,239 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_ARITHMETIC_SEQUENCE_H
 #define EIGEN_ARITHMETIC_SEQUENCE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 // Helper to cleanup the type of the increment:
 template <typename T>
 struct cleanup_seq_incr {
  typedef typename cleanup_index_type<T, DynamicIndex>::type type;
 };
 }  // namespace internal
 //--------------------------------------------------------------------------------
 // seq(first,last,incr) and seqN(first,size,incr)
 //--------------------------------------------------------------------------------
 template <typename FirstType = Index, typename SizeType = Index, typename IncrType = internal::FixedInt<1> >
 class ArithmeticSequence;
 template <typename FirstType, typename SizeType, typename IncrType>
 ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
                   typename internal::cleanup_index_type<SizeType>::type,
                   typename internal::cleanup_seq_incr<IncrType>::type>
 seqN(FirstType first, SizeType size, IncrType incr);
 /** \class ArithmeticSequence
 * \ingroup Core_Module
 *
 * This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by
 * its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride)
 * that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i.
 *
 * It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments
 * of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the
 * only way it is used.
 *
 * \tparam FirstType type of the first element, usually an Index,
 *                   but internally it can be a symbolic expression
 * \tparam SizeType type representing the size of the sequence, usually an Index
 *                  or a compile time integral constant. Internally, it can also be a symbolic expression
 * \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is
 * compile-time 1)
 *
 * \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView
 */
 template <typename FirstType, typename SizeType, typename IncrType>
 class ArithmeticSequence {
 public:
  constexpr ArithmeticSequence() = default;
  constexpr ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {}
  constexpr ArithmeticSequence(FirstType first, SizeType size, IncrType incr)
      : m_first(first), m_size(size), m_incr(incr) {}
  enum {
    // SizeAtCompileTime = internal::get_fixed_value<SizeType>::value,
    IncrAtCompileTime = internal::get_fixed_value<IncrType, DynamicIndex>::value
  };
  /** \returns the size, i.e., number of elements, of the sequence */
  constexpr Index size() const { return m_size; }
  /** \returns the first element \f$ a_0 \f$ in the sequence */
  constexpr Index first() const { return m_first; }
  /** \returns the value \f$ a_i \f$ at index \a i in the sequence. */
  constexpr Index operator[](Index i) const { return m_first + i * m_incr; }
  constexpr const FirstType& firstObject() const { return m_first; }
  constexpr const SizeType& sizeObject() const { return m_size; }
  constexpr const IncrType& incrObject() const { return m_incr; }
 protected:
  FirstType m_first;
  SizeType m_size;
  IncrType m_incr;
 public:
  constexpr auto reverse() const -> decltype(Eigen::seqN(m_first + (m_size + fix<-1>()) * m_incr, m_size, -m_incr)) {
    return seqN(m_first + (m_size + fix<-1>()) * m_incr, m_size, -m_incr);
  }
 };
 /** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr
 *
 * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
 template <typename FirstType, typename SizeType, typename IncrType>
 ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
                   typename internal::cleanup_index_type<SizeType>::type,
                   typename internal::cleanup_seq_incr<IncrType>::type>
 seqN(FirstType first, SizeType size, IncrType incr) {
  return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
                            typename internal::cleanup_index_type<SizeType>::type,
                            typename internal::cleanup_seq_incr<IncrType>::type>(first, size, incr);
 }
 /** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment
 *
 * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */
 template <typename FirstType, typename SizeType>
 ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
                   typename internal::cleanup_index_type<SizeType>::type>
 seqN(FirstType first, SizeType size) {
  return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
                            typename internal::cleanup_index_type<SizeType>::type>(first, size);
 }
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 /** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a
 * incr
 *
 * It is essentially an alias to:
 * \code
 * seqN(f, (l-f+incr)/incr, incr);
 * \endcode
 *
 * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType)
 */
 template <typename FirstType, typename LastType, typename IncrType>
 auto seq(FirstType f, LastType l, IncrType incr);
 /** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment
 *
 * It is essentially an alias to:
 * \code
 * seqN(f,l-f+1);
 * \endcode
 *
 * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType)
 */
 template <typename FirstType, typename LastType>
 auto seq(FirstType f, LastType l);
 #else  // EIGEN_PARSED_BY_DOXYGEN
 template <typename FirstType, typename LastType>
 auto seq(FirstType f, LastType l)
    -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
                     (typename internal::cleanup_index_type<LastType>::type(l) -
                      typename internal::cleanup_index_type<FirstType>::type(f) + fix<1>()))) {
  return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
              (typename internal::cleanup_index_type<LastType>::type(l) -
               typename internal::cleanup_index_type<FirstType>::type(f) + fix<1>()));
 }
 template <typename FirstType, typename LastType, typename IncrType>
 auto seq(FirstType f, LastType l, IncrType incr)
    -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
                     (typename internal::cleanup_index_type<LastType>::type(l) -
                      typename internal::cleanup_index_type<FirstType>::type(f) +
                      typename internal::cleanup_seq_incr<IncrType>::type(incr)) /
                         typename internal::cleanup_seq_incr<IncrType>::type(incr),
                     typename internal::cleanup_seq_incr<IncrType>::type(incr))) {
  typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
  return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
              (typename internal::cleanup_index_type<LastType>::type(l) -
               typename internal::cleanup_index_type<FirstType>::type(f) + CleanedIncrType(incr)) /
                  CleanedIncrType(incr),
              CleanedIncrType(incr));
 }
 #endif  // EIGEN_PARSED_BY_DOXYGEN
 namespace placeholders {
 /** \cpp11
 * \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr.
 *
 * It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode
 *
 * \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
 template <typename SizeType, typename IncrType>
 auto lastN(SizeType size, IncrType incr)
    -> decltype(seqN(Eigen::placeholders::last - (size - fix<1>()) * incr, size, incr)) {
  return seqN(Eigen::placeholders::last - (size - fix<1>()) * incr, size, incr);
 }
 /** \cpp11
 * \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment.
 *
 *  It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode
 *
 * \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */
 template <typename SizeType>
 auto lastN(SizeType size) -> decltype(seqN(Eigen::placeholders::last + fix<1>() - size, size)) {
  return seqN(Eigen::placeholders::last + fix<1>() - size, size);
 }
 }  // namespace placeholders
 /** \namespace Eigen::indexing
  * \ingroup Core_Module
  *
  * The sole purpose of this namespace is to be able to import all functions
  * and symbols that are expected to be used within operator() for indexing
  * and slicing. If you already imported the whole Eigen namespace:
  * \code using namespace Eigen; \endcode
  * then you are already all set. Otherwise, if you don't want/cannot import
  * the whole Eigen namespace, the following line:
  * \code using namespace Eigen::indexing; \endcode
  * is equivalent to:
  * \code
  using Eigen::fix;
  using Eigen::seq;
  using Eigen::seqN;
  using Eigen::placeholders::all;
  using Eigen::placeholders::last;
  using Eigen::placeholders::lastN;  // c++11 only
  using Eigen::placeholders::lastp1;
  \endcode
  */
 namespace indexing {
 using Eigen::fix;
 using Eigen::seq;
 using Eigen::seqN;
 using Eigen::placeholders::all;
 using Eigen::placeholders::last;
 using Eigen::placeholders::lastN;
 using Eigen::placeholders::lastp1;
 }  // namespace indexing
 }  // end namespace Eigen
 #endif  // EIGEN_ARITHMETIC_SEQUENCE_H
--- a/Eigen/src/Core/Array.h
+++ b/Eigen/src/Core/Array.h
@@ -10,19 +10,16 @@
 #ifndef EIGEN_ARRAY_H
 #define EIGEN_ARRAY_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
-template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
-struct traits<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>>
+struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_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;
+  typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
 };
-}  // namespace internal
+}
 /** \class Array
  * \ingroup Core_Module
@@ -44,13 +41,16 @@ struct traits<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>>
  *
  * \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
  */
-template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
-class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, 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_ };
+    enum { Options = _Options };
    typedef typename Base::PlainObject PlainObject;
  protected:
@@ -60,6 +60,7 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
    using Base::m_storage;
  public:
    using Base::base;
    using Base::coeff;
    using Base::coeffRef;
@@ -71,7 +72,9 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      * the usage of 'using'. This should be done only for operator=.
      */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
    {
      return Base::operator=(other);
    }
@@ -83,7 +86,9 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      * 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=.
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const Scalar& value) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array& operator=(const Scalar &value)
    {
      Base::setConstant(value);
      return *this;
    }
@@ -98,19 +103,20 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      * remain row-vectors and vectors remain vectors.
      */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other)
    {
      return Base::_set(other);
    }
-  /**
+    /** This is a special case of the templated operator=. Its purpose is to
-   * \brief Assigns arrays to each other.
+      * prevent a default operator= from hiding the templated operator=.
   *
   * \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_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const Array& other) { return Base::_set(other); }
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array& operator=(const Array& other)
    {
      return Base::_set(other);
    }
    /** Default constructor.
      *
@@ -122,77 +128,56 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      *
      * \sa resize(Index,Index)
      */
-#ifdef EIGEN_INITIALIZE_COEFFS
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() : Base() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
+    EIGEN_STRONG_INLINE Array() : Base()
-#else
+    {
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() = default;
+      Base::_check_template_params();
-#endif
+      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
  /** \brief Move constructor */
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(Array&&) = default;
  EIGEN_DEVICE_FUNC Array& operator=(Array&& other) noexcept(std::is_nothrow_move_assignable<Scalar>::value) {
    Base::operator=(std::move(other));
    return *this;
    }
-  /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
+#ifndef EIGEN_PARSED_BY_DOXYGEN
-   *
+    // FIXME is it still needed ??
-   * \only_for_vectors
+    /** \internal */
-   *
+    EIGEN_DEVICE_FUNC
-   * This constructor is for 1D array or vectors with more than 4 coefficients.
+    Array(internal::constructor_without_unaligned_array_assert)
-   *
+      : Base(internal::constructor_without_unaligned_array_assert())
-   * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
+    {
-   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+      Base::_check_template_params();
-   *
+      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
-   *
+    }
-   * Example: \include Array_variadic_ctor_cxx11.cpp
+#endif
   * Output: \verbinclude Array_variadic_ctor_cxx11.out
   *
   * \sa Array(const std::initializer_list<std::initializer_list<Scalar>>&)
   * \sa Array(const Scalar&), Array(const Scalar&,const Scalar&)
   */
  template <typename... ArgTypes>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3,
                                              const ArgTypes&... args)
      : Base(a0, a1, a2, a3, args...) {}
-  /** \brief Constructs an array and initializes it from the coefficients given as initializer-lists grouped by row.
+#if EIGEN_HAS_RVALUE_REFERENCES
-   * \cpp11
+    EIGEN_DEVICE_FUNC
-   *
+    Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
-   * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
+      : Base(std::move(other))
-   *
+    {
-   * Example: \include Array_initializer_list_23_cxx11.cpp
+      Base::_check_template_params();
-   * Output: \verbinclude Array_initializer_list_23_cxx11.out
+    }
-   *
+    EIGEN_DEVICE_FUNC
-   * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is
+    Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
-   * triggered.
+    {
-   *
+      other.swap(*this);
-   * In the case of a compile-time column 1D array, implicit transposition from a single row is allowed.
+      return *this;
-   * Therefore <code> Array<int,Dynamic,1>{{1,2,3,4,5}}</code> is legal and the more verbose syntax
+    }
-   * <code>Array<int,Dynamic,1>{{1},{2},{3},{4},{5}}</code> can be avoided:
+#endif
   *
   * Example: \include Array_initializer_list_vector_cxx11.cpp
   * Output: \verbinclude Array_initializer_list_vector_cxx11.out
   *
   * In the case of fixed-sized arrays, the initializer list sizes must exactly match the array sizes,
   * and implicit transposition is allowed for compile-time 1D arrays only.
   *
   * \sa  Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
   */
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(
      const std::initializer_list<std::initializer_list<Scalar>>& list)
      : Base(list) {}
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    template<typename T>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Array(const T& x) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE explicit Array(const T& x)
    {
      Base::_check_template_params();
      Base::template _init1<T>(x);
    }
    template<typename T0, typename T1>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1)
    {
      Base::_check_template_params();
      this->template _init2<T0,T1>(val0, val1);
    }
    #else
    /** \brief Constructs a fixed-sized array initialized with coefficients starting at \a data */
    EIGEN_DEVICE_FUNC explicit Array(const Scalar *data);
@@ -202,9 +187,9 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      * it is redundant to pass the dimension here, so it makes more sense to use the default
      * constructor Array() instead.
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Array(Index dim);
+    EIGEN_DEVICE_FUNC
-  /** constructs an initialized 1x1 Array with the given coefficient
+    EIGEN_STRONG_INLINE explicit Array(Index dim);
-   * \sa const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args */
+    /** constructs an initialized 1x1 Array with the given coefficient */
    Array(const Scalar& value);
    /** constructs an uninitialized array with \a rows rows and \a cols columns.
      *
@@ -212,25 +197,25 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
      * it is redundant to pass these parameters, so one should use the default constructor
      * Array() instead. */
    Array(Index rows, Index cols);
-  /** constructs an initialized 2D vector with given coefficients
+    /** constructs an initialized 2D vector with given coefficients */
   * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) */
    Array(const Scalar& val0, const Scalar& val1);
-#endif  // end EIGEN_PARSED_BY_DOXYGEN
+    #endif
-  /** constructs an initialized 3D vector with given coefficients
+    /** constructs an initialized 3D vector with given coefficients */
-   * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+    EIGEN_DEVICE_FUNC
-   */
+    EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2) {
+    {
      Base::_check_template_params();
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
      m_storage.data()[0] = val0;
      m_storage.data()[1] = val1;
      m_storage.data()[2] = val2;
    }
-  /** constructs an initialized 4D vector with given coefficients
+    /** constructs an initialized 4D vector with given coefficients */
-   * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+    EIGEN_DEVICE_FUNC
-   */
+    EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2,
+    {
-                                              const Scalar& val3) {
+      Base::_check_template_params();
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
      m_storage.data()[0] = val0;
      m_storage.data()[1] = val1;
@@ -239,28 +224,33 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
    }
    /** Copy constructor */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(const Array&) = default;
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Array(const Array& other)
            : Base(other)
    { }
  private:
    struct PrivateType {};
  public:
    /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(
+    EIGEN_DEVICE_FUNC
-      const EigenBase<OtherDerived>& other,
+    EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other,
-      std::enable_if_t<internal::is_convertible<typename OtherDerived::Scalar, Scalar>::value, PrivateType> =
+                              typename internal::enable_if<internal::is_convertible<typename OtherDerived::Scalar,Scalar>::value,
-          PrivateType())
+                                                           PrivateType>::type = PrivateType())
-      : Base(other.derived()) {}
+      : Base(other.derived())
    { }
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return 1; }
+    EIGEN_DEVICE_FUNC inline Index innerStride() const { return 1; }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return this->innerSize(); }
+    EIGEN_DEVICE_FUNC 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;
 };
@@ -268,26 +258,19 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
 /** \defgroup arraytypedefs Global array typedefs
  * \ingroup Core_Module
  *
- * %Eigen defines several typedef shortcuts for most common 1D and 2D array types.
+  * 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
+  * \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,
- * 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
+  * 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
- * cd for complex double.
+  * 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
+  * For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
 * floats.
  *
  * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
  * a fixed-size 1D array of 4 complex floats.
  *
 * With \cpp11, template alias are also defined for common sizes.
 * They follow the same pattern as above except that the scalar type suffix is replaced by a
 * template parameter, i.e.:
 *   - `ArrayRowsCols<Type>` where `Rows` and `Cols` can be \c 2,\c 3,\c 4, or \c X for fixed or dynamic size.
 *   - `ArraySize<Type>` where `Size` can be \c 2,\c 3,\c 4 or \c X for fixed or dynamic size 1D arrays.
 *
  * \sa class Array
  */
@@ -320,38 +303,8 @@ 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_FIXED_TYPEDEFS
-#define EIGEN_MAKE_ARRAY_TYPEDEFS(Size, SizeSuffix)              \
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_LARGE
  /** \ingroup arraytypedefs */                                  \
  /** \brief \cpp11 */                                           \
  template <typename Type>                                       \
  using Array##SizeSuffix##SizeSuffix = Array<Type, Size, Size>; \
  /** \ingroup arraytypedefs */                                  \
  /** \brief \cpp11 */                                           \
  template <typename Type>                                       \
  using Array##SizeSuffix = Array<Type, Size, 1>;
 #define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Size)        \
  /** \ingroup arraytypedefs */                      \
  /** \brief \cpp11 */                               \
  template <typename Type>                           \
  using Array##Size##X = Array<Type, Size, Dynamic>; \
  /** \ingroup arraytypedefs */                      \
  /** \brief \cpp11 */                               \
  template <typename Type>                           \
  using Array##X##Size = Array<Type, Dynamic, Size>;
 EIGEN_MAKE_ARRAY_TYPEDEFS(2, 2)
 EIGEN_MAKE_ARRAY_TYPEDEFS(3, 3)
 EIGEN_MAKE_ARRAY_TYPEDEFS(4, 4)
 EIGEN_MAKE_ARRAY_TYPEDEFS(Dynamic, X)
 EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(2)
 EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(3)
 EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4)
 #undef EIGEN_MAKE_ARRAY_TYPEDEFS
 #undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
 #define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
 using Eigen::Matrix##SizeSuffix##TypeSuffix; \
@@ -362,7 +315,7 @@ EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4)
 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)
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
 #define EIGEN_USING_ARRAY_TYPEDEFS \
 EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
--- a/Eigen/src/Core/ArrayBase.h
+++ b/Eigen/src/Core/ArrayBase.h
@@ -10,13 +10,9 @@
 #ifndef EIGEN_ARRAYBASE_H
 #define EIGEN_ARRAYBASE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
-template <typename ExpressionType>
+template<typename ExpressionType> class MatrixWrapper;
 class MatrixWrapper;
 /** \class ArrayBase
  * \ingroup Core_Module
@@ -25,7 +21,7 @@ class MatrixWrapper;
  *
  * 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 dimensional fashion. As the main consequence,
+  * 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
@@ -40,8 +36,9 @@ class MatrixWrapper;
  *
  * \sa class MatrixBase, \ref TopicClassHierarchy
  */
-template <typename Derived>
+template<typename Derived> class ArrayBase
-class ArrayBase : public DenseBase<Derived> {
+  : public DenseBase<Derived>
 {
  public:
 #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** The base class for a given storage type. */
@@ -55,24 +52,23 @@ class ArrayBase : public DenseBase<Derived> {
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef DenseBase<Derived> Base;
  using Base::ColsAtCompileTime;
  using Base::Flags;
  using Base::IsVectorAtCompileTime;
  using Base::MaxColsAtCompileTime;
  using Base::MaxRowsAtCompileTime;
  using Base::MaxSizeAtCompileTime;
    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::derived;
    using Base::const_cast_derived;
    using Base::rows;
    using Base::cols;
    using Base::size;
    using Base::coeff;
    using Base::coeffRef;
  using Base::cols;
  using Base::const_cast_derived;
  using Base::derived;
    using Base::lazyAssign;
  using Base::rows;
  using Base::size;
  using Base::operator-;
    using Base::operator=;
    using Base::operator+=;
    using Base::operator-=;
@@ -81,6 +77,9 @@ class ArrayBase : public DenseBase<Derived> {
    typedef typename Base::CoeffReturnType CoeffReturnType;
 #endif // not EIGEN_PARSED_BY_DOXYGEN
 #ifndef EIGEN_PARSED_BY_DOXYGEN
    typedef typename Base::PlainObject PlainObject;
    /** \internal Represents a matrix with all coefficients equal to one another*/
@@ -89,11 +88,12 @@ class ArrayBase : public DenseBase<Derived> {
 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
 #define EIGEN_DOC_UNARY_ADDONS(X,Y)
-#include "../plugins/MatrixCwiseUnaryOps.inc"
+#   include "../plugins/CommonCwiseUnaryOps.h"
-#include "../plugins/ArrayCwiseUnaryOps.inc"
+#   include "../plugins/MatrixCwiseUnaryOps.h"
-#include "../plugins/CommonCwiseBinaryOps.inc"
+#   include "../plugins/ArrayCwiseUnaryOps.h"
-#include "../plugins/MatrixCwiseBinaryOps.inc"
+#   include "../plugins/CommonCwiseBinaryOps.h"
-#include "../plugins/ArrayCwiseBinaryOps.inc"
+#   include "../plugins/MatrixCwiseBinaryOps.h"
 #   include "../plugins/ArrayCwiseBinaryOps.h"
 #   ifdef EIGEN_ARRAYBASE_PLUGIN
 #     include EIGEN_ARRAYBASE_PLUGIN
 #   endif
@@ -103,80 +103,51 @@ class ArrayBase : public DenseBase<Derived> {
    /** Special case of the template operator=, in order to prevent the compiler
      * from generating a default operator= (issue hit with g++ 4.1)
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const ArrayBase& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    Derived& operator=(const ArrayBase& other)
    {
      internal::call_assignment(derived(), other.derived());
      return derived();
    }
    /** Set all the entries to \a value.
      * \sa DenseBase::setConstant(), DenseBase::fill() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Scalar& value) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    Base::setConstant(value);
+    Derived& operator=(const Scalar &value)
-    return derived();
+    { Base::setConstant(value); return derived(); }
  }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const Scalar& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
+    Derived& operator+=(const Scalar& scalar);
-                              internal::add_assign_op<Scalar, Scalar>());
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    return derived();
+    Derived& operator-=(const Scalar& scalar);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const Scalar& other) {
    internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
                              internal::sub_assign_op<Scalar, Scalar>());
    return derived();
  }
  /** replaces \c *this by \c *this + \a other.
   *
   * \returns a reference to \c *this
   */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const ArrayBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
+    Derived& operator+=(const ArrayBase<OtherDerived>& other);
    return derived();
  }
  /** replaces \c *this by \c *this - \a other.
   *
   * \returns a reference to \c *this
   */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const ArrayBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
+    Derived& operator-=(const ArrayBase<OtherDerived>& other);
    return derived();
  }
  /** replaces \c *this by \c *this * \a other coefficient wise.
   *
   * \returns a reference to \c *this
   */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const ArrayBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar, typename OtherDerived::Scalar>());
+    Derived& operator*=(const ArrayBase<OtherDerived>& other);
    return derived();
  }
  /** replaces \c *this by \c *this / \a other coefficient wise.
   *
   * \returns a reference to \c *this
   */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const ArrayBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar, typename OtherDerived::Scalar>());
+    Derived& operator/=(const ArrayBase<OtherDerived>& other);
    return derived();
  }
  public:
-  EIGEN_DEVICE_FUNC ArrayBase<Derived>& array() { return *this; }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC const ArrayBase<Derived>& array() const { return *this; }
+    ArrayBase<Derived>& array() { return *this; }
    EIGEN_DEVICE_FUNC
    const ArrayBase<Derived>& array() const { return *this; }
    /** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array
      * \sa MatrixBase::array() */
-  EIGEN_DEVICE_FUNC MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC const MatrixWrapper<const Derived> matrix() const {
+    MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }
-    return MatrixWrapper<const Derived>(derived());
+    EIGEN_DEVICE_FUNC
-  }
+    const MatrixWrapper<const Derived> matrix() const { return MatrixWrapper<const Derived>(derived()); }
 //     template<typename Dest>
 //     inline void evalTo(Dest& dst) const { dst = matrix(); }
@@ -188,26 +159,68 @@ class ArrayBase : public DenseBase<Derived> {
  private:
    explicit ArrayBase(Index);
    ArrayBase(Index,Index);
-  template <typename OtherDerived>
+    template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
  explicit ArrayBase(const ArrayBase<OtherDerived>&);
  protected:
    // mixing arrays and matrices is not legal
-  template <typename OtherDerived>
+    template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
-  Derived& operator+=(const MatrixBase<OtherDerived>&) {
+    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
    EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
                        YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
    return *this;
  }
    // mixing arrays and matrices is not legal
-  template <typename OtherDerived>
+    template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
-  Derived& operator-=(const MatrixBase<OtherDerived>&) {
+    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
    EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
                        YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
    return *this;
  }
 };
 /** replaces \c *this by \c *this - \a other.
  *
  * \returns a reference to \c *this
  */
 template<typename Derived>
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
 {
  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
 /** replaces \c *this by \c *this + \a other.
  *
  * \returns a reference to \c *this
  */
 template<typename Derived>
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
 {
  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
  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_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
 {
  call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar,typename OtherDerived::Scalar>());
  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_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
 {
  call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
 } // end namespace Eigen
 #endif // EIGEN_ARRAYBASE_H
--- a/Eigen/src/Core/ArrayWrapper.h
+++ b/Eigen/src/Core/ArrayWrapper.h
@@ -10,9 +10,6 @@
 #ifndef EIGEN_ARRAYWRAPPER_H
 #define EIGEN_ARRAYWRAPPER_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 /** \class ArrayWrapper
@@ -28,63 +25,86 @@ namespace Eigen {
 namespace internal {
 template<typename ExpressionType>
-struct traits<ArrayWrapper<ExpressionType> > : public traits<remove_all_t<typename ExpressionType::Nested> > {
+struct traits<ArrayWrapper<ExpressionType> >
  : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
  typedef ArrayXpr XprKind;
  // Let's remove NestByRefBit
  enum {
-    Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
    LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
    Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
  };
 };
-}  // namespace internal
+}
 template<typename ExpressionType>
-class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> > {
+class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
 {
  public:
    typedef ArrayBase<ArrayWrapper> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
-  typedef internal::remove_all_t<ExpressionType> NestedExpression;
+    typedef typename internal::remove_all<ExpressionType>::type NestedExpression;
-  typedef std::conditional_t<internal::is_lvalue<ExpressionType>::value, Scalar, const Scalar>
+    typedef typename internal::conditional<
-      ScalarWithConstIfNotLvalue;
+                       internal::is_lvalue<ExpressionType>::value,
                       Scalar,
                       const Scalar
                     >::type ScalarWithConstIfNotLvalue;
    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
    using Base::coeffRef;
-  EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
+    EIGEN_DEVICE_FUNC
    explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+    inline Index rows() const { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
+    inline Index cols() const { return m_expression.cols(); }
    EIGEN_DEVICE_FUNC
    inline Index outerStride() const { return m_expression.outerStride(); }
    EIGEN_DEVICE_FUNC
    inline Index innerStride() const { return m_expression.innerStride(); }
-  EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
    EIGEN_DEVICE_FUNC
    inline const Scalar* data() const { return m_expression.data(); }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index rowId, Index colId) const
    {
      return m_expression.coeffRef(rowId, colId);
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const { return m_expression.coeffRef(index); }
+    EIGEN_DEVICE_FUNC
-
+    inline const Scalar& coeffRef(Index index) const
-  template <typename Dest>
+    {
-  EIGEN_DEVICE_FUNC inline void evalTo(Dest& dst) const {
+      return m_expression.coeffRef(index);
    dst = m_expression;
    }
-  EIGEN_DEVICE_FUNC const internal::remove_all_t<NestedExpressionType>& nestedExpression() const {
+    template<typename Dest>
    EIGEN_DEVICE_FUNC
    inline void evalTo(Dest& dst) const { dst = m_expression; }
    const typename internal::remove_all<NestedExpressionType>::type& 
    EIGEN_DEVICE_FUNC
    nestedExpression() const 
    {
      return m_expression;
    }
    /** Forwards the resizing request to the nested expression
      * \sa DenseBase::resize(Index)  */
-  EIGEN_DEVICE_FUNC void resize(Index newSize) { m_expression.resize(newSize); }
+    EIGEN_DEVICE_FUNC
    void resize(Index newSize) { m_expression.resize(newSize); }
    /** Forwards the resizing request to the nested expression
      * \sa DenseBase::resize(Index,Index)*/
-  EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) { m_expression.resize(rows, cols); }
+    EIGEN_DEVICE_FUNC
    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
  protected:
    NestedExpressionType m_expression;
@@ -103,58 +123,82 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> > {
 namespace internal {
 template<typename ExpressionType>
-struct traits<MatrixWrapper<ExpressionType> > : public traits<remove_all_t<typename ExpressionType::Nested> > {
+struct traits<MatrixWrapper<ExpressionType> >
 : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
  typedef MatrixXpr XprKind;
  // Let's remove NestByRefBit
  enum {
-    Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
    LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
    Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
  };
 };
-}  // namespace internal
+}
 template<typename ExpressionType>
-class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> > {
+class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
 {
  public:
    typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
-  typedef internal::remove_all_t<ExpressionType> NestedExpression;
+    typedef typename internal::remove_all<ExpressionType>::type NestedExpression;
-  typedef std::conditional_t<internal::is_lvalue<ExpressionType>::value, Scalar, const Scalar>
+    typedef typename internal::conditional<
-      ScalarWithConstIfNotLvalue;
+                       internal::is_lvalue<ExpressionType>::value,
                       Scalar,
                       const Scalar
                     >::type ScalarWithConstIfNotLvalue;
    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
    using Base::coeffRef;
-  EIGEN_DEVICE_FUNC explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
+    EIGEN_DEVICE_FUNC
    explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+    inline Index rows() const { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
+    inline Index cols() const { return m_expression.cols(); }
    EIGEN_DEVICE_FUNC
    inline Index outerStride() const { return m_expression.outerStride(); }
    EIGEN_DEVICE_FUNC
    inline Index innerStride() const { return m_expression.innerStride(); }
-  EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
    EIGEN_DEVICE_FUNC
    inline const Scalar* data() const { return m_expression.data(); }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index rowId, Index colId) const
    {
      return m_expression.derived().coeffRef(rowId, colId);
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const { return m_expression.coeffRef(index); }
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index index) const
    {
      return m_expression.coeffRef(index);
    }
-  EIGEN_DEVICE_FUNC const internal::remove_all_t<NestedExpressionType>& nestedExpression() const {
+    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<NestedExpressionType>::type& 
    nestedExpression() const 
    {
      return m_expression;
    }
    /** Forwards the resizing request to the nested expression
      * \sa DenseBase::resize(Index)  */
-  EIGEN_DEVICE_FUNC void resize(Index newSize) { m_expression.resize(newSize); }
+    EIGEN_DEVICE_FUNC
    void resize(Index newSize) { m_expression.resize(newSize); }
    /** Forwards the resizing request to the nested expression
      * \sa DenseBase::resize(Index,Index)*/
-  EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) { m_expression.resize(rows, cols); }
+    EIGEN_DEVICE_FUNC
    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
  protected:
    NestedExpressionType m_expression;
--- a/Eigen/src/Core/Assign.h
+++ b/Eigen/src/Core/Assign.h
@@ -12,21 +12,20 @@
 #ifndef EIGEN_ASSIGN_H
 #define EIGEN_ASSIGN_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::lazyAssign(const DenseBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
-  enum { SameType = internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value };
+  ::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(
+  EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
      SameType,
      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
  eigen_assert(rows() == other.rows() && cols() == other.cols());
  internal::call_assignment_no_alias(derived(),other.derived());
@@ -36,41 +35,52 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::lazyAssign(co
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
 {
  internal::call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other) {
+EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
 {
  internal::call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other) {
+EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
 {
  internal::call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
 template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
 {
  internal::call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
 template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
 {
  internal::call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(
+EIGEN_DEVICE_FUNC
-    const ReturnByValue<OtherDerived>& other) {
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
 {
  other.derived().evalTo(derived());
  return derived();
 }
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
--- a/Eigen/src/Core/Assign_MKL.h
+++ b/Eigen/src/Core/Assign_MKL.h
@@ -34,15 +34,13 @@
 #ifndef EIGEN_ASSIGN_VML_H
 #define EIGEN_ASSIGN_VML_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
 template<typename Dst, typename Src>
-class vml_assign_traits {
+class vml_assign_traits
 {
  private:
    enum {
      DstHasDirectAccess = Dst::Flags & DirectAccessBit,
@@ -56,69 +54,69 @@ class vml_assign_traits {
                    : int(Dst::MaxRowsAtCompileTime),
      MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
-    MightEnableVml = bool(StorageOrdersAgree) && bool(DstHasDirectAccess) && bool(SrcHasDirectAccess) &&
+      MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,
-                     Src::InnerStrideAtCompileTime == 1 && Dst::InnerStrideAtCompileTime == 1,
+      MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
-    MightLinearize = bool(MightEnableVml) && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
+      VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
-    VmlSize = bool(MightLinearize) ? MaxSizeAtCompileTime : InnerMaxSize,
+      LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD
    LargeEnough = (VmlSize == Dynamic) || VmlSize >= EIGEN_MKL_VML_THRESHOLD
    };
  public:
-  enum { EnableVml = MightEnableVml && LargeEnough, Traversal = MightLinearize ? LinearTraversal : DefaultTraversal };
+    enum {
      EnableVml = MightEnableVml && LargeEnough,
      Traversal = MightLinearize ? LinearTraversal : DefaultTraversal
    };
 };
 #define EIGEN_PP_EXPAND(ARG) ARG
 #if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
-#define EIGEN_VMLMODE_EXPAND_xLA , VML_HA
+#define EIGEN_VMLMODE_EXPAND_LA , VML_HA
 #else
-#define EIGEN_VMLMODE_EXPAND_xLA , VML_LA
+#define EIGEN_VMLMODE_EXPAND_LA , VML_LA
 #endif
-#define EIGEN_VMLMODE_EXPAND_x_
+#define EIGEN_VMLMODE_EXPAND__ 
-#define EIGEN_VMLMODE_PREFIX_xLA vm
+#define EIGEN_VMLMODE_PREFIX_LA vm
-#define EIGEN_VMLMODE_PREFIX_x_ v
+#define EIGEN_VMLMODE_PREFIX__  v
-#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_x, VMLMODE)
+#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_,VMLMODE)
 #define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE)                                           \
  template< typename DstXprType, typename SrcXprNested>                                                                         \
-  struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>,              \
+  struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE,EIGENTYPE>,   \
-                    assign_op<EIGENTYPE, EIGENTYPE>, Dense2Dense,                                          \
+                   Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> {              \
                    std::enable_if_t<vml_assign_traits<DstXprType, SrcXprNested>::EnableVml>> {            \
    typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType;                                            \
    static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) {                       \
      resize_if_allowed(dst, src, func);                                                                                        \
      eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());                                                       \
-      if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == (int)LinearTraversal) {                \
+      if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) {                                              \
        VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(),                                                        \
-              (VMLTYPE *)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE));                     \
+              (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE) );                                           \
      } else {                                                                                                                  \
        const Index outerSize = dst.outerSize();                                                                                \
        for(Index outer = 0; outer < outerSize; ++outer) {                                                                      \
-          const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer, 0))         \
+          const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) :                             \
-                                                    : &(src.nestedExpression().coeffRef(0, outer));        \
+                                                      &(src.nestedExpression().coeffRef(0, outer));                             \
          EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));                           \
          VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr,                                                                      \
-                (VMLTYPE *)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE));                      \
+                (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE));                                             \
        }                                                                                                                       \
      }                                                                                                                         \
    }                                                                                                                           \
-  };
+  };                                                                                                                            \
 #define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE)                                                         \
  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),s##VMLOP), float, float, VMLMODE)           \
  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),d##VMLOP), double, double, VMLMODE)
 #define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)                                                         \
-  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), c##VMLOP), scomplex, \
+  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),c##VMLOP), scomplex, MKL_Complex8, VMLMODE) \
-                                   MKL_Complex8, VMLMODE)                                                 \
+  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),z##VMLOP), dcomplex, MKL_Complex16, VMLMODE)
  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), z##VMLOP), dcomplex, \
                                   MKL_Complex16, VMLMODE)
 #define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE)                                                              \
  EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE)                                                               \
  EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin,   Sin,   LA)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin,  Asin,  LA)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh,  Sinh,  LA)
@@ -139,33 +137,30 @@ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg, _)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round,  _)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor,  _)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil,  Ceil,   _)
 EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(cbrt, Cbrt, _)
 #define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE)                                           \
  template< typename DstXprType, typename SrcXprNested, typename Plain>                                                       \
-  struct Assignment<DstXprType,                                                                            \
+  struct Assignment<DstXprType, CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested,                       \
-                    CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE, EIGENTYPE>, SrcXprNested,               \
+                    const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> >, assign_op<EIGENTYPE,EIGENTYPE>,    \
-                                  const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>, Plain>>,   \
+                   Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> {            \
                    assign_op<EIGENTYPE, EIGENTYPE>, Dense2Dense,                                          \
                    std::enable_if_t<vml_assign_traits<DstXprType, SrcXprNested>::EnableVml>> {            \
    typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested,                                           \
-                          const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>, Plain>>            \
+                    const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> > SrcXprType;                         \
        SrcXprType;                                                                                        \
    static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) {                     \
      resize_if_allowed(dst, src, func);                                                                                      \
      eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());                                                     \
      VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.rhs().functor().m_other);                                       \
-      if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == LinearTraversal) {                     \
+      if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal)                                              \
      {                                                                                                                       \
        VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent,                                                        \
-              (VMLTYPE *)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE));                     \
+              (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE) );                                         \
      } else {                                                                                                                \
        const Index outerSize = dst.outerSize();                                                                              \
        for(Index outer = 0; outer < outerSize; ++outer) {                                                                    \
-          const EIGENTYPE *src_ptr =                                                                       \
+          const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) :                                        \
-              src.IsRowMajor ? &(src.lhs().coeffRef(outer, 0)) : &(src.lhs().coeffRef(0, outer));          \
+                                                      &(src.lhs().coeffRef(0, outer));                                        \
          EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));                         \
          VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent,                                                          \
-                (VMLTYPE *)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE));                      \
+                 (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE));                                          \
        }                                                                                                                     \
      }                                                                                                                       \
    }                                                                                                                         \
--- a/Eigen/src/Core/BandMatrix.h
+++ b/Eigen/src/Core/BandMatrix.h
@@ -10,16 +10,15 @@
 #ifndef EIGEN_BANDMATRIX_H
 #define EIGEN_BANDMATRIX_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
 template<typename Derived>
-class BandMatrixBase : public EigenBase<Derived> {
+class BandMatrixBase : public EigenBase<Derived>
 {
  public:
    enum {
      Flags = internal::traits<Derived>::Flags,
      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
@@ -39,14 +38,17 @@ class BandMatrixBase : public EigenBase<Derived> {
  protected:
    enum {
-    DataRowsAtCompileTime = ((Supers != Dynamic) && (Subs != Dynamic)) ? 1 + Supers + Subs : Dynamic,
+      DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
-    SizeAtCompileTime = min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)
+                            ? 1 + Supers + Subs
                            : Dynamic,
      SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
    };
  public:
-  using Base::cols;
+    
    using Base::derived;
    using Base::rows;
    using Base::cols;
    /** \returns the number of super diagonals */
    inline Index supers() const { return derived().supers(); }
@@ -63,90 +65,94 @@ class BandMatrixBase : public EigenBase<Derived> {
    /** \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) {
+    inline Block<CoefficientsType,Dynamic,1> col(Index i)
-    EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+    {
      EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
      Index start = 0;
      Index len = coeffs().rows();
-    if (i <= supers()) {
+      if (i<=supers())
      {
        start = supers()-i;
        len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
-    } else if (i >= rows() - subs())
+      }
      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() {
+    inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
-    return Block<CoefficientsType, 1, SizeAtCompileTime>(coeffs(), supers(), 0, 1, (std::min)(rows(), cols()));
+    { 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 {
+    inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
-    return Block<const CoefficientsType, 1, SizeAtCompileTime>(coeffs(), supers(), 0, 1, (std::min)(rows(), cols()));
+    { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
  }
-  template <int Index>
+    template<int Index> struct DiagonalIntReturnType {
  struct DiagonalIntReturnType {
      enum {
-      ReturnOpposite =
+        ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),
          (int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)),
        Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
        ActualIndex = ReturnOpposite ? -Index : Index,
-      DiagonalSize =
+        DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
          (RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
                     ? Dynamic
-              : (ActualIndex < 0 ? min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
+                     : (ActualIndex<0
-                                 : min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
+                     ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
                     : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
      };
      typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
-    typedef std::conditional_t<Conjugate, CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, BuildType>, BuildType>
+      typedef typename internal::conditional<Conjugate,
-        Type;
+                 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>
+    template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
-  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>
+    template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
-  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) {
+    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 {
+    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,
+      return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
                                                     diagonalLength(i));
    }
-  template <typename Dest>
+    template<typename Dest> inline void evalTo(Dest& dst) const
-  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<=supers();++i)
-    for (Index i = 1; i <= subs(); ++i) dst.diagonal(-i) = diagonal(-i);
+        dst.diagonal(i) = diagonal(i);
      for (Index i=1; i<=subs();++i)
        dst.diagonal(-i) = diagonal(-i);
    }
-  DenseMatrixType toDenseMatrix() const {
+    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);
+    inline Index diagonalLength(Index i) const
-  }
+    { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
 };
 /**
@@ -155,12 +161,12 @@ class BandMatrixBase : public EigenBase<Derived> {
  *
  * \brief Represents a rectangular matrix with a banded storage
  *
- * \tparam Scalar_ Numeric type, i.e. float, double, int
+  * \tparam _Scalar Numeric type, i.e. float, double, int
- * \tparam Rows_ Number of rows, or \b Dynamic
+  * \tparam _Rows Number of rows, or \b Dynamic
- * \tparam Cols_ Number of columns, or \b Dynamic
+  * \tparam _Cols Number of columns, or \b Dynamic
- * \tparam Supers_ Number of super diagonal
+  * \tparam _Supers Number of super diagonal
- * \tparam Subs_ Number of sub diagonal
+  * \tparam _Subs Number of sub diagonal
- * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
+  * \tparam _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.
@@ -168,116 +174,126 @@ class BandMatrixBase : public EigenBase<Derived> {
  * \sa class TridiagonalMatrix
  */
-template <typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
-struct traits<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> > {
+struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
-  typedef Scalar_ Scalar;
+{
  typedef _Scalar Scalar;
  typedef Dense StorageKind;
  typedef Eigen::Index StorageIndex;
  enum {
    CoeffReadCost = NumTraits<Scalar>::ReadCost,
-    RowsAtCompileTime = Rows_,
+    RowsAtCompileTime = _Rows,
-    ColsAtCompileTime = Cols_,
+    ColsAtCompileTime = _Cols,
-    MaxRowsAtCompileTime = Rows_,
+    MaxRowsAtCompileTime = _Rows,
-    MaxColsAtCompileTime = Cols_,
+    MaxColsAtCompileTime = _Cols,
    Flags = LvalueBit,
-    Supers = Supers_,
+    Supers = _Supers,
-    Subs = Subs_,
+    Subs = _Subs,
-    Options = Options_,
+    Options = _Options,
    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
  };
-  typedef Matrix<Scalar, DataRowsAtCompileTime, ColsAtCompileTime, int(Options) & int(RowMajor) ? RowMajor : ColMajor>
+  typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;
      CoefficientsType;
 };
-template <typename Scalar_, int Rows, int Cols, int Supers, int Subs, int Options>
+template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
-class BandMatrix : public BandMatrixBase<BandMatrix<Scalar_, Rows, Cols, Supers, Subs, 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>::StorageIndex StorageIndex;
    typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
    explicit 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) {}
+      : m_coeffs(1+supers+subs,cols),
        m_rows(rows), m_supers(supers), m_subs(subs)
    {
    }
    /** \returns the number of columns */
-  constexpr Index rows() const { return m_rows.value(); }
+    inline Index rows() const { return m_rows.value(); }
    /** \returns the number of rows */
-  constexpr Index cols() const { return m_coeffs.cols(); }
+    inline Index cols() const { return m_coeffs.cols(); }
    /** \returns the number of super diagonals */
-  constexpr Index supers() const { return m_supers.value(); }
+    inline Index supers() const { return m_supers.value(); }
    /** \returns the number of sub diagonals */
-  constexpr Index subs() const { return m_subs.value(); }
+    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_>
+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_>
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
-struct traits<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> > {
+struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
-  typedef typename CoefficientsType_::Scalar Scalar;
+{
-  typedef typename CoefficientsType_::StorageKind StorageKind;
+  typedef typename _CoefficientsType::Scalar Scalar;
-  typedef typename CoefficientsType_::StorageIndex StorageIndex;
+  typedef typename _CoefficientsType::StorageKind StorageKind;
  typedef typename _CoefficientsType::StorageIndex StorageIndex;
  enum {
-    CoeffReadCost = internal::traits<CoefficientsType_>::CoeffReadCost,
+    CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
-    RowsAtCompileTime = Rows_,
+    RowsAtCompileTime = _Rows,
-    ColsAtCompileTime = Cols_,
+    ColsAtCompileTime = _Cols,
-    MaxRowsAtCompileTime = Rows_,
+    MaxRowsAtCompileTime = _Rows,
-    MaxColsAtCompileTime = Cols_,
+    MaxColsAtCompileTime = _Cols,
    Flags = LvalueBit,
-    Supers = Supers_,
+    Supers = _Supers,
-    Subs = Subs_,
+    Subs = _Subs,
-    Options = Options_,
+    Options = _Options,
    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
  };
-  typedef CoefficientsType_ CoefficientsType;
+  typedef _CoefficientsType CoefficientsType;
 };
-template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
-class BandMatrixWrapper
+class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
-    : 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>::StorageIndex StorageIndex;
-  explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows = Rows_, Index cols = Cols_,
+    explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
-                                    Index supers = Supers_, Index subs = Subs_)
+      : m_coeffs(coeffs),
-      : m_coeffs(coeffs), m_rows(rows), m_supers(supers), m_subs(subs) {
+        m_rows(rows), m_supers(supers), m_subs(subs)
    {
      EIGEN_UNUSED_VARIABLE(cols);
-    // eigen_assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
+      //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
    }
    /** \returns the number of columns */
-  constexpr Index rows() const { return m_rows.value(); }
+    inline Index rows() const { return m_rows.value(); }
    /** \returns the number of rows */
-  constexpr Index cols() const { return m_coeffs.cols(); }
+    inline Index cols() const { return m_coeffs.cols(); }
    /** \returns the number of super diagonals */
-  constexpr Index supers() const { return m_supers.value(); }
+    inline Index supers() const { return m_supers.value(); }
    /** \returns the number of sub diagonals */
-  constexpr Index subs() const { return m_subs.value(); }
+    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, _Rows>   m_rows;
-  internal::variable_if_dynamic<Index, Supers_> m_supers;
+    internal::variable_if_dynamic<Index, _Supers> m_supers;
-  internal::variable_if_dynamic<Index, Subs_> m_subs;
+    internal::variable_if_dynamic<Index, _Subs>   m_subs;
 };
 /**
@@ -293,43 +309,42 @@ class BandMatrixWrapper
  * \sa class BandMatrix
  */
 template<typename Scalar, int Size, int Options>
-class TridiagonalMatrix : public BandMatrix<Scalar, Size, Size, Options & SelfAdjoint ? 0 : 1, 1, Options | RowMajor> {
+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::StorageIndex StorageIndex;
  public:
    explicit 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 typename Base::template DiagonalIntReturnType<1>::Type super()
-  inline const typename Base::template DiagonalIntReturnType<1>::Type super() const {
+    { return Base::template diagonal<1>(); }
-    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 typename Base::template DiagonalIntReturnType<-1>::Type sub()
-  inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const {
+    { return Base::template diagonal<-1>(); }
-    return Base::template diagonal<-1>();
+    inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
-  }
+    { return Base::template diagonal<-1>(); }
  protected:
 };
 struct BandShape {};
-template <typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
-struct evaluator_traits<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> >
+struct evaluator_traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
-    : public evaluator_traits_base<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> > {
+  : public evaluator_traits_base<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
 {
  typedef BandShape Shape;
 };
-template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
-struct evaluator_traits<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> >
+struct evaluator_traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
-    : public evaluator_traits_base<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> > {
+  : public evaluator_traits_base<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
 {
  typedef BandShape Shape;
 };
-template <>
+template<> struct AssignmentKind<DenseShape,BandShape> { typedef EigenBase2EigenBase Kind; };
 struct AssignmentKind<DenseShape, BandShape> {
  typedef EigenBase2EigenBase Kind;
 };
 } // end namespace internal
--- a/Eigen/src/Core/Block.h
+++ b/Eigen/src/Core/Block.h
@@ -11,65 +11,60 @@
 #ifndef EIGEN_BLOCK_H
 #define EIGEN_BLOCK_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
-template <typename XprType_, int BlockRows, int BlockCols, bool InnerPanel_>
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
-struct traits<Block<XprType_, BlockRows, BlockCols, InnerPanel_>> : traits<XprType_> {
+struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>
-  typedef typename traits<XprType_>::Scalar Scalar;
+{
-  typedef typename traits<XprType_>::StorageKind StorageKind;
+  typedef typename traits<XprType>::Scalar Scalar;
-  typedef typename traits<XprType_>::XprKind XprKind;
+  typedef typename traits<XprType>::StorageKind StorageKind;
-  typedef typename ref_selector<XprType_>::type XprTypeNested;
+  typedef typename traits<XprType>::XprKind XprKind;
-  typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+  typedef typename ref_selector<XprType>::type XprTypeNested;
  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
  enum{
-    MatrixRows = traits<XprType_>::RowsAtCompileTime,
+    MatrixRows = traits<XprType>::RowsAtCompileTime,
-    MatrixCols = traits<XprType_>::ColsAtCompileTime,
+    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),
+                         : int(traits<XprType>::MaxRowsAtCompileTime),
    MaxColsAtCompileTime = BlockCols==0 ? 0
                         : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
-                                                          : int(traits<XprType_>::MaxColsAtCompileTime),
+                         : int(traits<XprType>::MaxColsAtCompileTime),
-    XprTypeIsRowMajor = (int(traits<XprType_>::Flags) & RowMajorBit) != 0,
+    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)
+    InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
-                                                            : int(outer_stride_at_compile_time<XprType_>::ret),
+                             ? int(inner_stride_at_compile_time<XprType>::ret)
-    OuterStrideAtCompileTime = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType_>::ret)
+                             : int(outer_stride_at_compile_time<XprType>::ret),
-                                                            : int(inner_stride_at_compile_time<XprType_>::ret),
+    OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
                             ? int(outer_stride_at_compile_time<XprType>::ret)
                             : int(inner_stride_at_compile_time<XprType>::ret),
    // FIXME, this traits is rather specialized for dense object and it needs to be cleaned further
-    FlagsLvalueBit = is_lvalue<XprType_>::value ? LvalueBit : 0,
+    FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
    FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
-    Flags = (traits<XprType_>::Flags & (DirectAccessBit | (InnerPanel_ ? CompressedAccessBit : 0))) | FlagsLvalueBit |
+    Flags = (traits<XprType>::Flags & (DirectAccessBit | (InnerPanel?CompressedAccessBit:0))) | FlagsLvalueBit | FlagsRowMajorBit,
            FlagsRowMajorBit,
    // FIXME DirectAccessBit should not be handled by expressions
    // 
    // Alignment is needed by MapBase's assertions
-    // We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the
+    // We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the respective evaluator
-    // respective evaluator
+    Alignment = 0
    Alignment = 0,
    InnerPanel = InnerPanel_ ? 1 : 0
  };
 };
 template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false,
-          bool HasDirectAccess = internal::has_direct_access<XprType>::ret>
+         bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class BlockImpl_dense;
 class BlockImpl_dense;
 } // end namespace internal
-template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind>
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;
 class BlockImpl;
 /** \class Block
  * \ingroup Core_Module
@@ -87,7 +82,7 @@ class BlockImpl;
  * 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 manipulate block expressions,
+  * 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.
  *
@@ -105,93 +100,82 @@ class BlockImpl;
  *
  * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
  */
-template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block
-class Block
+  : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>
-    : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> {
+{
    typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;
  using BlockHelper = internal::block_xpr_helper<Block>;
  public:
    //typedef typename Impl::Base Base;
    typedef Impl Base;
    EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
-  typedef internal::remove_all_t<XprType> NestedExpression;
+    typedef typename internal::remove_all<XprType>::type NestedExpression;
    /** Column or Row constructor
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index i) : Impl(xpr, i) {
+    EIGEN_DEVICE_FUNC
-    eigen_assert((i >= 0) && (((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) && i < xpr.rows()) ||
+    inline Block(XprType& xpr, Index i) : Impl(xpr,i)
-                              ((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) && i < 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
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index startRow, Index startCol)
+    EIGEN_DEVICE_FUNC
-      : Impl(xpr, startRow, startCol) {
+    inline Block(XprType& xpr, Index startRow, Index startCol)
-    EIGEN_STATIC_ASSERT(RowsAtCompileTime != Dynamic && ColsAtCompileTime != Dynamic,
+      : Impl(xpr, startRow, startCol)
-                        THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+    {
-    eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows() && startCol >= 0 &&
+      EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
-                 BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
+      eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows()
             && startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
    }
    /** Dynamic-size constructor
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index startRow, Index startCol, Index blockRows,
+    EIGEN_DEVICE_FUNC
-                                              Index blockCols)
+    inline Block(XprType& xpr,
-      : Impl(xpr, startRow, startCol, blockRows, blockCols) {
+          Index startRow, Index startCol,
-    eigen_assert((RowsAtCompileTime == Dynamic || RowsAtCompileTime == blockRows) &&
+          Index blockRows, Index blockCols)
-                 (ColsAtCompileTime == Dynamic || ColsAtCompileTime == blockCols));
+      : Impl(xpr, startRow, startCol, blockRows, blockCols)
-    eigen_assert(startRow >= 0 && blockRows >= 0 && startRow <= xpr.rows() - blockRows && startCol >= 0 &&
+    {
-                 blockCols >= 0 && startCol <= xpr.cols() - blockCols);
+      eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
-  }
+          && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
-
+      eigen_assert(startRow >= 0 && blockRows >= 0 && startRow  <= xpr.rows() - blockRows
-  // convert nested blocks (e.g. Block<Block<MatrixType>>) to a simple block expression (Block<MatrixType>)
+          && startCol >= 0 && blockCols >= 0 && startCol <= xpr.cols() - blockCols);
  using ConstUnwindReturnType = Block<const typename BlockHelper::BaseType, BlockRows, BlockCols, InnerPanel>;
  using UnwindReturnType = Block<typename BlockHelper::BaseType, BlockRows, BlockCols, InnerPanel>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ConstUnwindReturnType unwind() const {
    return ConstUnwindReturnType(BlockHelper::base(*this), BlockHelper::row(*this, 0), BlockHelper::col(*this, 0),
                                 this->rows(), this->cols());
  }
  template <typename T = Block, typename EnableIf = std::enable_if_t<!std::is_const<T>::value>>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UnwindReturnType unwind() {
    return UnwindReturnType(BlockHelper::base(*this), BlockHelper::row(*this, 0), BlockHelper::col(*this, 0),
                            this->rows(), this->cols());
    }
 };
-// The generic default implementation for dense block simply forward to the internal::BlockImpl_dense
+// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense
 // that must be specialized for direct and non-direct access...
 template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
 class BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>
-    : public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> {
+  : public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel>
 {
    typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;
    typedef typename XprType::StorageIndex StorageIndex;
  public:
    typedef Impl Base;
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index i) : Impl(xpr, i) {}
+    EIGEN_DEVICE_FUNC inline BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {}
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol)
+    EIGEN_DEVICE_FUNC inline BlockImpl(XprType& xpr, Index startRow, Index startCol) : Impl(xpr, startRow, startCol) {}
-      : Impl(xpr, startRow, startCol) {}
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows,
+    inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
                                                  Index blockCols)
      : Impl(xpr, startRow, startCol, blockRows, blockCols) {}
 };
 namespace internal {
 /** \internal Internal implementation of dense Blocks in the general case. */
-template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess>
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class BlockImpl_dense
-class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel>>::type {
+  : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type
 {
    typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
  public:
    typedef typename internal::dense_xpr_base<BlockType>::type Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
@@ -200,7 +184,8 @@ class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows
    /** Column or Row constructor
      */
-  EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index i)
+    EIGEN_DEVICE_FUNC
    inline BlockImpl_dense(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,
@@ -209,96 +194,132 @@ class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows
        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()) {}
+        m_blockCols(BlockCols==1 ? 1 : xpr.cols())
    {}
    /** Fixed-size constructor
      */
-  EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
+    EIGEN_DEVICE_FUNC
-      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), m_blockRows(BlockRows), m_blockCols(BlockCols) {}
+    inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
                    m_blockRows(BlockRows), m_blockCols(BlockCols)
    {}
    /** Dynamic-size constructor
      */
-  EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol, Index blockRows,
+    EIGEN_DEVICE_FUNC
-                                           Index blockCols)
+    inline BlockImpl_dense(XprType& xpr,
-      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), m_blockRows(blockRows), m_blockCols(blockCols) {}
+          Index startRow, Index startCol,
          Index blockRows, Index blockCols)
      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
                    m_blockRows(blockRows), m_blockCols(blockCols)
    {}
    EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); }
    EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index rowId, Index colId) {
+    EIGEN_DEVICE_FUNC
    inline Scalar& coeffRef(Index rowId, Index colId)
    {
      EIGEN_STATIC_ASSERT_LVALUE(XprType)
      return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index rowId, Index colId) const
    {
      return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
    {
      return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());
    }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index) {
+    EIGEN_DEVICE_FUNC
    inline Scalar& coeffRef(Index index)
    {
      EIGEN_STATIC_ASSERT_LVALUE(XprType)
      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index index) const
    {
      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
    }
-  EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const {
+    EIGEN_DEVICE_FUNC
    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>
-  EIGEN_DEVICE_FUNC inline PacketScalar packet(Index rowId, Index colId) const {
+    inline PacketScalar packet(Index rowId, Index colId) const
    {
      return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());
    }
    template<int LoadMode>
-  EIGEN_DEVICE_FUNC inline void writePacket(Index rowId, Index colId, const PacketScalar& val) {
+    inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
    {
      m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);
    }
    template<int LoadMode>
-  EIGEN_DEVICE_FUNC inline PacketScalar packet(Index index) const {
+    inline PacketScalar packet(Index index) const
-    return m_xpr.template packet<Unaligned>(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+    {
      return m_xpr.template packet<Unaligned>
              (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
               m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
    }
    template<int LoadMode>
-  EIGEN_DEVICE_FUNC inline void writePacket(Index index, const PacketScalar& val) {
+    inline void writePacket(Index index, const PacketScalar& val)
-    m_xpr.template writePacket<Unaligned>(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+    {
      m_xpr.template writePacket<Unaligned>
         (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
          m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
    }
    #ifdef EIGEN_PARSED_BY_DOXYGEN
    /** \sa MapBase::data() */
-  EIGEN_DEVICE_FUNC constexpr const Scalar* data() const;
+    EIGEN_DEVICE_FUNC inline const Scalar* data() const;
    EIGEN_DEVICE_FUNC inline Index innerStride() const;
    EIGEN_DEVICE_FUNC inline Index outerStride() const;
    #endif
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const {
+    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const
    { 
      return m_xpr; 
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
+    EIGEN_DEVICE_FUNC
    XprType& nestedExpression() { return m_xpr; }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
+    EIGEN_DEVICE_FUNC
    StorageIndex startRow() const
    { 
      return m_startRow.value(); 
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
+    EIGEN_DEVICE_FUNC
    StorageIndex startCol() const
    { 
      return m_startCol.value(); 
    }
  protected:
    XprTypeNested m_xpr;
-  const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows == 1) ? 0 : Dynamic>
+    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
-      m_startRow;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
  const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols == 1) ? 0 : Dynamic>
      m_startCol;
    const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;
    const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;
 };
@@ -306,92 +327,92 @@ class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows
 /** \internal Internal implementation of dense Blocks in the direct access case.*/
 template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
 class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
-    : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel>> {
+  : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >
 {
    typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
-  enum { XprTypeIsRowMajor = (int(traits<XprType>::Flags) & RowMajorBit) != 0 };
+    enum {
-
+      XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0
-  /** \internal Returns base+offset (unless base is null, in which case returns null).
+    };
   * Adding an offset to nullptr is undefined behavior, so we must avoid it.
   */
  template <typename Scalar>
  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE static Scalar* add_to_nullable_pointer(Scalar* base, Index offset) {
    return base != nullptr ? base + offset : nullptr;
  }
  public:
    typedef MapBase<BlockType> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
    /** Column or Row constructor
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index i)
+    EIGEN_DEVICE_FUNC
-      : Base((BlockRows == 0 || BlockCols == 0)
+    inline BlockImpl_dense(XprType& xpr, Index i)
-                 ? nullptr
+      : Base(xpr.data() + i * (    ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor)) 
-                 : add_to_nullable_pointer(
+                                || ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()),
-                       xpr.data(),
+             BlockRows==1 ? 1 : xpr.rows(),
-                       i * (((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor)) ||
+             BlockCols==1 ? 1 : xpr.cols()),
                                    ((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) &&
                                     (XprTypeIsRowMajor))
                                ? xpr.innerStride()
                                : xpr.outerStride())),
             BlockRows == 1 ? 1 : xpr.rows(), BlockCols == 1 ? 1 : xpr.cols()),
        m_xpr(xpr),
        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
-        m_startCol((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) ? i : 0) {
+        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)
    {
      init();
    }
    /** Fixed-size constructor
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
+    EIGEN_DEVICE_FUNC
-      : Base((BlockRows == 0 || BlockCols == 0)
+    inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
-                 ? nullptr
+      : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)),
-                 : add_to_nullable_pointer(xpr.data(),
+        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
-                                           xpr.innerStride() * (XprTypeIsRowMajor ? startCol : startRow) +
+    {
                                               xpr.outerStride() * (XprTypeIsRowMajor ? startRow : startCol))),
        m_xpr(xpr),
        m_startRow(startRow),
        m_startCol(startCol) {
      init();
    }
    /** Dynamic-size constructor
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index startRow, Index startCol, Index blockRows,
+    EIGEN_DEVICE_FUNC
-                                                        Index blockCols)
+    inline BlockImpl_dense(XprType& xpr,
-      : Base((blockRows == 0 || blockCols == 0)
+          Index startRow, Index startCol,
-                 ? nullptr
+          Index blockRows, Index blockCols)
-                 : add_to_nullable_pointer(xpr.data(),
+      : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols),
-                                           xpr.innerStride() * (XprTypeIsRowMajor ? startCol : startRow) +
+        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
-                                               xpr.outerStride() * (XprTypeIsRowMajor ? startRow : startCol)),
+    {
             blockRows, blockCols),
        m_xpr(xpr),
        m_startRow(startRow),
        m_startCol(startCol) {
      init();
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const noexcept {
+    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const
    { 
      return m_xpr; 
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
+    EIGEN_DEVICE_FUNC
    XprType& nestedExpression() { return m_xpr; }
    /** \sa MapBase::innerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index innerStride() const noexcept {
+    EIGEN_DEVICE_FUNC
-    return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.innerStride() : m_xpr.outerStride();
+    inline Index innerStride() const
    {
      return internal::traits<BlockType>::HasSameStorageOrderAsXprType
             ? m_xpr.innerStride()
             : m_xpr.outerStride();
    }
    /** \sa MapBase::outerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index outerStride() const noexcept {
+    EIGEN_DEVICE_FUNC
-    return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.outerStride() : m_xpr.innerStride();
+    inline Index outerStride() const
    {
      return m_outerStride;
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
+    EIGEN_DEVICE_FUNC
    StorageIndex startRow() const
    {
      return m_startRow.value();
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
+    EIGEN_DEVICE_FUNC
    StorageIndex startCol() const
    {
      return m_startCol.value();
    }
  #ifndef __SUNPRO_CC
  // FIXME sunstudio is not friendly with the above friend...
@@ -401,24 +422,26 @@ class BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel, true>
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** \internal used by allowAligned() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows,
+    EIGEN_DEVICE_FUNC
-                                                        Index blockCols)
+    inline BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
-      : Base(data, blockRows, blockCols), m_xpr(xpr) {
+      : Base(data, blockRows, blockCols), m_xpr(xpr)
    {
      init();
    }
    #endif
  protected:
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void init() {
+    EIGEN_DEVICE_FUNC
-    m_outerStride =
+    void init()
-        internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.outerStride() : m_xpr.innerStride();
+    {
      m_outerStride = internal::traits<BlockType>::HasSameStorageOrderAsXprType
                    ? m_xpr.outerStride()
                    : m_xpr.innerStride();
    }
    XprTypeNested m_xpr;
-  const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows == 1) ? 0 : Dynamic>
+    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
-      m_startRow;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
  const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols == 1) ? 0 : Dynamic>
      m_startCol;
    Index m_outerStride;
 };
--- a/Eigen/src/Core/BooleanRedux.h
+++ b/Eigen/src/Core/BooleanRedux.h
@@ -0,0 +1,164 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_ALLANDANY_H
 #define EIGEN_ALLANDANY_H
 namespace Eigen { 
 namespace internal {
 template<typename Derived, int UnrollCount>
 struct all_unroller
 {
  typedef typename Derived::ExpressionTraits Traits;
  enum {
    col = (UnrollCount-1) / Traits::RowsAtCompileTime,
    row = (UnrollCount-1) % Traits::RowsAtCompileTime
  };
  EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
  {
    return all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
  }
 };
 template<typename Derived>
 struct all_unroller<Derived, 0>
 {
  EIGEN_DEVICE_FUNC static inline bool run(const Derived &/*mat*/) { return true; }
 };
 template<typename Derived>
 struct all_unroller<Derived, Dynamic>
 {
  EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; }
 };
 template<typename Derived, int UnrollCount>
 struct any_unroller
 {
  typedef typename Derived::ExpressionTraits Traits;
  enum {
    col = (UnrollCount-1) / Traits::RowsAtCompileTime,
    row = (UnrollCount-1) % Traits::RowsAtCompileTime
  };
  EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
  {
    return any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
  }
 };
 template<typename Derived>
 struct any_unroller<Derived, 0>
 {
  EIGEN_DEVICE_FUNC static inline bool run(const Derived & /*mat*/) { return false; }
 };
 template<typename Derived>
 struct any_unroller<Derived, Dynamic>
 {
  EIGEN_DEVICE_FUNC static inline 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>
 EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::all() const
 {
  typedef internal::evaluator<Derived> Evaluator;
  enum {
    unroll = SizeAtCompileTime != Dynamic
          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
  };
  Evaluator evaluator(derived());
  if(unroll)
    return internal::all_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);
  else
  {
    for(Index j = 0; j < cols(); ++j)
      for(Index i = 0; i < rows(); ++i)
        if (!evaluator.coeff(i, j)) return false;
    return true;
  }
 }
 /** \returns true if at least one coefficient is true
  *
  * \sa all()
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::any() const
 {
  typedef internal::evaluator<Derived> Evaluator;
  enum {
    unroll = SizeAtCompileTime != Dynamic
          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
  };
  Evaluator evaluator(derived());
  if(unroll)
    return internal::any_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);
  else
  {
    for(Index j = 0; j < cols(); ++j)
      for(Index i = 0; i < rows(); ++i)
        if (evaluator.coeff(i, j)) return true;
    return false;
  }
 }
 /** \returns the number of coefficients which evaluate to true
  *
  * \sa all(), any()
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC inline Eigen::Index DenseBase<Derived>::count() const
 {
  return derived().template cast<bool>().template cast<Index>().sum();
 }
 /** \returns true is \c *this contains at least one Not A Number (NaN).
  *
  * \sa allFinite()
  */
 template<typename Derived>
 inline bool DenseBase<Derived>::hasNaN() const
 {
 #if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
  return derived().array().isNaN().any();
 #else
  return !((derived().array()==derived().array()).all());
 #endif
 }
 /** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values.
  *
  * \sa hasNaN()
  */
 template<typename Derived>
 inline bool DenseBase<Derived>::allFinite() const
 {
 #if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
  return derived().array().isFinite().all();
 #else
  return !((derived()-derived()).hasNaN());
 #endif
 }
 } // end namespace Eigen
 #endif // EIGEN_ALLANDANY_H
--- a/Eigen/src/Core/CommaInitializer.h
+++ b/Eigen/src/Core/CommaInitializer.h
@@ -11,9 +11,6 @@
 #ifndef EIGEN_COMMAINITIALIZER_H
 #define EIGEN_COMMAINITIALIZER_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 /** \class CommaInitializer
@@ -28,28 +25,30 @@ namespace Eigen {
  * \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
  */
 template<typename XprType>
-struct CommaInitializer {
+struct CommaInitializer
 {
  typedef typename XprType::Scalar Scalar;
-  EIGEN_DEVICE_FUNC inline CommaInitializer(XprType& xpr, const Scalar& s)
+  EIGEN_DEVICE_FUNC
-      : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1) {
+  inline CommaInitializer(XprType& xpr, const Scalar& s)
-    eigen_assert(m_xpr.rows() > 0 && m_xpr.cols() > 0 && "Cannot comma-initialize a 0x0 matrix (operator<<)");
+    : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
  {
    m_xpr.coeffRef(0,0) = s;
  }
  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
+  EIGEN_DEVICE_FUNC
-      : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows()) {
+  inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
-    eigen_assert(m_xpr.rows() >= other.rows() && m_xpr.cols() >= other.cols() &&
+    : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
-                 "Cannot comma-initialize a 0x0 matrix (operator<<)");
+  {
-    m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>(0, 0, other.rows(),
+    m_xpr.block(0, 0, other.rows(), other.cols()) = other;
                                                                                           other.cols()) = other;
  }
  /* Copy/Move constructor which transfers ownership. This is crucial in
   * absence of return value optimization to avoid assertions during destruction. */
  // FIXME in C++11 mode this could be replaced by a proper RValue constructor
-  EIGEN_DEVICE_FUNC inline CommaInitializer(const CommaInitializer& o)
+  EIGEN_DEVICE_FUNC
  inline CommaInitializer(const CommaInitializer& o)
  : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
    // Mark original object as finished. In absence of R-value references we need to const_cast:
    const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
@@ -58,14 +57,19 @@ struct CommaInitializer {
  }
  /* inserts a scalar value in the target matrix */
-  EIGEN_DEVICE_FUNC CommaInitializer &operator,(const Scalar& s) {
+  EIGEN_DEVICE_FUNC
-    if (m_col == m_xpr.cols()) {
+  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_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_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;
@@ -73,26 +77,30 @@ struct CommaInitializer {
  /* inserts a matrix expression in the target matrix */
  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC CommaInitializer &operator,(const DenseBase<OtherDerived>& other) {
+  EIGEN_DEVICE_FUNC
-    if (m_col == m_xpr.cols() && (other.cols() != 0 || other.rows() != m_currentBlockRows)) {
+  CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
  {
    if (m_col==m_xpr.cols() && (other.cols()!=0 || other.rows()!=m_currentBlockRows))
    {
      m_row+=m_currentBlockRows;
      m_col = 0;
      m_currentBlockRows = other.rows();
-      eigen_assert(m_row + m_currentBlockRows <= m_xpr.rows() &&
+      eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
-                   "Too many rows passed to comma initializer (operator<<)");
+        && "Too many rows passed to comma initializer (operator<<)");
    }
-    eigen_assert((m_col + other.cols() <= m_xpr.cols()) &&
+    eigen_assert((m_col + other.cols() <= m_xpr.cols())
-                 "Too many coefficients passed to comma initializer (operator<<)");
+      && "Too many coefficients passed to comma initializer (operator<<)");
    eigen_assert(m_currentBlockRows==other.rows());
-    m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>(m_row, m_col, other.rows(),
+    m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>
-                                                                                           other.cols()) = other;
+                    (m_row, m_col, other.rows(), other.cols()) = other;
    m_col += other.cols();
    return *this;
  }
-  EIGEN_DEVICE_FUNC inline ~CommaInitializer()
+  EIGEN_DEVICE_FUNC
  inline ~CommaInitializer()
 #if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS
-      noexcept(false)  // Eigen::eigen_assert_exception
+  EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception)
 #endif
  {
      finished();
@@ -105,9 +113,11 @@ struct CommaInitializer {
    * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
    * \endcode
    */
-  EIGEN_DEVICE_FUNC inline XprType& finished() {
+  EIGEN_DEVICE_FUNC
-    eigen_assert(((m_row + m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0) && m_col == m_xpr.cols() &&
+  inline XprType& finished() {
-                 "Too few coefficients passed to comma initializer (operator<<)");
+      eigen_assert(((m_row+m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0)
           && m_col == m_xpr.cols()
           && "Too few coefficients passed to comma initializer (operator<<)");
      return m_xpr;
  }
@@ -126,21 +136,22 @@ struct CommaInitializer {
  * Example: \include MatrixBase_set.cpp
  * Output: \verbinclude MatrixBase_set.out
  *
- * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary
+  * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
 * order.
  *
  * \sa CommaInitializer::finished(), class CommaInitializer
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<<(const Scalar& s) {
+EIGEN_DEVICE_FUNC 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>
-EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<<(
+EIGEN_DEVICE_FUNC inline CommaInitializer<Derived>
-    const DenseBase<OtherDerived>& other) {
+DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
 {
  return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
 }
--- a/Eigen/src/Core/ConditionEstimator.h
+++ b/Eigen/src/Core/ConditionEstimator.h
@@ -10,9 +10,6 @@
 #ifndef EIGEN_CONDITIONESTIMATOR_H
 #define EIGEN_CONDITIONESTIMATOR_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
@@ -56,7 +53,8 @@ struct rcond_compute_sign<Vector, Vector, false> {
  * \sa FullPivLU, PartialPivLU, LDLT, LLT.
  */
 template <typename Decomposition>
-typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec) {
+typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec)
 {
  typedef typename Decomposition::MatrixType MatrixType;
  typedef typename Decomposition::Scalar Scalar;
  typedef typename Decomposition::RealScalar RealScalar;
@@ -66,7 +64,8 @@ typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomp
  eigen_assert(dec.rows() == dec.cols());
  const Index n = dec.rows();
-  if (n == 0) return 0;
+  if (n == 0)
    return 0;
  // Disable Index to float conversion warning
 #ifdef __INTEL_COMPILER
@@ -83,7 +82,8 @@ typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomp
  // and is the objective maximized by the ("super-") gradient ascent
  // algorithm below.
  RealScalar lower_bound = v.template lpNorm<1>();
-  if (n == 1) return lower_bound;
+  if (n == 1)
    return lower_bound;
  // Gradient ascent algorithm follows: We know that the optimum is achieved at
  // one of the simplices v = e_i, so in each iteration we follow a
@@ -93,7 +93,8 @@ typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomp
  Vector old_sign_vector;
  Index v_max_abs_index = -1;
  Index old_v_max_abs_index = v_max_abs_index;
-  for (int k = 0; k < 4; ++k) {
+  for (int k = 0; k < 4; ++k)
  {
    sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);
    if (k > 0 && !is_complex && sign_vector == old_sign_vector) {
      // Break if the solution stagnated.
@@ -154,15 +155,16 @@ typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomp
  * \sa FullPivLU, PartialPivLU, LDLT, LLT.
  */
 template <typename Decomposition>
-typename Decomposition::RealScalar rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm,
+typename Decomposition::RealScalar
-                                                         const Decomposition& dec) {
+rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition& dec)
 {
  typedef typename Decomposition::RealScalar RealScalar;
  eigen_assert(dec.rows() == dec.cols());
  if (dec.rows() == 0)              return NumTraits<RealScalar>::infinity();
-  if (numext::is_exactly_zero(matrix_norm)) return RealScalar(0);
+  if (matrix_norm == RealScalar(0)) return RealScalar(0);
  if (dec.rows() == 1)              return RealScalar(1);
  const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);
-  return (numext::is_exactly_zero(inverse_matrix_norm) ? RealScalar(0)
+  return (inverse_matrix_norm == RealScalar(0) ? RealScalar(0)
                                               : (RealScalar(1) / inverse_matrix_norm) / matrix_norm);
 }
--- a/Eigen/src/Core/CoreEvaluators.h
+++ b/Eigen/src/Core/CoreEvaluators.h
--- a/Eigen/src/Core/CoreIterators.h
+++ b/Eigen/src/Core/CoreIterators.h
@@ -10,9 +10,6 @@
 #ifndef EIGEN_COREITERATORS_H
 #define EIGEN_COREITERATORS_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 /* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core
@@ -28,41 +25,29 @@ class inner_iterator_selector;
 /** \class InnerIterator
  * \brief An InnerIterator allows to loop over the element of any matrix expression.
  * 
- * \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is
+  * \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is constructed.
 * constructed.
  * 
  * TODO: add a usage example
  */
 template<typename XprType>
-class InnerIterator {
+class InnerIterator
 {
 protected:
  typedef internal::inner_iterator_selector<XprType, typename internal::evaluator_traits<XprType>::Kind> IteratorType;
  typedef internal::evaluator<XprType> EvaluatorType;
  typedef typename internal::traits<XprType>::Scalar Scalar;
 public:
  /** Construct an iterator over the \a outerId -th row or column of \a xpr */
-  InnerIterator(const XprType &xpr, const Index &outerId) : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize()) {}
+  InnerIterator(const XprType &xpr, const Index &outerId)
    : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize())
  {}
  /// \returns the value of the current coefficient.
  EIGEN_STRONG_INLINE Scalar value() const          { return m_iter.value(); }
  /** Increment the iterator \c *this to the next non-zero coefficient.
    * Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView
    */
-  EIGEN_STRONG_INLINE InnerIterator &operator++() {
+  EIGEN_STRONG_INLINE InnerIterator& operator++()   { m_iter.operator++(); return *this; }
    m_iter.operator++();
    return *this;
  }
  EIGEN_STRONG_INLINE InnerIterator &operator+=(Index i) {
    m_iter.operator+=(i);
    return *this;
  }
  EIGEN_STRONG_INLINE InnerIterator operator+(Index i) {
    InnerIterator result(*this);
    result += i;
    return result;
  }
  /// \returns the column or row index of the current coefficient.
  EIGEN_STRONG_INLINE Index index() const           { return m_iter.index(); }
  /// \returns the row index of the current coefficient.
@@ -75,20 +60,19 @@ class InnerIterator {
 protected:
  EvaluatorType m_eval;
  IteratorType m_iter;
 private:
  // If you get here, then you're not using the right InnerIterator type, e.g.:
  //   SparseMatrix<double,RowMajor> A;
  //   SparseMatrix<double>::InnerIterator it(A,0);
-  template <typename T>
+  template<typename T> InnerIterator(const EigenBase<T>&,Index outer);
  InnerIterator(const EigenBase<T> &, Index outer);
 };
 namespace internal {
 // Generic inner iterator implementation for dense objects
 template<typename XprType>
-class inner_iterator_selector<XprType, IndexBased> {
+class inner_iterator_selector<XprType, IndexBased>
 {
 protected:
  typedef evaluator<XprType> EvaluatorType;
  typedef typename traits<XprType>::Scalar Scalar;
@@ -96,16 +80,16 @@ class inner_iterator_selector<XprType, IndexBased> {
 public:
  EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize)
-      : m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize) {}
+    : m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize)
  {}
-  EIGEN_STRONG_INLINE Scalar value() const {
+  EIGEN_STRONG_INLINE Scalar value() const
-    return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner) : m_eval.coeff(m_inner, m_outer);
+  {
    return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner)
                        : m_eval.coeff(m_inner, m_outer);
  }
-  EIGEN_STRONG_INLINE inner_iterator_selector &operator++() {
+  EIGEN_STRONG_INLINE inner_iterator_selector& operator++() { m_inner++; return *this; }
    m_inner++;
    return *this;
  }
  EIGEN_STRONG_INLINE Index index() const { return m_inner; }
  inline Index row() const { return IsRowMajor ? m_outer : index(); }
@@ -123,15 +107,17 @@ class inner_iterator_selector<XprType, IndexBased> {
 // For iterator-based evaluator, inner-iterator is already implemented as
 // evaluator<>::InnerIterator
 template<typename XprType>
-class inner_iterator_selector<XprType, IteratorBased> : public evaluator<XprType>::InnerIterator {
+class inner_iterator_selector<XprType, IteratorBased>
 : public evaluator<XprType>::InnerIterator
 {
 protected:
  typedef typename evaluator<XprType>::InnerIterator Base;
  typedef evaluator<XprType> EvaluatorType;
 public:
-  EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId,
+  EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &/*innerSize*/)
-                                              const Index & /*innerSize*/)
+    : Base(eval, outerId)
-      : Base(eval, outerId) {}
+  {}  
 };
 } // end namespace internal
--- a/Eigen/src/Core/CwiseBinaryOp.h
+++ b/Eigen/src/Core/CwiseBinaryOp.h
@@ -11,17 +11,15 @@
 #ifndef EIGEN_CWISE_BINARY_OP_H
 #define EIGEN_CWISE_BINARY_OP_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 template<typename BinaryOp, typename Lhs, typename Rhs>
-struct traits<CwiseBinaryOp<BinaryOp, Lhs, 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 remove_all_t<Lhs> Ancestor;
+  typedef typename remove_all<Lhs>::type Ancestor;
  typedef typename traits<Ancestor>::XprKind XprKind;
  enum {
    RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
@@ -32,18 +30,23 @@ struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> {
  // 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(const typename Lhs::Scalar&, const typename Rhs::Scalar&)>::type Scalar;
+  typedef typename result_of<
-  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind,
+                     BinaryOp(
                       const typename Lhs::Scalar&,
                       const typename Rhs::Scalar&
                     )
                   >::type Scalar;
  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,
                                              typename traits<Rhs>::StorageKind,
                                              BinaryOp>::ret StorageKind;
-  typedef typename promote_index_type<typename traits<Lhs>::StorageIndex, typename traits<Rhs>::StorageIndex>::type
+  typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,
-      StorageIndex;
+                                      typename traits<Rhs>::StorageIndex>::type StorageIndex;
  typedef typename Lhs::Nested LhsNested;
  typedef typename Rhs::Nested RhsNested;
-  typedef std::remove_reference_t<LhsNested> LhsNested_;
+  typedef typename remove_reference<LhsNested>::type _LhsNested;
-  typedef std::remove_reference_t<RhsNested> RhsNested_;
+  typedef typename remove_reference<RhsNested>::type _RhsNested;
  enum {
-    Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind,
+    Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind,typename traits<Rhs>::StorageKind,_LhsNested::Flags & RowMajorBit,_RhsNested::Flags & RowMajorBit>::value
                                        LhsNested_::Flags & RowMajorBit, RhsNested_::Flags & RowMajorBit>::value
  };
 };
 } // end namespace internal
@@ -68,63 +71,71 @@ class CwiseBinaryOpImpl;
  * 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
+  * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
 * CwiseNullaryOp
  */
 template<typename BinaryOp, typename LhsType, typename RhsType>
-class CwiseBinaryOp : public CwiseBinaryOpImpl<BinaryOp, LhsType, RhsType,
+class CwiseBinaryOp :
-                                               typename internal::cwise_promote_storage_type<
+  public CwiseBinaryOpImpl<
-                                                   typename internal::traits<LhsType>::StorageKind,
+          BinaryOp, LhsType, RhsType,
-                                                   typename internal::traits<RhsType>::StorageKind, BinaryOp>::ret>,
+          typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
-                      internal::no_assignment_operator {
+                                                        typename internal::traits<RhsType>::StorageKind,
                                                        BinaryOp>::ret>,
  internal::no_assignment_operator
 {
  public:
-  typedef internal::remove_all_t<BinaryOp> Functor;
+
-  typedef internal::remove_all_t<LhsType> Lhs;
+    typedef typename internal::remove_all<BinaryOp>::type Functor;
-  typedef internal::remove_all_t<RhsType> Rhs;
+    typedef typename internal::remove_all<LhsType>::type Lhs;
    typedef typename internal::remove_all<RhsType>::type Rhs;
    typedef typename CwiseBinaryOpImpl<
        BinaryOp, LhsType, RhsType,
        typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
-                                                    typename internal::traits<Rhs>::StorageKind, BinaryOp>::ret>::Base
+                                                      typename internal::traits<Rhs>::StorageKind,
-      Base;
+                                                      BinaryOp>::ret>::Base Base;
    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
  EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp, typename Lhs::Scalar, typename Rhs::Scalar)
  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
    typedef typename internal::ref_selector<LhsType>::type LhsNested;
    typedef typename internal::ref_selector<RhsType>::type RhsNested;
-  typedef std::remove_reference_t<LhsNested> LhsNested_;
+    typedef typename internal::remove_reference<LhsNested>::type _LhsNested;
-  typedef std::remove_reference_t<RhsNested> RhsNested_;
+    typedef typename internal::remove_reference<RhsNested>::type _RhsNested;
-#if EIGEN_COMP_MSVC
+    EIGEN_DEVICE_FUNC
-  // Required for Visual Studio or the Copy constructor will probably not get inlined!
+    EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp())
-  EIGEN_STRONG_INLINE CwiseBinaryOp(const CwiseBinaryOp<BinaryOp, LhsType, RhsType>&) = default;
+      : m_lhs(aLhs), m_rhs(aRhs), m_functor(func)
-#endif
+    {
-
+      EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs,
+      // require the sizes to match
-                                                      const BinaryOp& func = BinaryOp())
+      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
      : m_lhs(aLhs), m_rhs(aRhs), m_functor(func) {
      eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Index rows() const {
      // return the fixed size type if available to enable compile time optimizations
-    return internal::traits<internal::remove_all_t<LhsNested>>::RowsAtCompileTime == Dynamic ? m_rhs.rows()
+      if (internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic)
-                                                                                             : m_lhs.rows();
+        return m_rhs.rows();
      else
        return m_lhs.rows();
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Index cols() const {
      // return the fixed size type if available to enable compile time optimizations
-    return internal::traits<internal::remove_all_t<LhsNested>>::ColsAtCompileTime == Dynamic ? m_rhs.cols()
+      if (internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic)
-                                                                                             : m_lhs.cols();
+        return m_rhs.cols();
      else
        return m_lhs.cols();
    }
    /** \returns the left hand side nested expression */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNested_& lhs() const { return m_lhs; }
+    EIGEN_DEVICE_FUNC
    const _LhsNested& lhs() const { return m_lhs; }
    /** \returns the right hand side nested expression */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNested_& rhs() const { return m_rhs; }
+    EIGEN_DEVICE_FUNC
    const _RhsNested& rhs() const { return m_rhs; }
    /** \returns the functor representing the binary operation */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const BinaryOp& functor() const { return m_functor; }
+    EIGEN_DEVICE_FUNC
    const BinaryOp& functor() const { return m_functor; }
  protected:
    LhsNested m_lhs;
@@ -134,7 +145,9 @@ class CwiseBinaryOp : public CwiseBinaryOpImpl<BinaryOp, LhsType, RhsType,
 // Generic API dispatcher
 template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
-class CwiseBinaryOpImpl : public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs>>::type {
+class CwiseBinaryOpImpl
  : public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
 {
 public:
  typedef typename internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
 };
@@ -145,7 +158,9 @@ class CwiseBinaryOpImpl : public internal::generic_xpr_base<CwiseBinaryOp<Binary
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
 {
  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
@@ -156,7 +171,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator-=(c
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
 MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
 {
  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
@@ -164,3 +181,4 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator+=(c
 } // end namespace Eigen
 #endif // EIGEN_CWISE_BINARY_OP_H
--- a/Eigen/src/Core/CwiseNullaryOp.h
+++ b/Eigen/src/Core/CwiseNullaryOp.h
@@ -10,15 +10,15 @@
 #ifndef EIGEN_CWISE_NULLARY_OP_H
 #define EIGEN_CWISE_NULLARY_OP_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 template<typename NullaryOp, typename PlainObjectType>
-struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType> {
+struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
-  enum { Flags = traits<PlainObjectType>::Flags & RowMajorBit };
+{
  enum {
    Flags = traits<PlainObjectType>::Flags & RowMajorBit
  };
 };
 } // namespace internal
@@ -40,14 +40,11 @@ struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectT
  *
  * The functor NullaryOp must expose one of the following method:
    <table class="manual">
-    <tr            ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries
+    <tr            ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>
-  (e.g., random numbers)</td></tr> <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes
+    <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr>
-  sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr> <tr ><td>\c
+    <tr            ><td>\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)</td></tr>
  operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g.,
  to generate a checkerboard with 0 and 1)</td></tr>
    </table>
-  * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized
+  * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.
  for vectors.
  *
  * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
  * C++11 random number generators.
@@ -60,27 +57,31 @@ struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectT
  * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
  */
 template<typename NullaryOp, typename PlainObjectType>
-class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp, PlainObjectType> >::type,
+class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator
-                       internal::no_assignment_operator {
+{
  public:
    typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
-  EIGEN_DEVICE_FUNC CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
+    EIGEN_DEVICE_FUNC
-      : m_rows(rows), m_cols(cols), m_functor(func) {
+    CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
-    eigen_assert(rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) && cols >= 0 &&
+      : m_rows(rows), m_cols(cols), m_functor(func)
-                 (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+    {
-  }
+      eigen_assert(rows >= 0
-  EIGEN_DEVICE_FUNC CwiseNullaryOp(Index size, const NullaryOp& func = NullaryOp())
+            && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
-      : CwiseNullaryOp(RowsAtCompileTime == 1 ? 1 : size, RowsAtCompileTime == 1 ? size : 1, func) {
+            &&  cols >= 0
-    EIGEN_STATIC_ASSERT(CwiseNullaryOp::IsVectorAtCompileTime, YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
+            && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows.value(); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols.value(); }
+    EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
    /** \returns the functor representing the nullary operation */
-  EIGEN_DEVICE_FUNC const NullaryOp& functor() const { return m_functor; }
+    EIGEN_DEVICE_FUNC
    const NullaryOp& functor() const { return m_functor; }
  protected:
    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
@@ -88,13 +89,14 @@ class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp,
    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 NullaryExpr(const CustomNullaryOp&) should be used
+  * 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.
@@ -103,13 +105,9 @@ class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp,
  */
 template<typename Derived>
 template<typename CustomNullaryOp>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
-#ifndef EIGEN_PARSED_BY_DOXYGEN
+DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
-    const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
+{
 #else
    const CwiseNullaryOp<CustomNullaryOp, PlainObject>
 #endif
    DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func) {
  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
 }
@@ -121,7 +119,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  * \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 NullaryExpr(const CustomNullaryOp&) should be used
+  * 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.
@@ -133,18 +131,12 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  */
 template<typename Derived>
 template<typename CustomNullaryOp>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
-#ifndef EIGEN_PARSED_BY_DOXYGEN
+DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
-    const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
+{
 #else
    const CwiseNullaryOp<CustomNullaryOp, PlainObject>
 #endif
    DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
-  if (RowsAtCompileTime == 1)
+  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
-    return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
+  else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
  else
    return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
 }
 /** \returns an expression of a matrix defined by a custom functor \a func
@@ -158,13 +150,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  */
 template<typename Derived>
 template<typename CustomNullaryOp>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
-#ifndef EIGEN_PARSED_BY_DOXYGEN
+DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
-    const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
+{
 #else
    const CwiseNullaryOp<CustomNullaryOp, PlainObject>
 #endif
    DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func) {
  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
 }
@@ -174,7 +162,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  * 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 Constant(const Scalar&) should be used
+  * 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.
@@ -183,7 +171,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) {
+DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
 {
  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
 }
@@ -195,7 +184,7 @@ DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) {
  * \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 Constant(const Scalar&) should be used
+  * 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.
@@ -204,7 +193,8 @@ DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) {
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-DenseBase<Derived>::Constant(Index size, const Scalar& value) {
+DenseBase<Derived>::Constant(Index size, const Scalar& value)
 {
  return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
 }
@@ -219,39 +209,35 @@ DenseBase<Derived>::Constant(Index size, const Scalar& value) {
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-DenseBase<Derived>::Constant(const Scalar& value) {
+DenseBase<Derived>::Constant(const Scalar& value)
 {
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
-  return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime,
+  return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
                                         internal::scalar_constant_op<Scalar>(value));
 }
 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
  *
- * \only_for_vectors
+  * \sa LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)
 *
 * Example: \include DenseBase_LinSpaced_seq_deprecated.cpp
 * Output: \verbinclude DenseBase_LinSpaced_seq_deprecated.out
 *
 * \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&)
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
-DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) {
+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>(low, high, size));
+  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
 }
 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
  *
- * \sa LinSpaced(const Scalar&, const Scalar&)
+  * \sa LinSpaced(Scalar,Scalar)
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
-DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) {
+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,
+  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
                                         internal::linspaced_op<Scalar>(low, high, Derived::SizeAtCompileTime));
 }
 /**
@@ -279,9 +265,10 @@ DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& hig
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
-DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high) {
+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>(low, high, size));
+  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
 }
 /**
@@ -290,34 +277,23 @@ DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
-DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high) {
+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,
+  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
                                         internal::linspaced_op<Scalar>(low, high, Derived::SizeAtCompileTime));
 }
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessEqualSpacedReturnType
 DenseBase<Derived>::EqualSpaced(Index size, const Scalar& low, const Scalar& step) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return DenseBase<Derived>::NullaryExpr(size, internal::equalspaced_op<Scalar>(low, step));
 }
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessEqualSpacedReturnType
 DenseBase<Derived>::EqualSpaced(const Scalar& low, const Scalar& step) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::equalspaced_op<Scalar>(low, step));
 }
 /** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
 template<typename Derived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant(const Scalar& val, const RealScalar& prec) const {
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant
 (const Scalar& val, const RealScalar& prec) const
 {
  typename internal::nested_eval<Derived,1>::type self(derived());
  for(Index j = 0; j < cols(); ++j)
    for(Index i = 0; i < rows(); ++i)
-      if (!internal::isApprox(self.coeff(i, j), val, prec)) return false;
+      if(!internal::isApprox(self.coeff(i, j), val, prec))
        return false;
  return true;
 }
@@ -325,7 +301,9 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant(const Scalar& val,
  *
  * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
 template<typename Derived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant(const Scalar& val, const RealScalar& prec) const {
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant
 (const Scalar& val, const RealScalar& prec) const
 {
  return isApproxToConstant(val, prec);
 }
@@ -334,19 +312,19 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant(const Scalar& val, const R
  * \sa setConstant(), Constant(), class CwiseNullaryOp
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
 {
  setConstant(val);
 }
 /** Sets all coefficients in this expression to value \a val.
  *
- * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(),
+  * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
 * Constant(), class CwiseNullaryOp, setZero(), setOnes()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
-  internal::eigen_fill_impl<Derived>::run(derived(), val);
+{
-  return derived();
+  return derived() = Constant(rows(), cols(), val);
 }
 /** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
@@ -356,11 +334,12 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(c
  * Example: \include Matrix_setConstant_int.cpp
  * Output: \verbinclude Matrix_setConstant_int.out
  *
- * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp,
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
 * MatrixBase::Constant(const Scalar&)
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
 PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
 {
  resize(size);
  return setConstant(val);
 }
@@ -374,42 +353,16 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setCons
  * 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,
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
 * MatrixBase::Constant(const Scalar&)
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index rows, Index cols,
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
-                                                                                     const Scalar& val) {
+PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)
 {
  resize(rows, cols);
  return setConstant(val);
 }
 /** Resizes to the given size, changing only the number of columns, and sets all
 * coefficients in this expression to the given value \a val. For the parameter
 * of type NoChange_t, just pass the special value \c NoChange.
 *
 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp,
 * MatrixBase::Constant(const Scalar&)
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(NoChange_t, Index cols,
                                                                                     const Scalar& val) {
  return setConstant(rows(), cols, val);
 }
 /** Resizes to the given size, changing only the number of rows, and sets all
 * coefficients in this expression to the given value \a val. For the parameter
 * of type NoChange_t, just pass the special value \c NoChange.
 *
 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp,
 * MatrixBase::Constant(const Scalar&)
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index rows, NoChange_t,
                                                                                     const Scalar& val) {
  return setConstant(rows, cols(), val);
 }
 /**
  * \brief Sets a linearly spaced vector.
  *
@@ -427,10 +380,10 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setCons
  * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low,
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)
-                                                                                const Scalar& high) {
+{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
-  return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar>(low, high, newSize));
+  return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize));
 }
 /**
@@ -447,24 +400,12 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(
  * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
 {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return setLinSpaced(size(), low, high);
 }
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpaced(Index newSize, const Scalar& low,
                                                                                  const Scalar& step) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return derived() = Derived::NullaryExpr(newSize, internal::equalspaced_op<Scalar>(low, step));
 }
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpaced(const Scalar& low,
                                                                                  const Scalar& step) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return setEqualSpaced(size(), low, step);
 }
 // zero:
 /** \returns an expression of a zero matrix.
@@ -482,9 +423,10 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpace
  * \sa Zero(), Zero(Index)
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-    Index rows, Index cols) {
+DenseBase<Derived>::Zero(Index rows, Index cols)
-  return ZeroReturnType(rows, cols);
+{
  return Constant(rows, cols, Scalar(0));
 }
 /** \returns an expression of a zero vector.
@@ -504,9 +446,10 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroRet
  * \sa Zero(), Zero(Index,Index)
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-    Index size) {
+DenseBase<Derived>::Zero(Index size)
-  return ZeroReturnType(size);
+{
  return Constant(size, Scalar(0));
 }
 /** \returns an expression of a fixed-size zero matrix or vector.
@@ -520,8 +463,10 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroRet
  * \sa Zero(Index), Zero(Index,Index)
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-  return ZeroReturnType(RowsAtCompileTime, ColsAtCompileTime);
+DenseBase<Derived>::Zero()
 {
  return Constant(Scalar(0));
 }
 /** \returns true if *this is approximately equal to the zero matrix,
@@ -533,11 +478,13 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroRet
  * \sa class CwiseNullaryOp, Zero()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const {
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const
 {
  typename internal::nested_eval<Derived,1>::type self(derived());
  for(Index j = 0; j < cols(); ++j)
    for(Index i = 0; i < rows(); ++i)
-      if (!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec)) return false;
+      if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec))
        return false;
  return true;
 }
@@ -549,9 +496,9 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const
  * \sa class CwiseNullaryOp, Zero()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
-  internal::eigen_zero_impl<Derived>::run(derived());
+{
-  return derived();
+  return setConstant(Scalar(0));
 }
 /** Resizes to the given \a size, and sets all coefficients in this expression to zero.
@@ -564,9 +511,11 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() {
  * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index newSize) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
 PlainObjectBase<Derived>::setZero(Index newSize)
 {
  resize(newSize);
-  return setZero();
+  return setConstant(Scalar(0));
 }
 /** Resizes to the given size, and sets all coefficients in this expression to zero.
@@ -580,33 +529,11 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero
  * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index rows, Index cols) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
 PlainObjectBase<Derived>::setZero(Index rows, Index cols)
 {
  resize(rows, cols);
-  return setZero();
+  return setConstant(Scalar(0));
 }
 /** Resizes to the given size, changing only the number of columns, and sets all
 * coefficients in this expression to zero. For the parameter of type NoChange_t,
 * just pass the special value \c NoChange.
 *
 * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(Index, NoChange_t), class CwiseNullaryOp,
 * DenseBase::Zero()
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(NoChange_t, Index cols) {
  return setZero(rows(), cols);
 }
 /** Resizes to the given size, changing only the number of rows, and sets all
 * coefficients in this expression to zero. For the parameter of type NoChange_t,
 * just pass the special value \c NoChange.
 *
 * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(NoChange_t, Index), class CwiseNullaryOp,
 * DenseBase::Zero()
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index rows, NoChange_t) {
  return setZero(rows, cols());
 }
 // ones:
@@ -626,8 +553,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero
  * \sa Ones(), Ones(Index), isOnes(), class Ones
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-    Index rows, Index cols) {
+DenseBase<Derived>::Ones(Index rows, Index cols)
 {
  return Constant(rows, cols, Scalar(1));
 }
@@ -648,8 +576,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::Constan
  * \sa Ones(), Ones(Index,Index), isOnes(), class Ones
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
-    Index newSize) {
+DenseBase<Derived>::Ones(Index newSize)
 {
  return Constant(newSize, Scalar(1));
 }
@@ -664,7 +593,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::Constan
  * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
 DenseBase<Derived>::Ones()
 {
  return Constant(Scalar(1));
 }
@@ -677,7 +608,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::Constan
  * \sa class CwiseNullaryOp, Ones()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes(const RealScalar& prec) const {
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes
 (const RealScalar& prec) const
 {
  return isApproxToConstant(Scalar(1), prec);
 }
@@ -689,7 +622,8 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes(const RealScalar& prec) const
  * \sa class CwiseNullaryOp, Ones()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
 {
  return setConstant(Scalar(1));
 }
@@ -703,7 +637,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes() {
  * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index newSize) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
 PlainObjectBase<Derived>::setOnes(Index newSize)
 {
  resize(newSize);
  return setConstant(Scalar(1));
 }
@@ -719,35 +655,13 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes
  * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index rows, Index cols) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
 PlainObjectBase<Derived>::setOnes(Index rows, Index cols)
 {
  resize(rows, cols);
  return setConstant(Scalar(1));
 }
 /** Resizes to the given size, changing only the number of rows, and sets all
 * coefficients in this expression to one. For the parameter of type NoChange_t,
 * just pass the special value \c NoChange.
 *
 * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(NoChange_t, Index), class CwiseNullaryOp,
 * MatrixBase::Ones()
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index rows, NoChange_t) {
  return setOnes(rows, cols());
 }
 /** Resizes to the given size, changing only the number of columns, and sets all
 * coefficients in this expression to one. For the parameter of type NoChange_t,
 * just pass the special value \c NoChange.
 *
 * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(Index, NoChange_t) class CwiseNullaryOp,
 * MatrixBase::Ones()
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(NoChange_t, Index cols) {
  return setOnes(rows(), cols);
 }
 // Identity:
 /** \returns an expression of the identity matrix (not necessarily square).
@@ -766,7 +680,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
-MatrixBase<Derived>::Identity(Index rows, Index cols) {
+MatrixBase<Derived>::Identity(Index rows, Index cols)
 {
  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
 }
@@ -782,7 +697,8 @@ MatrixBase<Derived>::Identity(Index rows, Index cols) {
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
-MatrixBase<Derived>::Identity() {
+MatrixBase<Derived>::Identity()
 {
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
  return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
 }
@@ -797,14 +713,23 @@ MatrixBase<Derived>::Identity() {
  * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
  */
 template<typename Derived>
-bool MatrixBase<Derived>::isIdentity(const RealScalar& prec) const {
+bool MatrixBase<Derived>::isIdentity
 (const RealScalar& prec) const
 {
  typename internal::nested_eval<Derived,1>::type self(derived());
-  for (Index j = 0; j < cols(); ++j) {
+  for(Index j = 0; j < cols(); ++j)
-    for (Index i = 0; i < rows(); ++i) {
+  {
-      if (i == j) {
+    for(Index i = 0; i < rows(); ++i)
-        if (!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec)) return false;
+    {
-      } else {
+      if(i == j)
-        if (!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec)) return false;
+      {
        if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec))
          return false;
      }
      else
      {
        if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec))
          return false;
      }
    }
  }
@@ -814,15 +739,21 @@ bool MatrixBase<Derived>::isIdentity(const RealScalar& prec) const {
 namespace internal {
 template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
-struct setIdentity_impl {
+struct setIdentity_impl
-  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Derived& run(Derived& m) {
+{
  EIGEN_DEVICE_FUNC
  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
  {
    return m = Derived::Identity(m.rows(), m.cols());
  }
 };
 template<typename Derived>
-struct setIdentity_impl<Derived, true> {
+struct setIdentity_impl<Derived, true>
-  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Derived& run(Derived& m) {
+{
  EIGEN_DEVICE_FUNC
  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
  {
    m.setZero();
    const Index size = numext::mini(m.rows(), m.cols());
    for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
@@ -840,7 +771,8 @@ struct setIdentity_impl<Derived, true> {
  * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
 {
  return internal::setIdentity_impl<Derived>::run(derived());
 }
@@ -855,7 +787,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(
  * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)
 {
  derived().resize(rows, cols);
  return setIdentity();
 }
@@ -867,8 +800,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(
  * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i)
-    Index newSize, Index i) {
+{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i);
 }
@@ -882,8 +815,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisR
  * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
-    Index i) {
+{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return BasisReturnType(SquareMatrixType::Identity(),i);
 }
@@ -892,83 +825,41 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisR
  *
  * \only_for_vectors
  *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(),
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
 * MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
-  return Derived::Unit(0);
+{ 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(),
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
 * MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
-  return Derived::Unit(1);
+{ 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(),
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
 * MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
-  return Derived::Unit(2);
+{ 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(),
+  * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
 * MatrixBase::UnitW()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
-  return Derived::Unit(3);
+{ return Derived::Unit(3); }
 }
 /** \brief Set the coefficients of \c *this to the i-th unit (basis) vector
 *
 * \param i index of the unique coefficient to be set to 1
 *
 * \only_for_vectors
 *
 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index i) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
  eigen_assert(i < size());
  derived().setZero();
  derived().coeffRef(i) = Scalar(1);
  return derived();
 }
 /** \brief Resizes to the given \a newSize, and writes the i-th unit (basis) vector into *this.
 *
 * \param newSize the new size of the vector
 * \param i index of the unique coefficient to be set to 1
 *
 * \only_for_vectors
 *
 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
 */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index newSize, Index i) {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
  eigen_assert(i < newSize);
  derived().resize(newSize);
  return setUnit(i);
 }
 } // end namespace Eigen
--- a/Eigen/src/Core/CwiseTernaryOp.h
+++ b/Eigen/src/Core/CwiseTernaryOp.h
@@ -12,9 +12,6 @@
 #ifndef EIGEN_CWISE_TERNARY_OP_H
 #define EIGEN_CWISE_TERNARY_OP_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
@@ -22,7 +19,7 @@ template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
 struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > {
  // we must not inherit from traits<Arg1> since it has
  // the potential to cause problems with MSVC
-  typedef remove_all_t<Arg1> Ancestor;
+  typedef typename remove_all<Arg1>::type Ancestor;
  typedef typename traits<Ancestor>::XprKind XprKind;
  enum {
    RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
@@ -34,7 +31,8 @@ struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> {
  // even though we require Arg1, Arg2, and Arg3 to have the same scalar type
  // (see CwiseTernaryOp constructor),
  // we still want to handle the case when the result type is different.
-  typedef typename result_of<TernaryOp(const typename Arg1::Scalar&, const typename Arg2::Scalar&,
+  typedef typename result_of<TernaryOp(
      const typename Arg1::Scalar&, const typename Arg2::Scalar&,
      const typename Arg3::Scalar&)>::type Scalar;
  typedef typename internal::traits<Arg1>::StorageKind StorageKind;
@@ -43,14 +41,15 @@ struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> {
  typedef typename Arg1::Nested Arg1Nested;
  typedef typename Arg2::Nested Arg2Nested;
  typedef typename Arg3::Nested Arg3Nested;
-  typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
+  typedef typename remove_reference<Arg1Nested>::type _Arg1Nested;
-  typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
+  typedef typename remove_reference<Arg2Nested>::type _Arg2Nested;
-  typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
+  typedef typename remove_reference<Arg3Nested>::type _Arg3Nested;
-  enum { Flags = Arg1Nested_::Flags & RowMajorBit };
+  enum { Flags = _Arg1Nested::Flags & RowMajorBit };
 };
 }  // end namespace internal
-template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3, typename StorageKind>
+template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
          typename StorageKind>
 class CwiseTernaryOpImpl;
 /** \class CwiseTernaryOp
@@ -80,77 +79,100 @@ class CwiseTernaryOpImpl;
 * MatrixBase<Argument3> &, const CustomTernaryOp &) const, class CwiseBinaryOp,
 * class CwiseUnaryOp, class CwiseNullaryOp
  */
-template <typename TernaryOp, typename Arg1Type, typename Arg2Type, typename Arg3Type>
+template <typename TernaryOp, typename Arg1Type, typename Arg2Type,
-class CwiseTernaryOp : public CwiseTernaryOpImpl<TernaryOp, Arg1Type, Arg2Type, Arg3Type,
+          typename Arg3Type>
 class CwiseTernaryOp : public CwiseTernaryOpImpl<
                           TernaryOp, Arg1Type, Arg2Type, Arg3Type,
                           typename internal::traits<Arg1Type>::StorageKind>,
-                       internal::no_assignment_operator {
+                       internal::no_assignment_operator
 {
 public:
-  typedef internal::remove_all_t<Arg1Type> Arg1;
+  typedef typename internal::remove_all<Arg1Type>::type Arg1;
-  typedef internal::remove_all_t<Arg2Type> Arg2;
+  typedef typename internal::remove_all<Arg2Type>::type Arg2;
-  typedef internal::remove_all_t<Arg3Type> Arg3;
+  typedef typename internal::remove_all<Arg3Type>::type Arg3;
-  // require the sizes to match
+  typedef typename CwiseTernaryOpImpl<
-  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
+      TernaryOp, Arg1Type, Arg2Type, Arg3Type,
  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
  // The index types should match
  EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
                                         typename internal::traits<Arg2Type>::StorageKind>::value),
                      STORAGE_KIND_MUST_MATCH)
  EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
                                         typename internal::traits<Arg3Type>::StorageKind>::value),
                      STORAGE_KIND_MUST_MATCH)
  typedef typename CwiseTernaryOpImpl<TernaryOp, Arg1Type, Arg2Type, Arg3Type,
      typename internal::traits<Arg1Type>::StorageKind>::Base Base;
  EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp)
  typedef typename internal::ref_selector<Arg1Type>::type Arg1Nested;
  typedef typename internal::ref_selector<Arg2Type>::type Arg2Nested;
  typedef typename internal::ref_selector<Arg3Type>::type Arg3Nested;
-  typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
+  typedef typename internal::remove_reference<Arg1Nested>::type _Arg1Nested;
-  typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
+  typedef typename internal::remove_reference<Arg2Nested>::type _Arg2Nested;
-  typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
+  typedef typename internal::remove_reference<Arg3Nested>::type _Arg3Nested;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2, const Arg3& a3,
+  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2,
                                     const Arg3& a3,
                                     const TernaryOp& func = TernaryOp())
      : m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) {
-    eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() && a1.rows() == a3.rows() && a1.cols() == a3.cols());
+    // require the sizes to match
    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
    // The index types should match
    EIGEN_STATIC_ASSERT((internal::is_same<
                         typename internal::traits<Arg1Type>::StorageKind,
                         typename internal::traits<Arg2Type>::StorageKind>::value),
                        STORAGE_KIND_MUST_MATCH)
    EIGEN_STATIC_ASSERT((internal::is_same<
                         typename internal::traits<Arg1Type>::StorageKind,
                         typename internal::traits<Arg3Type>::StorageKind>::value),
                        STORAGE_KIND_MUST_MATCH)
    eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() &&
                 a1.rows() == a3.rows() && a1.cols() == a3.cols());
  }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const {
+  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE Index rows() const {
    // return the fixed size type if available to enable compile time
    // optimizations
-    if (internal::traits<internal::remove_all_t<Arg1Nested>>::RowsAtCompileTime == Dynamic &&
+    if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
-        internal::traits<internal::remove_all_t<Arg2Nested>>::RowsAtCompileTime == Dynamic)
+                RowsAtCompileTime == Dynamic &&
        internal::traits<typename internal::remove_all<Arg2Nested>::type>::
                RowsAtCompileTime == Dynamic)
      return m_arg3.rows();
-    else if (internal::traits<internal::remove_all_t<Arg1Nested>>::RowsAtCompileTime == Dynamic &&
+    else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
-             internal::traits<internal::remove_all_t<Arg3Nested>>::RowsAtCompileTime == Dynamic)
+                     RowsAtCompileTime == Dynamic &&
             internal::traits<typename internal::remove_all<Arg3Nested>::type>::
                     RowsAtCompileTime == Dynamic)
      return m_arg2.rows();
    else
      return m_arg1.rows();
  }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const {
+  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE Index cols() const {
    // return the fixed size type if available to enable compile time
    // optimizations
-    if (internal::traits<internal::remove_all_t<Arg1Nested>>::ColsAtCompileTime == Dynamic &&
+    if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
-        internal::traits<internal::remove_all_t<Arg2Nested>>::ColsAtCompileTime == Dynamic)
+                ColsAtCompileTime == Dynamic &&
        internal::traits<typename internal::remove_all<Arg2Nested>::type>::
                ColsAtCompileTime == Dynamic)
      return m_arg3.cols();
-    else if (internal::traits<internal::remove_all_t<Arg1Nested>>::ColsAtCompileTime == Dynamic &&
+    else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
-             internal::traits<internal::remove_all_t<Arg3Nested>>::ColsAtCompileTime == Dynamic)
+                     ColsAtCompileTime == Dynamic &&
             internal::traits<typename internal::remove_all<Arg3Nested>::type>::
                     ColsAtCompileTime == Dynamic)
      return m_arg2.cols();
    else
      return m_arg1.cols();
  }
  /** \returns the first argument nested expression */
-  EIGEN_DEVICE_FUNC const Arg1Nested_& arg1() const { return m_arg1; }
+  EIGEN_DEVICE_FUNC
  const _Arg1Nested& arg1() const { return m_arg1; }
  /** \returns the first argument nested expression */
-  EIGEN_DEVICE_FUNC const Arg2Nested_& arg2() const { return m_arg2; }
+  EIGEN_DEVICE_FUNC
  const _Arg2Nested& arg2() const { return m_arg2; }
  /** \returns the third argument nested expression */
-  EIGEN_DEVICE_FUNC const Arg3Nested_& arg3() const { return m_arg3; }
+  EIGEN_DEVICE_FUNC
  const _Arg3Nested& arg3() const { return m_arg3; }
  /** \returns the functor representing the ternary operation */
-  EIGEN_DEVICE_FUNC const TernaryOp& functor() const { return m_functor; }
+  EIGEN_DEVICE_FUNC
  const TernaryOp& functor() const { return m_functor; }
 protected:
  Arg1Nested m_arg1;
@@ -160,10 +182,14 @@ class CwiseTernaryOp : public CwiseTernaryOpImpl<TernaryOp, Arg1Type, Arg2Type,
 };
 // Generic API dispatcher
-template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3, typename StorageKind>
+template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
-class CwiseTernaryOpImpl : public internal::generic_xpr_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>>::type {
+          typename StorageKind>
 class CwiseTernaryOpImpl
    : public internal::generic_xpr_base<
          CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type {
 public:
-  typedef typename internal::generic_xpr_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>>::type Base;
+  typedef typename internal::generic_xpr_base<
      CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type Base;
 };
 }  // end namespace Eigen
--- a/Eigen/src/Core/CwiseUnaryOp.h
+++ b/Eigen/src/Core/CwiseUnaryOp.h
@@ -11,20 +11,23 @@
 #ifndef EIGEN_CWISE_UNARY_OP_H
 #define EIGEN_CWISE_UNARY_OP_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
 template<typename UnaryOp, typename XprType>
-struct traits<CwiseUnaryOp<UnaryOp, XprType> > : traits<XprType> {
+struct traits<CwiseUnaryOp<UnaryOp, XprType> >
-  typedef typename result_of<UnaryOp(const typename XprType::Scalar&)>::type Scalar;
+ : traits<XprType>
 {
  typedef typename result_of<
                     UnaryOp(const typename XprType::Scalar&)
                   >::type Scalar;
  typedef typename XprType::Nested XprTypeNested;
-  typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
-  enum { Flags = XprTypeNested_::Flags & RowMajorBit };
+  enum {
    Flags = _XprTypeNested::Flags & RowMajorBit 
  };
-}  // namespace internal
+};
 }
 template<typename UnaryOp, typename XprType, typename StorageKind>
 class CwiseUnaryOpImpl;
@@ -49,30 +52,37 @@ class CwiseUnaryOpImpl;
  * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
  */
 template<typename UnaryOp, typename XprType>
-class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>,
+class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>, internal::no_assignment_operator
-                     internal::no_assignment_operator {
+{
  public:
    typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
    typedef typename internal::ref_selector<XprType>::type XprTypeNested;
-  typedef internal::remove_all_t<XprType> NestedExpression;
+    typedef typename internal::remove_all<XprType>::type NestedExpression;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
      : m_xpr(xpr), m_functor(func) {}
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_xpr.rows(); }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_xpr.cols(); }
+    Index rows() const { return m_xpr.rows(); }
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    Index cols() const { return m_xpr.cols(); }
    /** \returns the functor representing the unary operation */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryOp& functor() const { return m_functor; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    const UnaryOp& functor() const { return m_functor; }
    /** \returns the nested expression */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const {
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    return m_xpr;
+    const typename internal::remove_all<XprTypeNested>::type&
-  }
+    nestedExpression() const { return m_xpr; }
    /** \returns the nested expression */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::remove_all_t<XprTypeNested>& nestedExpression() { return m_xpr; }
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    typename internal::remove_all<XprTypeNested>::type&
    nestedExpression() { return m_xpr; }
  protected:
    XprTypeNested m_xpr;
@@ -81,7 +91,9 @@ class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal
 // Generic API dispatcher
 template<typename UnaryOp, typename XprType, typename StorageKind>
-class CwiseUnaryOpImpl : public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type {
+class CwiseUnaryOpImpl
  : public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
 {
 public:
  typedef typename internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
 };
--- a/Eigen/src/Core/CwiseUnaryView.h
+++ b/Eigen/src/Core/CwiseUnaryView.h
@@ -10,112 +10,36 @@
 #ifndef EIGEN_CWISE_UNARY_VIEW_H
 #define EIGEN_CWISE_UNARY_VIEW_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
-template <typename ViewOp, typename MatrixType, typename StrideType>
+template<typename ViewOp, typename MatrixType>
-struct traits<CwiseUnaryView<ViewOp, MatrixType, StrideType> > : traits<MatrixType> {
+struct traits<CwiseUnaryView<ViewOp, MatrixType> >
-  typedef typename result_of<ViewOp(typename traits<MatrixType>::Scalar&)>::type1 ScalarRef;
+ : traits<MatrixType>
-  static_assert(std::is_reference<ScalarRef>::value, "Views must return a reference type.");
+{
-  typedef remove_all_t<ScalarRef> Scalar;
+  typedef typename result_of<
                     ViewOp(const typename traits<MatrixType>::Scalar&)
                   >::type Scalar;
  typedef typename MatrixType::Nested MatrixTypeNested;
-  typedef remove_all_t<MatrixTypeNested> MatrixTypeNested_;
+  typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
  enum {
    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
-    Flags =
+    Flags = traits<_MatrixTypeNested>::Flags & (RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions
        traits<MatrixTypeNested_>::Flags &
        (RowMajorBit | FlagsLvalueBit | DirectAccessBit),  // FIXME DirectAccessBit should not be handled by expressions
    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 =
+    InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic
        StrideType::InnerStrideAtCompileTime == 0
            ? (MatrixTypeInnerStride == Dynamic
                             ? int(Dynamic)
-                   : int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
+                             : int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),
-            : int(StrideType::InnerStrideAtCompileTime),
+    OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret == Dynamic
    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
                                   ? (outer_stride_at_compile_time<MatrixType>::ret == Dynamic
                             ? int(Dynamic)
-                                          : outer_stride_at_compile_time<MatrixType>::ret *
+                             : outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar))
                                                int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
                                   : int(StrideType::OuterStrideAtCompileTime)
  };
 };
 // Generic API dispatcher
 template <typename ViewOp, typename XprType, typename StrideType, typename StorageKind,
          bool Mutable = !std::is_const<XprType>::value>
 class CwiseUnaryViewImpl : public generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type {
 public:
  typedef typename generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type Base;
 };
 template <typename ViewOp, typename MatrixType, typename StrideType>
 class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false>
    : public dense_xpr_base<CwiseUnaryView<ViewOp, MatrixType, StrideType> >::type {
 public:
  typedef CwiseUnaryView<ViewOp, MatrixType, StrideType> Derived;
  typedef typename dense_xpr_base<CwiseUnaryView<ViewOp, MatrixType, StrideType> >::type Base;
  EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
  EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeffRef(0)); }
  EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
    return StrideType::InnerStrideAtCompileTime != 0 ? int(StrideType::InnerStrideAtCompileTime)
                                                     : derived().nestedExpression().innerStride() *
                                                           sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
 }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
+template<typename ViewOp, typename MatrixType, typename StorageKind>
-    return StrideType::OuterStrideAtCompileTime != 0 ? int(StrideType::OuterStrideAtCompileTime)
+class CwiseUnaryViewImpl;
                                                     : derived().nestedExpression().outerStride() *
                                                           sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
  }
 protected:
  EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
  // Allow const access to coeffRef for the case of direct access being enabled.
  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
    return internal::evaluator<Derived>(derived()).coeffRef(index);
  }
  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index row, Index col) const {
    return internal::evaluator<Derived>(derived()).coeffRef(row, col);
  }
 };
 template <typename ViewOp, typename MatrixType, typename StrideType>
 class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, true>
    : public CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false> {
 public:
  typedef CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false> Base;
  typedef CwiseUnaryView<ViewOp, MatrixType, StrideType> Derived;
  EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
  using Base::data;
  EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    return internal::evaluator<Derived>(derived()).coeffRef(row, col);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    return internal::evaluator<Derived>(derived()).coeffRef(index);
  }
 protected:
  EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
 };
 }  // namespace internal
 /** \class CwiseUnaryView
  * \ingroup Core_Module
@@ -130,38 +54,77 @@ class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, true>
  *
  * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
  */
-template <typename ViewOp, typename MatrixType, typename StrideType>
+template<typename ViewOp, typename MatrixType>
-class CwiseUnaryView : public internal::CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType,
+class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
-                                                           typename internal::traits<MatrixType>::StorageKind> {
+{
  public:
-  typedef typename internal::CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType,
+
-                                                typename internal::traits<MatrixType>::StorageKind>::Base Base;
+    typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
-  typedef internal::remove_all_t<MatrixType> NestedExpression;
+    typedef typename internal::remove_all<MatrixType>::type NestedExpression;
-  explicit EIGEN_DEVICE_FUNC inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
+    explicit inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
      : m_matrix(mat), m_functor(func) {}
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_matrix.rows(); }
+    EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_matrix.cols(); }
+    EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
    /** \returns the functor representing unary operation */
-  EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; }
+    const ViewOp& functor() const { return m_functor; }
    /** \returns the nested expression */
-  EIGEN_DEVICE_FUNC const internal::remove_all_t<MatrixTypeNested>& nestedExpression() const { return m_matrix; }
+    const typename internal::remove_all<MatrixTypeNested>::type&
    nestedExpression() const { return m_matrix; }
    /** \returns the nested expression */
-  EIGEN_DEVICE_FUNC std::remove_reference_t<MatrixTypeNested>& nestedExpression() { return m_matrix; }
+    typename internal::remove_reference<MatrixTypeNested>::type&
    nestedExpression() { return m_matrix.const_cast_derived(); }
  protected:
    MatrixTypeNested m_matrix;
    ViewOp m_functor;
 };
-}  // namespace Eigen
+// Generic API dispatcher
 template<typename ViewOp, typename XprType, typename StorageKind>
 class CwiseUnaryViewImpl
  : public internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type
 {
 public:
  typedef typename internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type Base;
 };
 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)
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
    EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }
    EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeff(0)); }
    EIGEN_DEVICE_FUNC inline Index innerStride() const
    {
      return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
    }
    EIGEN_DEVICE_FUNC inline Index outerStride() const
    {
      return derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
    }
  protected:
    EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
 };
 } // end namespace Eigen
 #endif // EIGEN_CWISE_UNARY_VIEW_H
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -11,13 +11,17 @@
 #ifndef EIGEN_DENSEBASE_H
 #define EIGEN_DENSEBASE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 // The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
-EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned, THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
+// This dummy function simply aims at checking that at compile time.
 static inline void check_DenseIndex_is_signed() {
  EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE); 
 }
 } // end namespace internal
 /** \class DenseBase
  * \ingroup Core_Module
@@ -34,8 +38,7 @@ EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned, THE_INDEX_TYPE_MUST_BE_A_SI
  *
  * \sa \blank \ref TopicClassHierarchy
  */
-template <typename Derived>
+template<typename Derived> class DenseBase
 class DenseBase
 #ifndef EIGEN_PARSED_BY_DOXYGEN
  : public DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value>
 #else
@@ -43,6 +46,7 @@ class DenseBase
 #endif // not EIGEN_PARSED_BY_DOXYGEN
 {
  public:
    /** Inner iterator type to iterate over the coefficients of a row or column.
      * \sa class InnerIterator
      */
@@ -69,26 +73,26 @@ class DenseBase
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> 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::colIndexByOuterInner;
  using Base::cols;
  using Base::const_cast_derived;
  using Base::derived;
  using Base::rowIndexByOuterInner;
  using Base::rows;
  using Base::size;
    using Base::operator();
    using Base::operator[];
  using Base::colStride;
  using Base::innerStride;
  using Base::outerStride;
  using Base::rowStride;
  using Base::stride;
  using Base::w;
    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 {
@@ -105,7 +109,9 @@ class DenseBase
          * it is set to the \a Dynamic constant.
          * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
-    SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+
      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 */
@@ -132,8 +138,8 @@ class DenseBase
          * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
          */
-    MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime,
+      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
-                                                          internal::traits<Derived>::MaxColsAtCompileTime),
+                                                      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.
@@ -144,20 +150,13 @@ class DenseBase
          * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
          */
-    IsVectorAtCompileTime =
+      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
-        internal::traits<Derived>::RowsAtCompileTime == 1 || internal::traits<Derived>::ColsAtCompileTime == 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). */
    NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0
                    : bool(IsVectorAtCompileTime)  ? 1
                                                   : 2,
    /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
     * and 2 for matrices.
     */
      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".
@@ -166,8 +165,7 @@ class DenseBase
      IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
      InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
-                             : int(IsRowMajor)          ? int(ColsAtCompileTime)
+                             : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
                                                        : int(RowsAtCompileTime),
      InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
      OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
@@ -179,19 +177,23 @@ class DenseBase
    /** The plain matrix type corresponding to this expression.
      * \sa PlainObject */
-  typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime,
+    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>
+                internal::traits<Derived>::MaxRowsAtCompileTime,
-      PlainMatrix;
+                internal::traits<Derived>::MaxColsAtCompileTime
          > PlainMatrix;
    /** The plain array type corresponding to this expression.
      * \sa PlainObject */
-  typedef Array<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime,
+    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>
+                internal::traits<Derived>::MaxRowsAtCompileTime,
-      PlainArray;
+                internal::traits<Derived>::MaxColsAtCompileTime
          > PlainArray;
    /** \brief The plain matrix or array type corresponding to this expression.
      *
@@ -199,17 +201,24 @@ class DenseBase
      * 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 std::conditional_t<internal::is_same<typename internal::traits<Derived>::XprKind, MatrixXpr>::value,
+    typedef typename internal::conditional<internal::is_same<typename internal::traits<Derived>::XprKind,MatrixXpr >::value,
-                             PlainMatrix, PlainArray>
+                                 PlainMatrix, PlainArray>::type PlainObject;
-      PlainObject;
+
    /** \returns the number of nonzero coefficients which is in practice the number
      * of stored coefficients. */
    EIGEN_DEVICE_FUNC
    inline Index nonZeros() const { return size(); }
    /** \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. */
-  EIGEN_DEVICE_FUNC constexpr Index outerSize() const {
+    EIGEN_DEVICE_FUNC
-    return IsVectorAtCompileTime ? 1 : int(IsRowMajor) ? this->rows() : this->cols();
+    Index outerSize() const
    {
      return IsVectorAtCompileTime ? 1
           : int(IsRowMajor) ? this->rows() : this->cols();
    }
    /** \returns the inner size.
@@ -217,122 +226,134 @@ class DenseBase
      * \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. */
-  EIGEN_DEVICE_FUNC constexpr Index innerSize() const {
+    EIGEN_DEVICE_FUNC
-    return IsVectorAtCompileTime ? this->size() : int(IsRowMajor) ? this->cols() : this->rows();
+    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
+      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
-   * does nothing else.
+      * nothing else.
      */
-  EIGEN_DEVICE_FUNC void resize(Index newSize) {
+    EIGEN_DEVICE_FUNC
    void resize(Index newSize)
    {
      EIGEN_ONLY_USED_FOR_DEBUG(newSize);
-    eigen_assert(newSize == this->size() && "DenseBase::resize() does not actually allow to resize.");
+      eigen_assert(newSize == 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
+      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
-   * does nothing else.
+      * nothing else.
      */
-  EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) {
+    EIGEN_DEVICE_FUNC
    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() &&
+      eigen_assert(rows == this->rows() && cols == this->cols()
-                 "DenseBase::resize() does not actually allow to resize.");
+                && "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>,PlainObject> ConstantReturnType;
  /** \internal Represents a matrix with all coefficients equal to zero*/
  typedef CwiseNullaryOp<internal::scalar_zero_op<Scalar>, PlainObject> ZeroReturnType;
    /** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */
-  EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> SequentialLinSpacedReturnType;
+    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,PacketScalar>,PlainObject> SequentialLinSpacedReturnType;
    /** \internal Represents a vector with linearly spaced coefficients that allows random access. */
-  typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> RandomAccessLinSpacedReturnType;
+    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,PacketScalar>,PlainObject> RandomAccessLinSpacedReturnType;
  /** \internal Represents a vector with equally spaced coefficients that allows random access. */
  typedef CwiseNullaryOp<internal::equalspaced_op<Scalar>, PlainObject> RandomAccessEqualSpacedReturnType;
    /** \internal the return type of MatrixBase::eigenvalues() */
-  typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real,
+    typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
                 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>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other);
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    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)
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase& other);
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    Derived& operator=(const DenseBase& other);
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Derived& operator=(const EigenBase<OtherDerived>& other);
+    EIGEN_DEVICE_FUNC
    Derived& operator=(const EigenBase<OtherDerived> &other);
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Derived& operator+=(const EigenBase<OtherDerived>& other);
+    EIGEN_DEVICE_FUNC
    Derived& operator+=(const EigenBase<OtherDerived> &other);
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Derived& operator-=(const EigenBase<OtherDerived>& other);
+    EIGEN_DEVICE_FUNC
    Derived& operator-=(const EigenBase<OtherDerived> &other);
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Derived& operator=(const ReturnByValue<OtherDerived>& func);
+    EIGEN_DEVICE_FUNC
    Derived& operator=(const ReturnByValue<OtherDerived>& func);
    /** \internal
-   * Copies \a other into *this without evaluating other. \returns a reference to *this. */
+      * Copies \a other into *this without evaluating other. \returns a reference to *this.
      * \deprecated */
    template<typename OtherDerived>
-  /** \deprecated */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived& lazyAssign(const DenseBase<OtherDerived>& other);
+    Derived& lazyAssign(const DenseBase<OtherDerived>& other);
-  EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const Scalar& s);
+    EIGEN_DEVICE_FUNC
    CommaInitializer<Derived> operator<< (const Scalar& s);
  template <unsigned int Added, unsigned int Removed>
    /** \deprecated it now returns \c *this */
-  EIGEN_DEPRECATED const Derived& flagged() const {
+    template<unsigned int Added,unsigned int Removed>
-    return derived();
+    EIGEN_DEPRECATED
-  }
+    const Derived& flagged() const
    { return derived(); }
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const DenseBase<OtherDerived>& other);
+    EIGEN_DEVICE_FUNC
    CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
    typedef Transpose<Derived> TransposeReturnType;
-  EIGEN_DEVICE_FUNC TransposeReturnType transpose();
+    EIGEN_DEVICE_FUNC
-  typedef Transpose<const Derived> ConstTransposeReturnType;
+    TransposeReturnType transpose();
-  EIGEN_DEVICE_FUNC const ConstTransposeReturnType transpose() const;
+    typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;
-  EIGEN_DEVICE_FUNC void transposeInPlace();
+    EIGEN_DEVICE_FUNC
    ConstTransposeReturnType transpose() const;
    EIGEN_DEVICE_FUNC
    void transposeInPlace();
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index rows, Index cols, const Scalar& value);
+    EIGEN_DEVICE_FUNC static const ConstantReturnType
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index size, const Scalar& value);
+    Constant(Index rows, Index cols, const Scalar& value);
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(const Scalar& value);
+    EIGEN_DEVICE_FUNC static const ConstantReturnType
    Constant(Index size, const Scalar& value);
    EIGEN_DEVICE_FUNC static const ConstantReturnType
    Constant(const Scalar& value);
-  EIGEN_DEPRECATED_WITH_REASON("The method may result in accuracy loss. Use .EqualSpaced() instead.")
+    EIGEN_DEVICE_FUNC static const SequentialLinSpacedReturnType
-  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, Index size, const Scalar& low,
+    LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
-                                                                           const Scalar& high);
+    EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
-  EIGEN_DEPRECATED_WITH_REASON("The method may result in accuracy loss. Use .EqualSpaced() instead.")
+    LinSpaced(Index size, const Scalar& low, const Scalar& high);
-  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, const Scalar& low,
+    EIGEN_DEVICE_FUNC static const SequentialLinSpacedReturnType
-                                                                           const Scalar& high);
+    LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
    EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
    LinSpaced(const Scalar& low, const Scalar& high);
-  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Index size, const Scalar& low,
+    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
-                                                                           const Scalar& high);
+    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
-  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(const Scalar& low, const Scalar& high);
+    NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
    NullaryExpr(Index size, const CustomNullaryOp& func);
    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
    NullaryExpr(const CustomNullaryOp& func);
-  EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(Index size, const Scalar& low,
+    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols);
-                                                                               const Scalar& step);
+    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size);
-  EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(const Scalar& low, const Scalar& step);
+    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero();
  template <typename CustomNullaryOp>
  EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index rows, Index cols,
                                                                                          const CustomNullaryOp& func);
  template <typename CustomNullaryOp>
  EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index size,
                                                                                          const CustomNullaryOp& func);
  template <typename CustomNullaryOp>
  EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(const CustomNullaryOp& func);
  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index rows, Index cols);
  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index size);
  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero();
    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);
    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);
    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();
@@ -341,49 +362,44 @@ class DenseBase
    EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value);
    EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
    EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high);
  EIGEN_DEVICE_FUNC Derived& setEqualSpaced(Index size, const Scalar& low, const Scalar& step);
  EIGEN_DEVICE_FUNC Derived& setEqualSpaced(const Scalar& low, const Scalar& step);
    EIGEN_DEVICE_FUNC Derived& setZero();
    EIGEN_DEVICE_FUNC Derived& setOnes();
    EIGEN_DEVICE_FUNC Derived& setRandom();
-  template <typename OtherDerived>
+    template<typename OtherDerived> EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC bool isApprox(const DenseBase<OtherDerived>& other,
+    bool isApprox(const DenseBase<OtherDerived>& other,
                  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
-  EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const RealScalar& other,
+    EIGEN_DEVICE_FUNC 
    bool isMuchSmallerThan(const RealScalar& other,
                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
-  template <typename OtherDerived>
+    template<typename OtherDerived> EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
+    bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
-  EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value,
+    EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
-                                            const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
  EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value,
                                    const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
-  EIGEN_DEVICE_FUNC inline bool hasNaN() const;
+    inline bool hasNaN() const;
-  EIGEN_DEVICE_FUNC inline bool allFinite() const;
+    inline bool allFinite() const;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const Scalar& other);
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-  template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
+    Derived& operator*=(const Scalar& other);
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const RealScalar& other);
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    Derived& operator/=(const Scalar& other);
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const Scalar& other);
+    typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;
  template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const RealScalar& other);
  typedef internal::add_const_on_value_type_t<typename internal::eval<Derived>::type> EvalReturnType;
    /** \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.
      * 
-   * \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page
+      * \warning Be carefull with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page \endlink.
   * \endlink.
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType eval() const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE EvalReturnType 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.
@@ -394,7 +410,9 @@ class DenseBase
      *
      */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(const DenseBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC
    void swap(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
      eigen_assert(rows()==other.rows() && cols()==other.cols());
      call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
@@ -404,7 +422,9 @@ class DenseBase
      *
      */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(PlainObjectBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC
    void swap(PlainObjectBase<OtherDerived>& other)
    {
      eigen_assert(rows()==other.rows() && cols()==other.cols());
      call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());
    }
@@ -412,11 +432,10 @@ class DenseBase
    EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const;
    EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
    EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess();
-  template <bool Enable>
+    template<bool Enable> EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline const std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&>
+    inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;
-  forceAlignedAccessIf() const;
+    template<bool Enable> EIGEN_DEVICE_FUNC
-  template <bool Enable>
+    inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
  EIGEN_DEVICE_FUNC inline std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> forceAlignedAccessIf();
    EIGEN_DEVICE_FUNC Scalar sum() const;
    EIGEN_DEVICE_FUNC Scalar mean() const;
@@ -424,54 +443,25 @@ class DenseBase
    EIGEN_DEVICE_FUNC Scalar prod() const;
  template <int NaNPropagation>
    EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const;
  template <int NaNPropagation>
    EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const;
-  // By default, the fastest version with undefined NaN propagation semantics is
+    template<typename IndexType> EIGEN_DEVICE_FUNC
-  // used.
+    typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
-  // TODO(rmlarsen): Replace with default template argument when we move to
+    template<typename IndexType> EIGEN_DEVICE_FUNC
-  // c++11 or beyond.
+    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
-  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff() const {
+    template<typename IndexType> EIGEN_DEVICE_FUNC
-    return minCoeff<PropagateFast>();
+    typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
-  }
+    template<typename IndexType> EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff() const {
+    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
    return maxCoeff<PropagateFast>();
  }
  template <int NaNPropagation, typename IndexType>
  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
  template <int NaNPropagation, typename IndexType>
  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
  template <int NaNPropagation, typename IndexType>
  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
  template <int NaNPropagation, typename IndexType>
  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
  // TODO(rmlarsen): Replace these methods with a default template argument.
  template <typename IndexType>
  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const {
    return minCoeff<PropagateFast>(row, col);
  }
  template <typename IndexType>
  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const {
    return maxCoeff<PropagateFast>(row, col);
  }
  template <typename IndexType>
  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const {
    return minCoeff<PropagateFast>(index);
  }
  template <typename IndexType>
  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const {
    return maxCoeff<PropagateFast>(index);
  }
    template<typename BinaryOp>
-  EIGEN_DEVICE_FUNC Scalar redux(const BinaryOp& func) const;
+    EIGEN_DEVICE_FUNC
    Scalar redux(const BinaryOp& func) const;
    template<typename Visitor>
-  EIGEN_DEVICE_FUNC void visit(Visitor& func) const;
+    EIGEN_DEVICE_FUNC
    void visit(Visitor& func) const;
    /** \returns a WithFormat proxy object allowing to print a matrix the with given
      * format \a fmt.
@@ -480,11 +470,17 @@ class DenseBase
      *
      * \sa class IOFormat, class WithFormat
      */
-  inline const WithFormat<Derived> format(const IOFormat& fmt) const { return WithFormat<Derived>(derived(), fmt); }
+    inline const WithFormat<Derived> format(const IOFormat& fmt) const
    {
      return WithFormat<Derived>(derived(), fmt);
    }
    /** \returns the unique coefficient of a 1x1 expression */
-  EIGEN_DEVICE_FUNC CoeffReturnType value() const {
+    EIGEN_DEVICE_FUNC
-    EIGEN_STATIC_ASSERT_SIZE_1x1(Derived) eigen_assert(this->rows() == 1 && this->cols() == 1);
+    CoeffReturnType value() const
    {
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      return derived().coeff(0,0);
    }
@@ -497,7 +493,7 @@ class DenseBase
    typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
    typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
-  /** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions
+    /** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
    *
    * Example: \include MatrixBase_rowwise.cpp
    * Output: \verbinclude MatrixBase_rowwise.out
@@ -505,17 +501,21 @@ class DenseBase
    * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
    */
    //Code moved here due to a CUDA compiler bug
-  EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const { return ConstRowwiseReturnType(derived()); }
+    EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const {
      return ConstRowwiseReturnType(derived());
    }
    EIGEN_DEVICE_FUNC RowwiseReturnType rowwise();
-  /** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions
+    /** \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, \ref TutorialReductionsVisitorsBroadcasting
    */
-  EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const { return ConstColwiseReturnType(derived()); }
+    EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const {
      return ConstColwiseReturnType(derived());
    }
    EIGEN_DEVICE_FUNC ColwiseReturnType colwise();
    typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>,PlainObject> RandomReturnType;
@@ -524,31 +524,23 @@ class DenseBase
    static const RandomReturnType Random();
    template<typename ThenDerived,typename ElseDerived>
-  inline EIGEN_DEVICE_FUNC
+    const Select<Derived,ThenDerived,ElseDerived>
-      CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+    select(const DenseBase<ThenDerived>& thenMatrix,
-                                                        typename DenseBase<ElseDerived>::Scalar, Scalar>,
+           const DenseBase<ElseDerived>& elseMatrix) const;
                     ThenDerived, ElseDerived, Derived>
      select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const;
    template<typename ThenDerived>
-  inline EIGEN_DEVICE_FUNC
+    inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
-      CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
+    select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;
                                                        typename DenseBase<ThenDerived>::Scalar, Scalar>,
                     ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType, Derived>
      select(const DenseBase<ThenDerived>& thenMatrix, const typename DenseBase<ThenDerived>::Scalar& elseScalar) const;
    template<typename ElseDerived>
-  inline EIGEN_DEVICE_FUNC
+    inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
-      CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
+    select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
                                                        typename DenseBase<ElseDerived>::Scalar, Scalar>,
                     typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived, Derived>
      select(const typename DenseBase<ElseDerived>::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
-  template <int p>
+    template<int p> RealScalar lpNorm() const;
  RealScalar lpNorm() const;
    template<int RowFactor, int ColFactor>
-  EIGEN_DEVICE_FUNC const Replicate<Derived, RowFactor, ColFactor> replicate() const;
+    EIGEN_DEVICE_FUNC
    const Replicate<Derived,RowFactor,ColFactor> replicate() const;
    /**
    * \return an expression of the replication of \c *this
    *
@@ -558,7 +550,9 @@ class DenseBase
    * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
    */
    //Code moved here due to a CUDA compiler bug
-  EIGEN_DEVICE_FUNC const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const {
+    EIGEN_DEVICE_FUNC
    const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const
    {
      return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);
    }
@@ -567,107 +561,52 @@ class DenseBase
    EIGEN_DEVICE_FUNC ReverseReturnType reverse();
    /** This is the const version of reverse(). */
    //Code moved here due to a CUDA compiler bug
-  EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const { return ConstReverseReturnType(derived()); }
+    EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const
    {
      return ConstReverseReturnType(derived());
    }
    EIGEN_DEVICE_FUNC void reverseInPlace();
 #ifdef EIGEN_PARSED_BY_DOXYGEN
  /** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
   * iterator type as returned by the begin() and end() methods.
   */
  typedef random_access_iterator_type iterator;
  /** This is the const version of iterator (aka read-only) */
  typedef random_access_iterator_type const_iterator;
 #else
  typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit,
                             internal::pointer_based_stl_iterator<Derived>,
                             internal::generic_randaccess_stl_iterator<Derived> >
      iterator_type;
  typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit,
                             internal::pointer_based_stl_iterator<const Derived>,
                             internal::generic_randaccess_stl_iterator<const Derived> >
      const_iterator_type;
  // Stl-style iterators are supported only for vectors.
  typedef std::conditional_t<IsVectorAtCompileTime, iterator_type, void> iterator;
  typedef std::conditional_t<IsVectorAtCompileTime, const_iterator_type, void> const_iterator;
 #endif
  inline iterator begin();
  inline const_iterator begin() const;
  inline const_iterator cbegin() const;
  inline iterator end();
  inline const_iterator end() const;
  inline const_iterator cend() const;
  using RealViewReturnType = std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<Derived>, Derived&>;
  using ConstRealViewReturnType =
      std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<const Derived>, const Derived&>;
  EIGEN_DEVICE_FUNC RealViewReturnType realView();
  EIGEN_DEVICE_FUNC ConstRealViewReturnType realView() const;
 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
 #define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
 #define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
-#define EIGEN_DOC_UNARY_ADDONS(X, Y)
+#   include "../plugins/BlockMethods.h"
 #include "../plugins/CommonCwiseUnaryOps.inc"
 #include "../plugins/BlockMethods.inc"
 #include "../plugins/IndexedViewMethods.inc"
 #include "../plugins/ReshapedMethods.inc"
 #   ifdef EIGEN_DENSEBASE_PLUGIN
 #     include EIGEN_DENSEBASE_PLUGIN
 #   endif
 #undef EIGEN_CURRENT_STORAGE_BASE_CLASS
 #undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
 #undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
 #undef EIGEN_DOC_UNARY_ADDONS
    // disable the use of evalTo for dense objects with a nice compilation error
    template<typename Dest>
-  EIGEN_DEVICE_FUNC inline void evalTo(Dest&) const {
+    EIGEN_DEVICE_FUNC
-    EIGEN_STATIC_ASSERT((internal::is_same<Dest, void>::value),
+    inline void evalTo(Dest& ) const
-                        THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
+    {
      EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
    }
  protected:
    EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase)
    /** Default constructor. Do nothing. */
-#ifdef EIGEN_INTERNAL_DEBUGGING
+    EIGEN_DEVICE_FUNC DenseBase()
-  EIGEN_DEVICE_FUNC constexpr DenseBase() {
+    {
      /* Just checks for self-consistency of the flags.
       * Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down
       */
-    EIGEN_STATIC_ASSERT(
+#ifdef EIGEN_INTERNAL_DEBUGGING
-        (internal::check_implication(MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1, int(IsRowMajor)) &&
+      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
-         internal::check_implication(MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1, int(!IsRowMajor))),
+                        && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
                          INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
  }
 #else
  EIGEN_DEVICE_FUNC constexpr DenseBase() = default;
 #endif
    }
  private:
    EIGEN_DEVICE_FUNC explicit DenseBase(int);
    EIGEN_DEVICE_FUNC DenseBase(int,int);
-  template <typename OtherDerived>
+    template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
  EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
 };
 /** Free-function swap.
 */
 template <typename DerivedA, typename DerivedB>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    // Use forwarding references to capture all combinations of cv-qualified l+r-value cases.
    std::enable_if_t<std::is_base_of<DenseBase<std::decay_t<DerivedA>>, std::decay_t<DerivedA>>::value &&
                         std::is_base_of<DenseBase<std::decay_t<DerivedB>>, std::decay_t<DerivedB>>::value,
                     void>
    swap(DerivedA&& a, DerivedB&& b) {
  a.swap(b);
 }
 } // end namespace Eigen
 #endif // EIGEN_DENSEBASE_H
--- a/Eigen/src/Core/DenseCoeffsBase.h
+++ b/Eigen/src/Core/DenseCoeffsBase.h
@@ -10,23 +10,19 @@
 #ifndef EIGEN_DENSECOEFFSBASE_H
 #define EIGEN_DENSECOEFFSBASE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
-template <typename T>
+template<typename T> struct add_const_on_value_type_if_arithmetic
-struct add_const_on_value_type_if_arithmetic {
+{
-  typedef std::conditional_t<is_arithmetic<T>::value, T, add_const_on_value_type_t<T>> type;
+  typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
 };
-}  // namespace internal
+}
 /** \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
 * \note #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.
@@ -35,7 +31,8 @@ struct add_const_on_value_type_if_arithmetic {
  *     \ref TopicClassHierarchy
  */
 template<typename Derived>
-class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
+class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
 {
  public:
    typedef typename internal::traits<Derived>::StorageKind StorageKind;
    typedef typename internal::traits<Derived>::Scalar Scalar;
@@ -45,36 +42,36 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    // - 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 DirectAccessBit means exactly that the underlying data of coefficients can be directly accessed as a plain
+    // - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
  // strided array, which means exactly that the underlying data of coefficients does exist in memory, which means
  // exactly that the coefficients is const-referencable, which means exactly that we can have coeff() return a const
  // reference. For example, Map<const Matrix> have DirectAccessBit but not LvalueBit, so that Map<const Matrix>.coeff()
  // does points to a const Scalar& which exists in memory, while does not allow coeffRef() as it would not provide a
  // lvalue. Notice that DirectAccessBit and LvalueBit are mutually orthogonal.
  // - The is_arithmetic 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 std::conditional_t<bool(internal::traits<Derived>::Flags&(LvalueBit | DirectAccessBit)), const Scalar&,
+    typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
-                             std::conditional_t<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>>
+                         const Scalar&,
-      CoeffReturnType;
+                         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
+    typedef typename internal::add_const_on_value_type_if_arithmetic<
-      PacketReturnType;
+                         typename internal::packet_traits<Scalar>::type
                     >::type PacketReturnType;
    typedef EigenBase<Derived> Base;
  using Base::cols;
  using Base::derived;
    using Base::rows;
    using Base::cols;
    using Base::size;
    using Base::derived;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const {
+    EIGEN_DEVICE_FUNC
    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_DEVICE_FUNC EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const {
+    EIGEN_DEVICE_FUNC
    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
@@ -95,21 +92,30 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      *
      * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index row, Index col) const {
+    EIGEN_DEVICE_FUNC
-    eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+    EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
    {
      eigen_internal_assert(row >= 0 && row < rows()
                         && col >= 0 && col < cols());
      return internal::evaluator<Derived>(derived()).coeff(row,col);
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeffByOuterInner(Index outer, Index inner) const {
+    EIGEN_DEVICE_FUNC
-    return coeff(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
+    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_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index row, Index col) const {
+    EIGEN_DEVICE_FUNC
-    eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+    EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
    {
      eigen_assert(row >= 0 && row < rows()
          && col >= 0 && col < cols());
      return coeff(row, col);
    }
@@ -128,13 +134,17 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index index) const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    coeff(Index index) const
    {
      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
      eigen_internal_assert(index >= 0 && index < size());
      return internal::evaluator<Derived>(derived()).coeff(index);
    }
    /** \returns the coefficient at given index.
      *
      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
@@ -143,7 +153,10 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      * z() const, w() const
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator[](Index index) const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    operator[](Index index) const
    {
      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
      eigen_assert(index >= 0 && index < size());
@@ -160,32 +173,46 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      * z() const, w() const
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index index) const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    operator()(Index index) const
    {
      eigen_assert(index >= 0 && index < size());
      return coeff(index);
    }
    /** equivalent to operator[](0).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType x() const { return (*this)[0]; }
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    x() const { return (*this)[0]; }
    /** equivalent to operator[](1).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType y() const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    y() const
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
      return (*this)[1];
    }
    /** equivalent to operator[](2).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType z() const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    z() const
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
      return (*this)[2];
    }
    /** equivalent to operator[](3).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType w() const {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE CoeffReturnType
    w() const
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
      return (*this)[3];
    }
@@ -201,16 +228,20 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      */
    template<int LoadMode>
-  EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const {
+    EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
    {
      typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
      eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
      return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(row,col);
    }
    /** \internal */
    template<int LoadMode>
-  EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const {
+    EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
-    return packet<LoadMode>(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
+    {
      return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
                              colIndexByOuterInner(outer, inner));
    }
    /** \internal
@@ -224,7 +255,8 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
      */
    template<int LoadMode>
-  EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
+    EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
    {
      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
      typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
@@ -256,8 +288,7 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
 /** \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
 * \note #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
@@ -266,8 +297,10 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
  * \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
  */
 template<typename Derived>
-class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors> {
+class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
 {
  public:
    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
    typedef typename internal::traits<Derived>::StorageKind StorageKind;
@@ -276,18 +309,18 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    typedef typename NumTraits<Scalar>::Real RealScalar;
    using Base::coeff;
-  using Base::colIndexByOuterInner;
+    using Base::rows;
    using Base::cols;
    using Base::size;
    using Base::derived;
    using Base::rowIndexByOuterInner;
-  using Base::rows;
+    using Base::colIndexByOuterInner;
  using Base::size;
    using Base::operator[];
    using Base::operator();
  using Base::w;
    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.
@@ -303,13 +336,20 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
      *
      * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index row, Index col) {
+    EIGEN_DEVICE_FUNC
-    eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+    EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
    {
      eigen_internal_assert(row >= 0 && row < rows()
                         && col >= 0 && col < cols());
      return internal::evaluator<Derived>(derived()).coeffRef(row,col);
    }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRefByOuterInner(Index outer, Index inner) {
+    EIGEN_DEVICE_FUNC
-    return coeffRef(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
+    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.
@@ -317,11 +357,16 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
      * \sa operator[](Index)
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index row, Index col) {
+    EIGEN_DEVICE_FUNC
-    eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+    EIGEN_STRONG_INLINE Scalar&
    operator()(Index row, Index col)
    {
      eigen_assert(row >= 0 && row < rows()
          && col >= 0 && col < cols());
      return coeffRef(row, col);
    }
    /** Short version: don't use this function, use
      * \link operator[](Index) \endlink instead.
      *
@@ -337,7 +382,10 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
      * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index index) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    coeffRef(Index index)
    {
      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
      eigen_internal_assert(index >= 0 && index < size());
@@ -351,7 +399,10 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
      * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator[](Index index) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    operator[](Index index)
    {
      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
      eigen_assert(index >= 0 && index < size());
@@ -367,32 +418,46 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
      * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
      */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index index) {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    operator()(Index index)
    {
      eigen_assert(index >= 0 && index < size());
      return coeffRef(index);
    }
    /** equivalent to operator[](0).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& x() { return (*this)[0]; }
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    x() { return (*this)[0]; }
    /** equivalent to operator[](1).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& y() {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    y()
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
      return (*this)[1];
    }
    /** equivalent to operator[](2).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& z() {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    z()
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
      return (*this)[2];
    }
    /** equivalent to operator[](3).  */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& w() {
+    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE Scalar&
    w()
    {
      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
      return (*this)[3];
    }
@@ -401,8 +466,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
 /** \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
 * \note #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
@@ -411,51 +475,71 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
  * \sa \blank \ref TopicClassHierarchy
  */
 template<typename Derived>
-class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors> {
+class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
 {
  public:
    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
    typedef typename internal::traits<Derived>::Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
  using Base::cols;
  using Base::derived;
    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()
      */
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const { return derived().innerStride(); }
+    EIGEN_DEVICE_FUNC
    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()
      */
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const { return derived().outerStride(); }
+    EIGEN_DEVICE_FUNC
    inline Index outerStride() const
    {
      return derived().outerStride();
    }
    // FIXME shall we remove it ?
-  constexpr Index stride() const { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
+    inline Index stride() const
    {
      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
    }
    /** \returns the pointer increment between two consecutive rows.
      *
      * \sa innerStride(), outerStride(), colStride()
      */
-  EIGEN_DEVICE_FUNC constexpr Index rowStride() const { return Derived::IsRowMajor ? outerStride() : innerStride(); }
+    EIGEN_DEVICE_FUNC
    inline Index rowStride() const
    {
      return Derived::IsRowMajor ? outerStride() : innerStride();
    }
    /** \returns the pointer increment between two consecutive columns.
      *
      * \sa innerStride(), outerStride(), rowStride()
      */
-  EIGEN_DEVICE_FUNC constexpr Index colStride() const { return Derived::IsRowMajor ? innerStride() : outerStride(); }
+    EIGEN_DEVICE_FUNC
    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
 * \note #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
@@ -464,38 +548,54 @@ class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived
  * \sa \blank \ref TopicClassHierarchy
  */
 template<typename Derived>
-class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<Derived, WriteAccessors> {
+class DenseCoeffsBase<Derived, DirectWriteAccessors>
  : public DenseCoeffsBase<Derived, WriteAccessors>
 {
  public:
    typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
    typedef typename internal::traits<Derived>::Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
  using Base::cols;
  using Base::derived;
    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()
      */
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return derived().innerStride(); }
+    EIGEN_DEVICE_FUNC
    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()
      */
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return derived().outerStride(); }
+    EIGEN_DEVICE_FUNC
    inline Index outerStride() const
    {
      return derived().outerStride();
    }
    // FIXME shall we remove it ?
-  constexpr Index stride() const noexcept { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
+    inline Index stride() const
    {
      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
    }
    /** \returns the pointer increment between two consecutive rows.
      *
      * \sa innerStride(), outerStride(), colStride()
      */
-  EIGEN_DEVICE_FUNC constexpr Index rowStride() const noexcept {
+    EIGEN_DEVICE_FUNC
    inline Index rowStride() const
    {
      return Derived::IsRowMajor ? outerStride() : innerStride();
    }
@@ -503,7 +603,9 @@ class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<De
      *
      * \sa innerStride(), outerStride(), rowStride()
      */
-  EIGEN_DEVICE_FUNC constexpr Index colStride() const noexcept {
+    EIGEN_DEVICE_FUNC
    inline Index colStride() const
    {
      return Derived::IsRowMajor ? innerStride() : outerStride();
    }
 };
@@ -511,17 +613,22 @@ class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<De
 namespace internal {
 template<int Alignment, typename Derived, bool JustReturnZero>
-struct first_aligned_impl {
+struct first_aligned_impl
-  static constexpr Index run(const Derived&) noexcept { return 0; }
+{
  static inline Index run(const Derived&)
  { return 0; }
 };
 template<int Alignment, typename Derived>
-struct first_aligned_impl<Alignment, Derived, false> {
+struct first_aligned_impl<Alignment, Derived, false>
-  static inline Index run(const Derived& m) { return internal::first_aligned<Alignment>(m.data(), m.size()); }
+{
  static inline Index run(const Derived& m)
  {
    return internal::first_aligned<Alignment>(m.data(), m.size());
  }
 };
-/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect
+/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization.
 * to \a Alignment for vectorization.
  *
  * \tparam Alignment requested alignment in Bytes.
  *
@@ -529,35 +636,41 @@ struct first_aligned_impl<Alignment, Derived, false> {
  * documentation.
  */
 template<int Alignment, typename Derived>
-static inline Index first_aligned(const DenseBase<Derived>& m) {
+static inline Index first_aligned(const DenseBase<Derived>& m)
 {
  enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };
  return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());
 }
 template<typename Derived>
-static inline Index first_default_aligned(const DenseBase<Derived>& m) {
+static inline Index first_default_aligned(const DenseBase<Derived>& m)
 {
  typedef typename Derived::Scalar Scalar;
  typedef typename packet_traits<Scalar>::type DefaultPacketType;
  return internal::first_aligned<int(unpacket_traits<DefaultPacketType>::alignment),Derived>(m);
 }
 template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
-struct inner_stride_at_compile_time {
+struct inner_stride_at_compile_time
 {
  enum { ret = traits<Derived>::InnerStrideAtCompileTime };
 };
 template<typename Derived>
-struct inner_stride_at_compile_time<Derived, false> {
+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 {
+struct outer_stride_at_compile_time
 {
  enum { ret = traits<Derived>::OuterStrideAtCompileTime };
 };
 template<typename Derived>
-struct outer_stride_at_compile_time<Derived, false> {
+struct outer_stride_at_compile_time<Derived, false>
 {
  enum { ret = 0 };
 };
--- a/Eigen/src/Core/DenseStorage.h
+++ b/Eigen/src/Core/DenseStorage.h
--- a/Eigen/src/Core/DeviceWrapper.h
+++ b/Eigen/src/Core/DeviceWrapper.h
@@ -1,153 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2023 Charlie Schlosser <cs.schlosser@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_DEVICEWRAPPER_H
 #define EIGEN_DEVICEWRAPPER_H
 namespace Eigen {
 template <typename Derived, typename Device>
 struct DeviceWrapper {
  using Base = EigenBase<internal::remove_all_t<Derived>>;
  using Scalar = typename Derived::Scalar;
  EIGEN_DEVICE_FUNC DeviceWrapper(Base& xpr, Device& device) : m_xpr(xpr.derived()), m_device(device) {}
  EIGEN_DEVICE_FUNC DeviceWrapper(const Base& xpr, Device& device) : m_xpr(xpr.derived()), m_device(device) {}
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived>& other) {
    using AssignOp = internal::assign_op<Scalar, typename OtherDerived::Scalar>;
    internal::call_assignment(*this, other.derived(), AssignOp());
    return m_xpr;
  }
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const EigenBase<OtherDerived>& other) {
    using AddAssignOp = internal::add_assign_op<Scalar, typename OtherDerived::Scalar>;
    internal::call_assignment(*this, other.derived(), AddAssignOp());
    return m_xpr;
  }
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const EigenBase<OtherDerived>& other) {
    using SubAssignOp = internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>;
    internal::call_assignment(*this, other.derived(), SubAssignOp());
    return m_xpr;
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& derived() { return m_xpr; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Device& device() { return m_device; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NoAlias<DeviceWrapper, EigenBase> noalias() {
    return NoAlias<DeviceWrapper, EigenBase>(*this);
  }
  Derived& m_xpr;
  Device& m_device;
 };
 namespace internal {
 // this is where we differentiate between lazy assignment and specialized kernels (e.g. matrix products)
 template <typename DstXprType, typename SrcXprType, typename Functor, typename Device,
          typename Kind = typename AssignmentKind<typename evaluator_traits<DstXprType>::Shape,
                                                  typename evaluator_traits<SrcXprType>::Shape>::Kind,
          typename EnableIf = void>
 struct AssignmentWithDevice;
 // unless otherwise specified, use the default product implementation
 template <typename DstXprType, typename Lhs, typename Rhs, int Options, typename Functor, typename Device,
          typename Weak>
 struct AssignmentWithDevice<DstXprType, Product<Lhs, Rhs, Options>, Functor, Device, Dense2Dense, Weak> {
  using SrcXprType = Product<Lhs, Rhs, Options>;
  using Base = Assignment<DstXprType, SrcXprType, Functor>;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(DstXprType& dst, const SrcXprType& src, const Functor& func,
                                                        Device&) {
    Base::run(dst, src, func);
  }
 };
 // specialization for coeffcient-wise assignment
 template <typename DstXprType, typename SrcXprType, typename Functor, typename Device, typename Weak>
 struct AssignmentWithDevice<DstXprType, SrcXprType, Functor, Device, Dense2Dense, Weak> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(DstXprType& dst, const SrcXprType& src, const Functor& func,
                                                        Device& device) {
 #ifndef EIGEN_NO_DEBUG
    internal::check_for_aliasing(dst, src);
 #endif
    call_dense_assignment_loop(dst, src, func, device);
  }
 };
 // this allows us to use the default evaluation scheme if it is not specialized for the device
 template <typename Kernel, typename Device, int Traversal = Kernel::AssignmentTraits::Traversal,
          int Unrolling = Kernel::AssignmentTraits::Unrolling>
 struct dense_assignment_loop_with_device {
  using Base = dense_assignment_loop<Kernel, Traversal, Unrolling>;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Kernel& kernel, Device&) { Base::run(kernel); }
 };
 // entry point for a generic expression with device
 template <typename Dst, typename Src, typename Func, typename Device>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_assignment_no_alias(DeviceWrapper<Dst, Device> dst,
                                                                              const Src& src, const Func& func) {
  enum {
    NeedToTranspose = ((int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1) ||
                       (int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1)) &&
                      int(Dst::SizeAtCompileTime) != 1
  };
  using ActualDstTypeCleaned = std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst>;
  using ActualDstType = std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst&>;
  ActualDstType actualDst(dst.derived());
  // TODO check whether this is the right place to perform these checks:
  EIGEN_STATIC_ASSERT_LVALUE(Dst)
  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned, Src)
  EIGEN_CHECK_BINARY_COMPATIBILIY(Func, typename ActualDstTypeCleaned::Scalar, typename Src::Scalar);
  // this provides a mechanism for specializing simple assignments, matrix products, etc
  AssignmentWithDevice<ActualDstTypeCleaned, Src, Func, Device>::run(actualDst, src, func, dst.device());
 }
 // copy and pasted from AssignEvaluator except forward device to kernel
 template <typename DstXprType, typename SrcXprType, typename Functor, typename Device>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src,
                                                                                const Functor& func, Device& device) {
  using DstEvaluatorType = evaluator<DstXprType>;
  using SrcEvaluatorType = evaluator<SrcXprType>;
  SrcEvaluatorType srcEvaluator(src);
  // NOTE To properly handle A = (A*A.transpose())/s with A rectangular,
  // we need to resize the destination after the source evaluator has been created.
  resize_if_allowed(dst, src, func);
  DstEvaluatorType dstEvaluator(dst);
  using Kernel = generic_dense_assignment_kernel<DstEvaluatorType, SrcEvaluatorType, Functor>;
  Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
  dense_assignment_loop_with_device<Kernel, Device>::run(kernel, device);
 }
 }  // namespace internal
 template <typename Derived>
 template <typename Device>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<Derived, Device> EigenBase<Derived>::device(Device& device) {
  return DeviceWrapper<Derived, Device>(derived(), device);
 }
 template <typename Derived>
 template <typename Device>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<const Derived, Device> EigenBase<Derived>::device(
    Device& device) const {
  return DeviceWrapper<const Derived, Device>(derived(), device);
 }
 }  // namespace Eigen
 #endif
--- a/Eigen/src/Core/Diagonal.h
+++ b/Eigen/src/Core/Diagonal.h
@@ -11,9 +11,6 @@
 #ifndef EIGEN_DIAGONAL_H
 #define EIGEN_DIAGONAL_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 /** \class Diagonal
@@ -21,8 +18,8 @@ namespace Eigen {
  *
  * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
  *
- * \tparam MatrixType the type of the object in which we are taking a sub/main/super diagonal
+  * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
- * \tparam DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main 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 DynamicIndex so the index can be set at runtime.
  *
@@ -37,94 +34,132 @@ namespace Eigen {
 namespace internal {
 template<typename MatrixType, int DiagIndex>
-struct traits<Diagonal<MatrixType, DiagIndex> > : traits<MatrixType> {
+struct traits<Diagonal<MatrixType,DiagIndex> >
 : traits<MatrixType>
 {
  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
-  typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
  typedef typename MatrixType::StorageKind StorageKind;
  enum {
-    RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic)
+    RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
-                            ? Dynamic
+                      : (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
-                            : (plain_enum_min(MatrixType::RowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
+                                              MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
                                              MatrixType::ColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
    ColsAtCompileTime = 1,
-    MaxRowsAtCompileTime =
+    MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
-        int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
+                         : DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
-        : DiagIndex == DynamicIndex
+                                                                              MatrixType::MaxColsAtCompileTime)
-            ? min_size_prefer_fixed(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime)
+                         : (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
-            : (plain_enum_min(MatrixType::MaxRowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
+                                                 MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
                              MatrixType::MaxColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
    MaxColsAtCompileTime = 1,
    MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
-    Flags = (unsigned int)MatrixTypeNested_::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) &
+    Flags = (unsigned int)_MatrixTypeNested::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions
            ~RowMajorBit,  // FIXME DirectAccessBit should not be handled by expressions
    MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
    InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
    OuterStrideAtCompileTime = 0
  };
 };
-}  // namespace internal
+}
-template <typename MatrixType, int DiagIndex_>
+template<typename MatrixType, int _DiagIndex> class Diagonal
-class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_> >::type {
+   : public internal::dense_xpr_base< Diagonal<MatrixType,_DiagIndex> >::type
 {
  public:
-  enum { DiagIndex = DiagIndex_ };
+
    enum { DiagIndex = _DiagIndex };
    typedef typename internal::dense_xpr_base<Diagonal>::type Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
-  EIGEN_DEVICE_FUNC explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex)
+    EIGEN_DEVICE_FUNC
-      : m_matrix(matrix), m_index(a_index) {
+    explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index)
    {
      eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() );
    }
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
-  EIGEN_DEVICE_FUNC inline Index rows() const {
+    EIGEN_DEVICE_FUNC
    inline Index rows() const
    {
      return m_index.value()<0 ? numext::mini<Index>(m_matrix.cols(),m_matrix.rows()+m_index.value())
                               : numext::mini<Index>(m_matrix.rows(),m_matrix.cols()-m_index.value());
    }
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return 1; }
+    EIGEN_DEVICE_FUNC
    inline Index cols() const { return 1; }
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.outerStride() + 1; }
+    EIGEN_DEVICE_FUNC
    inline Index innerStride() const
    {
      return m_matrix.outerStride() + 1;
    }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 0; }
+    EIGEN_DEVICE_FUNC
    inline Index outerStride() const
    {
      return 0;
    }
-  typedef std::conditional_t<internal::is_lvalue<MatrixType>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;
+    typedef typename internal::conditional<
                       internal::is_lvalue<MatrixType>::value,
                       Scalar,
                       const Scalar
                     >::type ScalarWithConstIfNotLvalue;
-  EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
+    inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
    EIGEN_DEVICE_FUNC
    inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index) {
+    EIGEN_DEVICE_FUNC
    inline Scalar& coeffRef(Index row, Index)
    {
      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index row, Index) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index row, Index) const
    {
      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index row, Index) const {
+    EIGEN_DEVICE_FUNC
    inline CoeffReturnType coeff(Index row, Index) const
    {
      return m_matrix.coeff(row+rowOffset(), row+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index idx) {
+    EIGEN_DEVICE_FUNC
    inline Scalar& coeffRef(Index idx)
    {
      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index idx) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index idx) const
    {
      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index idx) const {
+    EIGEN_DEVICE_FUNC
    inline CoeffReturnType coeff(Index idx) const
    {
      return m_matrix.coeff(idx+rowOffset(), idx+colOffset());
    }
-  EIGEN_DEVICE_FUNC inline const internal::remove_all_t<typename MatrixType::Nested>& nestedExpression() const {
+    EIGEN_DEVICE_FUNC
    inline const typename internal::remove_all<typename MatrixType::Nested>::type&
    nestedExpression() const
    {
      return m_matrix;
    }
-  EIGEN_DEVICE_FUNC inline Index index() const { return m_index.value(); }
+    EIGEN_DEVICE_FUNC
    inline Index index() const
    {
      return m_index.value();
    }
  protected:
    typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
@@ -132,20 +167,15 @@ class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_
  private:
    // some compilers may fail to optimize std::max etc in case of compile-time constants...
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index absDiagIndex() const noexcept {
+    EIGEN_DEVICE_FUNC
-    return m_index.value() > 0 ? m_index.value() : -m_index.value();
+    EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
-  }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rowOffset() const noexcept {
+    EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
-    return m_index.value() > 0 ? 0 : -m_index.value();
+    EIGEN_DEVICE_FUNC
-  }
+    EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index colOffset() const noexcept {
    return m_index.value() > 0 ? m_index.value() : 0;
  }
    // trigger a compile-time error if someone try to call packet
-  template <int LoadMode>
+    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
-  typename MatrixType::PacketReturnType packet(Index) const;
+    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
  template <int LoadMode>
  typename MatrixType::PacketReturnType packet(Index, Index) const;
 };
 /** \returns an expression of the main diagonal of the matrix \c *this
@@ -157,14 +187,17 @@ class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_
  *
  * \sa class Diagonal */
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalReturnType MatrixBase<Derived>::diagonal() {
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalReturnType
 MatrixBase<Derived>::diagonal()
 {
  return DiagonalReturnType(derived());
 }
 /** This is the const version of diagonal(). */
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::ConstDiagonalReturnType MatrixBase<Derived>::diagonal()
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::ConstDiagonalReturnType
-    const {
+MatrixBase<Derived>::diagonal() const
 {
  return ConstDiagonalReturnType(derived());
 }
@@ -180,14 +213,18 @@ EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::ConstDiagonalReturn
  *
  * \sa MatrixBase::diagonal(), class Diagonal */
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline Diagonal<Derived, DynamicIndex> MatrixBase<Derived>::diagonal(Index index) {
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType
-  return Diagonal<Derived, DynamicIndex>(derived(), index);
+MatrixBase<Derived>::diagonal(Index index)
 {
  return DiagonalDynamicIndexReturnType(derived(), index);
 }
 /** This is the const version of diagonal(Index). */
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, DynamicIndex> MatrixBase<Derived>::diagonal(Index index) const {
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType
-  return Diagonal<const Derived, DynamicIndex>(derived(), index);
+MatrixBase<Derived>::diagonal(Index index) const
 {
  return ConstDiagonalDynamicIndexReturnType(derived(), index);
 }
 /** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
@@ -203,15 +240,19 @@ EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, DynamicIndex> MatrixBase<
  * \sa MatrixBase::diagonal(), class Diagonal */
 template<typename Derived>
 template<int Index_>
-EIGEN_DEVICE_FUNC inline Diagonal<Derived, Index_> MatrixBase<Derived>::diagonal() {
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index_>::Type
-  return Diagonal<Derived, Index_>(derived());
+MatrixBase<Derived>::diagonal()
 {
  return typename DiagonalIndexReturnType<Index_>::Type(derived());
 }
 /** This is the const version of diagonal<int>(). */
 template<typename Derived>
 template<int Index_>
-EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, Index_> MatrixBase<Derived>::diagonal() const {
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index_>::Type
-  return Diagonal<const Derived, Index_>(derived());
+MatrixBase<Derived>::diagonal() const
 {
  return typename ConstDiagonalIndexReturnType<Index_>::Type(derived());
 }
 } // end namespace Eigen
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -11,26 +11,12 @@
 #ifndef EIGEN_DIAGONALMATRIX_H
 #define EIGEN_DIAGONALMATRIX_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
-/** \class DiagonalBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
 * \ingroup Core_Module
 *
 * \brief Base class for diagonal matrices and expressions
 *
 * This is the base class that is inherited by diagonal matrix and related expression
 * types, which internally use a vector for storing the diagonal entries. Diagonal
 * types always represent square matrices.
 *
 * \tparam Derived is the derived type, a DiagonalMatrix or DiagonalWrapper.
 *
 * \sa class DiagonalMatrix, class DiagonalWrapper
 */
 template<typename Derived>
-class DiagonalBase : public EigenBase<Derived> {
+class DiagonalBase : public EigenBase<Derived>
 {
  public:
    typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
    typedef typename DiagonalVectorType::Scalar Scalar;
@@ -47,185 +33,131 @@ class DiagonalBase : public EigenBase<Derived> {
      Flags = NoPreferredStorageOrderBit
    };
-  typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
+    typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
      DenseMatrixType;
    typedef DenseMatrixType DenseType;
-  typedef DiagonalMatrix<Scalar, DiagonalVectorType::SizeAtCompileTime, DiagonalVectorType::MaxSizeAtCompileTime>
+    typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
      PlainObject;
-  /** \returns a reference to the derived object. */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
-  /** \returns a const reference to the derived object. */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
+    inline Derived& derived() { return *static_cast<Derived*>(this); }
-  /**
+    EIGEN_DEVICE_FUNC
-   * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
+    DenseMatrixType toDenseMatrix() const { return derived(); }
   * not an expression.
   * \returns A dense matrix, with its diagonal entries set from the the derived object. */
  EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix() const { return derived(); }
-  /** \returns a reference to the derived object's vector of diagonal coefficients. */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
+    inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
-  /** \returns a const reference to the derived object's vector of diagonal coefficients. */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
+    inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
-  /** \returns the value of the coefficient as if \c *this was a dense matrix. */
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC inline Scalar coeff(Index row, Index col) const {
+    inline Index rows() const { return diagonal().size(); }
-    eigen_assert(row >= 0 && col >= 0 && row < rows() && col <= cols());
+    EIGEN_DEVICE_FUNC
-    return row == col ? diagonal().coeff(row) : Scalar(0);
+    inline Index cols() const { return diagonal().size(); }
  }
  /** \returns the number of rows. */
  EIGEN_DEVICE_FUNC constexpr Index rows() const { return diagonal().size(); }
  /** \returns the number of columns. */
  EIGEN_DEVICE_FUNC constexpr Index cols() const { return diagonal().size(); }
  /** \returns the diagonal matrix product of \c *this by the dense matrix, \a matrix */
    template<typename MatrixDerived>
-  EIGEN_DEVICE_FUNC const Product<Derived, MatrixDerived, LazyProduct> operator*(
+    EIGEN_DEVICE_FUNC
-      const MatrixBase<MatrixDerived>& matrix) const {
+    const Product<Derived,MatrixDerived,LazyProduct>
    operator*(const MatrixBase<MatrixDerived> &matrix) const
    {
      return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
    }
-  template <typename OtherDerived>
+    typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;
-  using DiagonalProductReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+    EIGEN_DEVICE_FUNC
-      DiagonalVectorType, typename OtherDerived::DiagonalVectorType, product)>;
+    inline const InverseReturnType
-
+    inverse() const
-  /** \returns the diagonal matrix product of \c *this by the diagonal matrix \a other */
+    {
-  template <typename OtherDerived>
+      return InverseReturnType(diagonal().cwiseInverse());
  EIGEN_DEVICE_FUNC const DiagonalProductReturnType<OtherDerived> operator*(
      const DiagonalBase<OtherDerived>& other) const {
    return diagonal().cwiseProduct(other.diagonal()).asDiagonal();
    }
-  using DiagonalInverseReturnType =
+    EIGEN_DEVICE_FUNC
-      DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType>>;
+    inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
-
+    operator*(const Scalar& scalar) const
-  /** \returns the inverse \c *this. Computed as the coefficient-wise inverse of the diagonal. */
+    {
-  EIGEN_DEVICE_FUNC inline const DiagonalInverseReturnType inverse() const {
+      return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
    return diagonal().cwiseInverse().asDiagonal();
    }
-
+    EIGEN_DEVICE_FUNC
-  using DiagonalScaleReturnType =
+    friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
-      DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType, Scalar, product)>;
+    operator*(const Scalar& scalar, const DiagonalBase& other)
-
+    {
-  /** \returns the product of \c *this by the scalar \a scalar */
+      return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
  EIGEN_DEVICE_FUNC inline const DiagonalScaleReturnType operator*(const Scalar& scalar) const {
    return (diagonal() * scalar).asDiagonal();
  }
  using ScaleDiagonalReturnType =
      DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, DiagonalVectorType, product)>;
  /** \returns the product of a scalar and the diagonal matrix \a other */
  EIGEN_DEVICE_FUNC friend inline const ScaleDiagonalReturnType operator*(const Scalar& scalar,
                                                                          const DiagonalBase& other) {
    return (scalar * other.diagonal()).asDiagonal();
  }
  template <typename OtherDerived>
  using DiagonalSumReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
      DiagonalVectorType, typename OtherDerived::DiagonalVectorType, sum)>;
  /** \returns the sum of \c *this and the diagonal matrix \a other */
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline const DiagonalSumReturnType<OtherDerived> operator+(
      const DiagonalBase<OtherDerived>& other) const {
    return (diagonal() + other.diagonal()).asDiagonal();
  }
  template <typename OtherDerived>
  using DiagonalDifferenceReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
      DiagonalVectorType, typename OtherDerived::DiagonalVectorType, difference)>;
  /** \returns the difference of \c *this and the diagonal matrix \a other */
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline const DiagonalDifferenceReturnType<OtherDerived> operator-(
      const DiagonalBase<OtherDerived>& other) const {
    return (diagonal() - other.diagonal()).asDiagonal();
    }
 };
 #endif
 /** \class DiagonalMatrix
  * \ingroup Core_Module
  *
  * \brief Represents a diagonal matrix with its storage
  *
- * \tparam Scalar_ the type of coefficients
+  * \param _Scalar the type of coefficients
- * \tparam SizeAtCompileTime the dimension of the matrix, or Dynamic
+  * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
- * \tparam MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
+  * \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 DiagonalBase, class DiagonalWrapper
+  * \sa class DiagonalWrapper
  */
 namespace internal {
-template <typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
-struct traits<DiagonalMatrix<Scalar_, SizeAtCompileTime, MaxSizeAtCompileTime>>
+struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
-    : traits<Matrix<Scalar_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime>> {
+ : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
-  typedef Matrix<Scalar_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> DiagonalVectorType;
+{
  typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
  typedef DiagonalShape StorageKind;
-  enum { Flags = LvalueBit | NoPreferredStorageOrderBit | NestByRefBit };
+  enum {
    Flags = LvalueBit | NoPreferredStorageOrderBit
  };
-}  // namespace internal
+};
-template <typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+}
-class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompileTime, MaxSizeAtCompileTime>> {
+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 _Scalar Scalar;
    typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
    typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
    #endif
  protected:
    DiagonalVectorType m_diagonal;
  public:
    /** const version of diagonal(). */
-  EIGEN_DEVICE_FUNC inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
+    EIGEN_DEVICE_FUNC
    inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
    /** \returns a reference to the stored vector of diagonal coefficients. */
-  EIGEN_DEVICE_FUNC inline DiagonalVectorType& diagonal() { return m_diagonal; }
+    EIGEN_DEVICE_FUNC
    inline DiagonalVectorType& diagonal() { return m_diagonal; }
    /** Default constructor without initialization */
-  EIGEN_DEVICE_FUNC inline DiagonalMatrix() {}
+    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix() {}
    /** Constructs a diagonal matrix with given dimension  */
-  EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
+    EIGEN_DEVICE_FUNC
    explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
    /** 2D constructor. */
-  EIGEN_DEVICE_FUNC inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x, y) {}
+    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
    /** 3D constructor. */
-  EIGEN_DEVICE_FUNC inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x, y, z) {}
+    EIGEN_DEVICE_FUNC
-
+    inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
  /** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients.
   *
   * \warning To construct a diagonal matrix of fixed size, the number of values passed to this
   * constructor must match the fixed dimension of \c *this.
   *
   * \sa DiagonalMatrix(const Scalar&, const Scalar&)
   * \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&)
   */
  template <typename... ArgTypes>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2,
                                                       const ArgTypes&... args)
      : m_diagonal(a0, a1, a2, args...) {}
  /** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer
   * lists \cpp11
   */
  EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE DiagonalMatrix(
      const std::initializer_list<std::initializer_list<Scalar>>& list)
      : m_diagonal(list) {}
  /** \brief Constructs a DiagonalMatrix from an r-value diagonal vector type */
  EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(DiagonalVectorType&& diag) : m_diagonal(std::move(diag)) {}
    /** Copy constructor. */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
+    EIGEN_DEVICE_FUNC
    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 */
@@ -234,11 +166,15 @@ class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompile
    /** generic constructor from expression of the diagonal coefficients */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other) {}
+    EIGEN_DEVICE_FUNC
    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
    {}
    /** Copy operator. */
    template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other) {
+    EIGEN_DEVICE_FUNC
    DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }
@@ -247,41 +183,29 @@ class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompile
    /** This is a special case of the templated operator=. Its purpose is to
      * prevent a default operator= from hiding the templated operator=.
      */
-  EIGEN_DEVICE_FUNC DiagonalMatrix& operator=(const DiagonalMatrix& other) {
+    EIGEN_DEVICE_FUNC
    DiagonalMatrix& operator=(const DiagonalMatrix& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }
    #endif
  typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, DiagonalVectorType>>
      InitializeReturnType;
  typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_zero_op<Scalar>, DiagonalVectorType>>
      ZeroInitializeReturnType;
  /** Initializes a diagonal matrix of size SizeAtCompileTime with coefficients set to zero */
  EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
  /** Initializes a diagonal matrix of size dim with coefficients set to zero */
  EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero(Index size) {
    return DiagonalVectorType::Zero(size).asDiagonal();
  }
  /** Initializes a identity matrix of size SizeAtCompileTime */
  EIGEN_DEVICE_FUNC static const InitializeReturnType Identity() { return DiagonalVectorType::Ones().asDiagonal(); }
  /** Initializes a identity matrix of size dim */
  EIGEN_DEVICE_FUNC static const InitializeReturnType Identity(Index size) {
    return DiagonalVectorType::Ones(size).asDiagonal();
  }
    /** Resizes to given size. */
-  EIGEN_DEVICE_FUNC inline void resize(Index size) { m_diagonal.resize(size); }
+    EIGEN_DEVICE_FUNC
    inline void resize(Index size) { m_diagonal.resize(size); }
    /** Sets all coefficients to zero. */
-  EIGEN_DEVICE_FUNC inline void setZero() { m_diagonal.setZero(); }
+    EIGEN_DEVICE_FUNC
    inline void setZero() { m_diagonal.setZero(); }
    /** Resizes and sets all coefficients to zero. */
-  EIGEN_DEVICE_FUNC inline void setZero(Index size) { m_diagonal.setZero(size); }
+    EIGEN_DEVICE_FUNC
    inline void setZero(Index size) { m_diagonal.setZero(size); }
    /** Sets this matrix to be the identity matrix of the current size. */
-  EIGEN_DEVICE_FUNC inline void setIdentity() { m_diagonal.setOnes(); }
+    EIGEN_DEVICE_FUNC
    inline void setIdentity() { m_diagonal.setOnes(); }
    /** Sets this matrix to be the identity matrix of the given size. */
-  EIGEN_DEVICE_FUNC inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
+    EIGEN_DEVICE_FUNC
    inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
 };
 /** \class DiagonalWrapper
@@ -289,7 +213,7 @@ class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompile
  *
  * \brief Expression of a diagonal matrix
  *
- * \tparam DiagonalVectorType_ the type of the vector of diagonal coefficients
+  * \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()
@@ -299,9 +223,10 @@ class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompile
  */
 namespace internal {
-template <typename DiagonalVectorType_>
+template<typename _DiagonalVectorType>
-struct traits<DiagonalWrapper<DiagonalVectorType_>> {
+struct traits<DiagonalWrapper<_DiagonalVectorType> >
-  typedef DiagonalVectorType_ DiagonalVectorType;
+{
  typedef _DiagonalVectorType DiagonalVectorType;
  typedef typename DiagonalVectorType::Scalar Scalar;
  typedef typename DiagonalVectorType::StorageIndex StorageIndex;
  typedef DiagonalShape StorageKind;
@@ -314,21 +239,25 @@ struct traits<DiagonalWrapper<DiagonalVectorType_>> {
    Flags =  (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
  };
 };
-}  // namespace internal
+}
-template <typename DiagonalVectorType_>
+template<typename _DiagonalVectorType>
-class DiagonalWrapper : public DiagonalBase<DiagonalWrapper<DiagonalVectorType_>>, internal::no_assignment_operator {
+class DiagonalWrapper
  : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
 {
  public:
    #ifndef EIGEN_PARSED_BY_DOXYGEN
-  typedef DiagonalVectorType_ DiagonalVectorType;
+    typedef _DiagonalVectorType DiagonalVectorType;
    typedef DiagonalWrapper Nested;
    #endif
    /** Constructor from expression of diagonal coefficients to wrap. */
-  EIGEN_DEVICE_FUNC explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
+    EIGEN_DEVICE_FUNC
    explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
    /** \returns a const reference to the wrapped expression of diagonal coefficients. */
-  EIGEN_DEVICE_FUNC const DiagonalVectorType& diagonal() const { return m_diagonal; }
+    EIGEN_DEVICE_FUNC
    const DiagonalVectorType& diagonal() const { return m_diagonal; }
  protected:
    typename DiagonalVectorType::Nested m_diagonal;
@@ -344,7 +273,9 @@ class DiagonalWrapper : public DiagonalBase<DiagonalWrapper<DiagonalVectorType_>
  * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
  **/
 template<typename Derived>
-EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived> MatrixBase<Derived>::asDiagonal() const {
+EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived>
 MatrixBase<Derived>::asDiagonal() const
 {
  return DiagonalWrapper<const Derived>(derived());
 }
@@ -357,15 +288,18 @@ EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived> MatrixBase<Derived
  * \sa asDiagonal()
  */
 template<typename Derived>
-bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const {
+bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
 {
  if(cols() != rows()) return false;
  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
-  for (Index j = 0; j < cols(); ++j) {
+  for(Index j = 0; j < cols(); ++j)
  {
    RealScalar absOnDiagonal = numext::abs(coeff(j,j));
    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
  }
  for(Index j = 0; j < cols(); ++j)
-    for (Index i = 0; i < j; ++i) {
+    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;
    }
@@ -374,43 +308,32 @@ bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const {
 namespace internal {
-template <>
+template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };
 struct storage_kind_to_shape<DiagonalShape> {
  typedef DiagonalShape Shape;
 };
 struct Diagonal2Dense {};
-template <>
+template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };
 struct AssignmentKind<DenseShape, DiagonalShape> {
  typedef Diagonal2Dense Kind;
 };
 // Diagonal matrix to Dense assignment
 template< typename DstXprType, typename SrcXprType, typename Functor>
-struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense> {
+struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
-  static EIGEN_DEVICE_FUNC void run(
+{
-      DstXprType& dst, const SrcXprType& src,
+  static EIGEN_DEVICE_FUNC void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
-      const internal::assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
+  {
    Index dstRows = src.rows();
    Index dstCols = src.cols();
-    if ((dst.rows() != dstRows) || (dst.cols() != dstCols)) dst.resize(dstRows, dstCols);
+    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
      dst.resize(dstRows, dstCols);
    dst.setZero();
    dst.diagonal() = src.diagonal();
  }
-  static EIGEN_DEVICE_FUNC void run(
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
-      DstXprType& dst, const SrcXprType& src,
+  { dst.diagonal() += src.diagonal(); }
      const internal::add_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
    dst.diagonal() += src.diagonal();
  }
-  static EIGEN_DEVICE_FUNC void run(
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
-      DstXprType& dst, const SrcXprType& src,
+  { dst.diagonal() -= src.diagonal(); }
      const internal::sub_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
    dst.diagonal() -= src.diagonal();
  }
 };
 } // namespace internal
--- a/Eigen/src/Core/DiagonalProduct.h
+++ b/Eigen/src/Core/DiagonalProduct.h
@@ -11,17 +11,15 @@
 #ifndef EIGEN_DIAGONALPRODUCT_H
 #define EIGEN_DIAGONALPRODUCT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 /** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
  */
 template<typename Derived>
 template<typename DiagonalDerived>
-EIGEN_DEVICE_FUNC inline const Product<Derived, DiagonalDerived, LazyProduct> MatrixBase<Derived>::operator*(
+EIGEN_DEVICE_FUNC inline const Product<Derived, DiagonalDerived, LazyProduct>
-    const DiagonalBase<DiagonalDerived> &a_diagonal) const {
+MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &a_diagonal) const
 {
  return Product<Derived, DiagonalDerived, LazyProduct>(derived(),a_diagonal.derived());
 }
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -10,25 +10,45 @@
 #ifndef EIGEN_DOT_H
 #define EIGEN_DOT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
-template <typename Derived, typename Scalar = typename traits<Derived>::Scalar>
+// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
-struct squared_norm_impl {
+// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
-  using Real = typename NumTraits<Scalar>::Real;
+// looking at the static assertions. Thus this is a trick to get better compile errors.
-  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Real run(const Derived& a) {
+template<typename T, typename U,
-    Scalar result = a.unaryExpr(squared_norm_functor<Scalar>()).sum();
+// the NeedToTranspose condition here is taken straight from Assign.h
-    return numext::real(result) + numext::imag(result);
+         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 scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
  typedef typename conj_prod::result_type ResScalar;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE
  static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
  {
    return a.template binaryExpr<conj_prod>(b).sum();
  }
 };
-template <typename Derived>
+template<typename T, typename U>
-struct squared_norm_impl<Derived, bool> {
+struct dot_nocheck<T, U, true>
-  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Derived& a) { return a.any(); }
+{
  typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
  typedef typename conj_prod::result_type ResScalar;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE
  static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
  {
    return a.transpose().template binaryExpr<conj_prod>(b).sum();
  }
 };
 } // end namespace internal
@@ -46,11 +66,22 @@ struct squared_norm_impl<Derived, bool> {
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+EIGEN_DEVICE_FUNC
-    typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
+EIGEN_STRONG_INLINE
-                                  typename internal::traits<OtherDerived>::Scalar>::ReturnType
+typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
-    MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const {
+MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
-  return internal::dot_impl<Derived, OtherDerived>::run(derived(), other.derived());
+{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
 #if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))
  typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
 #endif
  eigen_assert(size() == other.size());
  return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
 }
 //---------- implementation of L2 norm and related functions ----------
@@ -62,9 +93,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  * \sa dot(), norm(), lpNorm()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
-MatrixBase<Derived>::squaredNorm() const {
+{
-  return internal::squared_norm_impl<Derived>::run(derived());
+  return numext::real((*this).cwiseAbs2().sum());
 }
 /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
@@ -74,8 +105,8 @@ MatrixBase<Derived>::squaredNorm() const {
  * \sa lpNorm(), dot(), squaredNorm()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
-MatrixBase<Derived>::norm() const {
+{
  return numext::sqrt(squaredNorm());
 }
@@ -89,10 +120,11 @@ MatrixBase<Derived>::norm() const {
  * \sa norm(), normalize()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::normalized()
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
-    const {
+MatrixBase<Derived>::normalized() const
-  typedef typename internal::nested_eval<Derived, 2>::type Nested_;
+{
-  Nested_ n(derived());
+  typedef typename internal::nested_eval<Derived,2>::type _Nested;
  _Nested n(derived());
  RealScalar z = n.squaredNorm();
  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
  if(z>RealScalar(0))
@@ -110,10 +142,12 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainO
  * \sa norm(), normalized()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize()
 {
  RealScalar z = squaredNorm();
  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
-  if (z > RealScalar(0)) derived() /= numext::sqrt(z);
+  if(z>RealScalar(0))
    derived() /= numext::sqrt(z);
 }
 /** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow.
@@ -130,9 +164,10 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize() {
  */
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
-MatrixBase<Derived>::stableNormalized() const {
+MatrixBase<Derived>::stableNormalized() const
-  typedef typename internal::nested_eval<Derived, 3>::type Nested_;
+{
-  Nested_ n(derived());
+  typedef typename internal::nested_eval<Derived,3>::type _Nested;
  _Nested n(derived());
  RealScalar w = n.cwiseAbs().maxCoeff();
  RealScalar z = (n/w).squaredNorm();
  if(z>RealScalar(0))
@@ -153,10 +188,12 @@ MatrixBase<Derived>::stableNormalized() const {
  * \sa stableNorm(), stableNormalized(), normalize()
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize() {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize()
 {
  RealScalar w = cwiseAbs().maxCoeff();
  RealScalar z = (derived()/w).squaredNorm();
-  if (z > RealScalar(0)) derived() /= numext::sqrt(z) * w;
+  if(z>RealScalar(0))
    derived() /= numext::sqrt(z)*w;
 }
 //---------- implementation of other norms ----------
@@ -164,34 +201,44 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize(
 namespace internal {
 template<typename Derived, int p>
-struct lpNorm_selector {
+struct lpNorm_selector
 {
  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
-  EIGEN_DEVICE_FUNC static inline RealScalar run(const MatrixBase<Derived>& m) {
+  EIGEN_DEVICE_FUNC
-    EIGEN_USING_STD(pow)
+  static inline RealScalar run(const MatrixBase<Derived>& m)
  {
    EIGEN_USING_STD_MATH(pow)
    return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
  }
 };
 template<typename Derived>
-struct lpNorm_selector<Derived, 1> {
+struct lpNorm_selector<Derived, 1>
-  EIGEN_DEVICE_FUNC static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
+{
-      const MatrixBase<Derived>& m) {
+  EIGEN_DEVICE_FUNC
  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
  {
    return m.cwiseAbs().sum();
  }
 };
 template<typename Derived>
-struct lpNorm_selector<Derived, 2> {
+struct lpNorm_selector<Derived, 2>
-  EIGEN_DEVICE_FUNC static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
+{
-      const MatrixBase<Derived>& m) {
+  EIGEN_DEVICE_FUNC
  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
  {
    return m.norm();
  }
 };
 template<typename Derived>
-struct lpNorm_selector<Derived, Infinity> {
+struct lpNorm_selector<Derived, Infinity>
 {
  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
-  EIGEN_DEVICE_FUNC static inline RealScalar run(const MatrixBase<Derived>& m) {
+  EIGEN_DEVICE_FUNC
  static inline RealScalar run(const MatrixBase<Derived>& m)
  {
    if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0))
      return RealScalar(0);
    return m.cwiseAbs().maxCoeff();
@@ -200,17 +247,13 @@ struct lpNorm_selector<Derived, Infinity> {
 } // end namespace internal
-/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the
+/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
- * p-th powers of the absolute values of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity,
+  *          of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
- * this function returns the \f$ \ell^\infty \f$ norm, that is the maximum of the absolute values of the coefficients of
+  *          norm, that is the maximum of the absolute values of the coefficients of \c *this.
 * \c *this.
  *
  * In all cases, if \c *this is empty, then the value 0 is returned.
  *
- * \note For matrices, this function does not compute the <a
+  * \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
 * href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its
 * coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm
 * matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
  *
  * \sa norm()
  */
@@ -221,7 +264,8 @@ EIGEN_DEVICE_FUNC inline typename NumTraits<typename internal::traits<Derived>::
 #else
 EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar
 #endif
-MatrixBase<Derived>::lpNorm() const {
+MatrixBase<Derived>::lpNorm() const
 {
  return internal::lpNorm_selector<Derived, p>::run(*this);
 }
@@ -235,7 +279,9 @@ MatrixBase<Derived>::lpNorm() const {
  */
 template<typename Derived>
 template<typename OtherDerived>
-bool MatrixBase<Derived>::isOrthogonal(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const {
+bool MatrixBase<Derived>::isOrthogonal
 (const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
 {
  typename internal::nested_eval<Derived,2>::type nested(derived());
  typename internal::nested_eval<OtherDerived,2>::type otherNested(other.derived());
  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
@@ -253,12 +299,16 @@ bool MatrixBase<Derived>::isOrthogonal(const MatrixBase<OtherDerived>& other, co
  * Output: \verbinclude MatrixBase_isUnitary.out
  */
 template<typename Derived>
-bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const {
+bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
 {
  typename internal::nested_eval<Derived,1>::type self(derived());
-  for (Index i = 0; i < cols(); ++i) {
+  for(Index i = 0; i < cols(); ++i)
-    if (!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) return false;
+  {
    if(!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
      return false;
    for(Index j = 0; j < i; ++j)
-      if (!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec)) return false;
+      if(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec))
        return false;
  }
  return true;
 }
--- a/Eigen/src/Core/EigenBase.h
+++ b/Eigen/src/Core/EigenBase.h
@@ -11,9 +11,6 @@
 #ifndef EIGEN_EIGENBASE_H
 #define EIGEN_EIGENBASE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 /** \class EigenBase
@@ -29,16 +26,14 @@ namespace Eigen {
  *
  * \sa \blank \ref TopicClassHierarchy
  */
-template <typename Derived>
+template<typename Derived> struct EigenBase
-struct EigenBase {
+{
 //   typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
  /** \brief The interface type of indices
    * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
    * \deprecated Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
    * \sa StorageIndex, \ref TopicPreprocessorDirectives.
   * DEPRECATED: Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
   * Deprecation is not marked with a doxygen comment because there are too many existing usages to add the deprecation
   * attribute.
    */
  typedef Eigen::Index Index;
@@ -46,32 +41,41 @@ struct EigenBase {
  typedef typename internal::traits<Derived>::StorageKind StorageKind;
  /** \returns a reference to the derived object */
-  EIGEN_DEVICE_FUNC constexpr Derived& derived() { return *static_cast<Derived*>(this); }
+  EIGEN_DEVICE_FUNC
  Derived& derived() { return *static_cast<Derived*>(this); }
  /** \returns a const reference to the derived object */
-  EIGEN_DEVICE_FUNC constexpr const Derived& derived() const { return *static_cast<const Derived*>(this); }
+  EIGEN_DEVICE_FUNC
  const Derived& derived() const { return *static_cast<const Derived*>(this); }
-  EIGEN_DEVICE_FUNC inline constexpr Derived& const_cast_derived() const {
+  EIGEN_DEVICE_FUNC
-    return *static_cast<Derived*>(const_cast<EigenBase*>(this));
+  inline Derived& const_cast_derived() const
-  }
+  { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
-  EIGEN_DEVICE_FUNC inline const Derived& const_derived() const { return *static_cast<const Derived*>(this); }
+  EIGEN_DEVICE_FUNC
  inline const Derived& const_derived() const
  { return *static_cast<const Derived*>(this); }
  /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return derived().rows(); }
+  EIGEN_DEVICE_FUNC
  inline Index rows() const { return derived().rows(); }
  /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return derived().cols(); }
+  EIGEN_DEVICE_FUNC
  inline Index cols() const { return derived().cols(); }
  /** \returns the number of coefficients, which is rows()*cols().
    * \sa rows(), cols(), SizeAtCompileTime. */
-  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return rows() * cols(); }
+  EIGEN_DEVICE_FUNC
  inline Index size() const { return rows() * cols(); }
  /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
  template<typename Dest>
-  EIGEN_DEVICE_FUNC inline void evalTo(Dest& dst) const {
+  EIGEN_DEVICE_FUNC
-    derived().evalTo(dst);
+  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>
-  EIGEN_DEVICE_FUNC inline void addTo(Dest& dst) const {
+  EIGEN_DEVICE_FUNC
  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());
@@ -81,7 +85,9 @@ struct EigenBase {
  /** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
  template<typename Dest>
-  EIGEN_DEVICE_FUNC inline void subTo(Dest& dst) const {
+  EIGEN_DEVICE_FUNC
  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());
@@ -91,7 +97,8 @@ struct EigenBase {
  /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
  template<typename Dest>
-  EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const {
+  EIGEN_DEVICE_FUNC 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();
@@ -99,16 +106,13 @@ struct EigenBase {
  /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
  template<typename Dest>
-  EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const {
+  EIGEN_DEVICE_FUNC 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;
  }
  template <typename Device>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<Derived, Device> device(Device& device);
  template <typename Device>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<const Derived, Device> device(Device& device) const;
 };
 /***************************************************************************
@@ -125,21 +129,27 @@ struct EigenBase {
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
 {
  call_assignment(derived(), other.derived());
  return derived();
 }
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
 {
  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived>& other) {
+EIGEN_DEVICE_FUNC
 Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
 {
  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
  return derived();
 }
--- a/Eigen/src/Core/Fill.h
+++ b/Eigen/src/Core/Fill.h
@@ -1,138 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2024 Charles Schlosser <cs.schlosser@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_FILL_H
 #define EIGEN_FILL_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 template <typename Xpr>
 struct eigen_fill_helper : std::false_type {};
 template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
 struct eigen_fill_helper<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
 template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
 struct eigen_fill_helper<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
 template <typename Xpr, int BlockRows, int BlockCols>
 struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ true>> : eigen_fill_helper<Xpr> {};
 template <typename Xpr, int BlockRows, int BlockCols>
 struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ false>>
    : std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
                                       (Xpr::IsRowMajor ? (BlockRows == 1) : (BlockCols == 1))> {};
 template <typename Xpr, int Options>
 struct eigen_fill_helper<Map<Xpr, Options, Stride<0, 0>>> : eigen_fill_helper<Xpr> {};
 template <typename Xpr, int Options, int OuterStride_>
 struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>>
    : std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
                                       enum_eq_not_dynamic(OuterStride_, Xpr::InnerSizeAtCompileTime)> {};
 template <typename Xpr, int Options, int OuterStride_>
 struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 1>>>
    : eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
 template <typename Xpr, int Options, int InnerStride_>
 struct eigen_fill_helper<Map<Xpr, Options, InnerStride<InnerStride_>>>
    : eigen_fill_helper<Map<Xpr, Options, Stride<0, InnerStride_>>> {};
 template <typename Xpr, int Options, int OuterStride_>
 struct eigen_fill_helper<Map<Xpr, Options, OuterStride<OuterStride_>>>
    : eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
 template <typename Xpr>
 struct eigen_fill_impl<Xpr, /*use_fill*/ false> {
  using Scalar = typename Xpr::Scalar;
  using Func = scalar_constant_op<Scalar>;
  using PlainObject = typename Xpr::PlainObject;
  using Constant = typename PlainObject::ConstantReturnType;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const Scalar& val) {
    const Constant src(dst.rows(), dst.cols(), val);
    run(dst, src);
  }
  template <typename SrcXpr>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
    call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
  }
 };
 #if EIGEN_COMP_MSVC || defined(EIGEN_GPU_COMPILE_PHASE)
 template <typename Xpr>
 struct eigen_fill_impl<Xpr, /*use_fill*/ true> : eigen_fill_impl<Xpr, /*use_fill*/ false> {};
 #else
 template <typename Xpr>
 struct eigen_fill_impl<Xpr, /*use_fill*/ true> {
  using Scalar = typename Xpr::Scalar;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const Scalar& val) {
    const Scalar val_copy = val;
    using std::fill_n;
    fill_n(dst.data(), dst.size(), val_copy);
  }
  template <typename SrcXpr>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
    resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
    const Scalar& val = src.functor()();
    run(dst, val);
  }
 };
 #endif
 template <typename Xpr>
 struct eigen_memset_helper {
  static constexpr bool value =
      std::is_trivially_copyable<typename Xpr::Scalar>::value && eigen_fill_helper<Xpr>::value;
 };
 template <typename Xpr>
 struct eigen_zero_impl<Xpr, /*use_memset*/ false> {
  using Scalar = typename Xpr::Scalar;
  using PlainObject = typename Xpr::PlainObject;
  using Zero = typename PlainObject::ZeroReturnType;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst) {
    const Zero src(dst.rows(), dst.cols());
    run(dst, src);
  }
  template <typename SrcXpr>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
    call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
  }
 };
 template <typename Xpr>
 struct eigen_zero_impl<Xpr, /*use_memset*/ true> {
  using Scalar = typename Xpr::Scalar;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst) {
    const std::ptrdiff_t num_bytes = dst.size() * static_cast<std::ptrdiff_t>(sizeof(Scalar));
    if (num_bytes <= 0) return;
    void* dst_ptr = static_cast<void*>(dst.data());
 #ifndef EIGEN_NO_DEBUG
    eigen_assert((dst_ptr != nullptr) && "null pointer dereference error!");
 #endif
    EIGEN_USING_STD(memset);
    memset(dst_ptr, 0, static_cast<std::size_t>(num_bytes));
  }
  template <typename SrcXpr>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
    resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
    run(dst);
  }
 };
 }  // namespace internal
 }  // namespace Eigen
 #endif  // EIGEN_FILL_H
--- a/Eigen/src/Core/FindCoeff.h
+++ b/Eigen/src/Core/FindCoeff.h
@@ -1,464 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_FIND_COEFF_H
 #define EIGEN_FIND_COEFF_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
 struct max_coeff_functor {
  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
    return candidate > incumbent;
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
    return pcmp_lt(incumbent, candidate);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_max(a);
  }
 };
 template <typename Scalar>
 struct max_coeff_functor<Scalar, PropagateNaN, false> {
  EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
    return (candidate > incumbent) || ((candidate != candidate) && (incumbent == incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
    return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_max<PropagateNaN>(a);
  }
 };
 template <typename Scalar>
 struct max_coeff_functor<Scalar, PropagateNumbers, false> {
  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
    return (candidate > incumbent) || ((candidate == candidate) && (incumbent != incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
    return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(candidate));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_max<PropagateNumbers>(a);
  }
 };
 template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
 struct min_coeff_functor {
  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
    return candidate < incumbent;
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
    return pcmp_lt(candidate, incumbent);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_min(a);
  }
 };
 template <typename Scalar>
 struct min_coeff_functor<Scalar, PropagateNaN, false> {
  EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
    return (candidate < incumbent) || ((candidate != candidate) && (incumbent == incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
    return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_min<PropagateNaN>(a);
  }
 };
 template <typename Scalar>
 struct min_coeff_functor<Scalar, PropagateNumbers, false> {
  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
    return (candidate < incumbent) || ((candidate == candidate) && (incumbent != incumbent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
    return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(candidate));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
    return predux_min<PropagateNumbers>(a);
  }
 };
 template <typename Scalar>
 struct min_max_traits {
  static constexpr bool PacketAccess = packet_traits<Scalar>::Vectorizable;
 };
 template <typename Scalar, int NaNPropagation>
 struct functor_traits<max_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
 template <typename Scalar, int NaNPropagation>
 struct functor_traits<min_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
 template <typename Evaluator, typename Func, bool Linear, bool Vectorize>
 struct find_coeff_loop;
 template <typename Evaluator, typename Func>
 struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ false> {
  using Scalar = typename Evaluator::Scalar;
  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& outer, Index& inner) {
    Index outerSize = eval.outerSize();
    Index innerSize = eval.innerSize();
    /* initialization performed in calling function */
    /* result = eval.coeff(0, 0); */
    /* outer = 0; */
    /* inner = 0; */
    for (Index j = 0; j < outerSize; j++) {
      for (Index i = 0; i < innerSize; i++) {
        Scalar xprCoeff = eval.coeffByOuterInner(j, i);
        bool newRes = func.compareCoeff(res, xprCoeff);
        if (newRes) {
          outer = j;
          inner = i;
          res = xprCoeff;
        }
      }
    }
  }
 };
 template <typename Evaluator, typename Func>
 struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ false> {
  using Scalar = typename Evaluator::Scalar;
  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& index) {
    Index size = eval.size();
    /* initialization performed in calling function */
    /* result = eval.coeff(0); */
    /* index = 0; */
    for (Index k = 0; k < size; k++) {
      Scalar xprCoeff = eval.coeff(k);
      bool newRes = func.compareCoeff(res, xprCoeff);
      if (newRes) {
        index = k;
        res = xprCoeff;
      }
    }
  }
 };
 template <typename Evaluator, typename Func>
 struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ true> {
  using ScalarImpl = find_coeff_loop<Evaluator, Func, false, false>;
  using Scalar = typename Evaluator::Scalar;
  using Packet = typename Evaluator::Packet;
  static constexpr int PacketSize = unpacket_traits<Packet>::size;
  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& outer,
                                           Index& inner) {
    Index outerSize = eval.outerSize();
    Index innerSize = eval.innerSize();
    Index packetEnd = numext::round_down(innerSize, PacketSize);
    /* initialization performed in calling function */
    /* result = eval.coeff(0, 0); */
    /* outer = 0; */
    /* inner = 0; */
    bool checkPacket = false;
    for (Index j = 0; j < outerSize; j++) {
      Packet resultPacket = pset1<Packet>(result);
      for (Index i = 0; i < packetEnd; i += PacketSize) {
        Packet xprPacket = eval.template packetByOuterInner<Unaligned, Packet>(j, i);
        if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
          outer = j;
          inner = i;
          result = func.predux(xprPacket);
          resultPacket = pset1<Packet>(result);
          checkPacket = true;
        }
      }
      for (Index i = packetEnd; i < innerSize; i++) {
        Scalar xprCoeff = eval.coeffByOuterInner(j, i);
        if (func.compareCoeff(result, xprCoeff)) {
          outer = j;
          inner = i;
          result = xprCoeff;
          checkPacket = false;
        }
      }
    }
    if (checkPacket) {
      result = eval.coeffByOuterInner(outer, inner);
      Index i_end = inner + PacketSize;
      for (Index i = inner; i < i_end; i++) {
        Scalar xprCoeff = eval.coeffByOuterInner(outer, i);
        if (func.compareCoeff(result, xprCoeff)) {
          inner = i;
          result = xprCoeff;
        }
      }
    }
  }
 };
 template <typename Evaluator, typename Func>
 struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ true> {
  using ScalarImpl = find_coeff_loop<Evaluator, Func, true, false>;
  using Scalar = typename Evaluator::Scalar;
  using Packet = typename Evaluator::Packet;
  static constexpr int PacketSize = unpacket_traits<Packet>::size;
  static constexpr int Alignment = Evaluator::Alignment;
  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& index) {
    Index size = eval.size();
    Index packetEnd = numext::round_down(size, PacketSize);
    /* initialization performed in calling function */
    /* result = eval.coeff(0); */
    /* index = 0; */
    Packet resultPacket = pset1<Packet>(result);
    bool checkPacket = false;
    for (Index k = 0; k < packetEnd; k += PacketSize) {
      Packet xprPacket = eval.template packet<Alignment, Packet>(k);
      if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
        index = k;
        result = func.predux(xprPacket);
        resultPacket = pset1<Packet>(result);
        checkPacket = true;
      }
    }
    for (Index k = packetEnd; k < size; k++) {
      Scalar xprCoeff = eval.coeff(k);
      if (func.compareCoeff(result, xprCoeff)) {
        index = k;
        result = xprCoeff;
        checkPacket = false;
      }
    }
    if (checkPacket) {
      result = eval.coeff(index);
      Index k_end = index + PacketSize;
      for (Index k = index; k < k_end; k++) {
        Scalar xprCoeff = eval.coeff(k);
        if (func.compareCoeff(result, xprCoeff)) {
          index = k;
          result = xprCoeff;
        }
      }
    }
  }
 };
 template <typename Derived>
 struct find_coeff_evaluator : public evaluator<Derived> {
  using Base = evaluator<Derived>;
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  static constexpr int Flags = Base::Flags;
  static constexpr bool IsRowMajor = bool(Flags & RowMajorBit);
  EIGEN_DEVICE_FUNC inline find_coeff_evaluator(const Derived& xpr) : Base(xpr), m_xpr(xpr) {}
  EIGEN_DEVICE_FUNC inline Scalar coeffByOuterInner(Index outer, Index inner) const {
    Index row = IsRowMajor ? outer : inner;
    Index col = IsRowMajor ? inner : outer;
    return Base::coeff(row, col);
  }
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC inline PacketType packetByOuterInner(Index outer, Index inner) const {
    Index row = IsRowMajor ? outer : inner;
    Index col = IsRowMajor ? inner : outer;
    return Base::template packet<LoadMode, PacketType>(row, col);
  }
  EIGEN_DEVICE_FUNC inline Index innerSize() const { return m_xpr.innerSize(); }
  EIGEN_DEVICE_FUNC inline Index outerSize() const { return m_xpr.outerSize(); }
  EIGEN_DEVICE_FUNC inline Index size() const { return m_xpr.size(); }
  const Derived& m_xpr;
 };
 template <typename Derived, typename Func>
 struct find_coeff_impl {
  using Evaluator = find_coeff_evaluator<Derived>;
  static constexpr int Flags = Evaluator::Flags;
  static constexpr int Alignment = Evaluator::Alignment;
  static constexpr bool IsRowMajor = Derived::IsRowMajor;
  static constexpr int MaxInnerSizeAtCompileTime =
      IsRowMajor ? Derived::MaxColsAtCompileTime : Derived::MaxRowsAtCompileTime;
  static constexpr int MaxSizeAtCompileTime = Derived::MaxSizeAtCompileTime;
  using Scalar = typename Derived::Scalar;
  using Packet = typename Evaluator::Packet;
  static constexpr int PacketSize = unpacket_traits<Packet>::size;
  static constexpr bool Linearize = bool(Flags & LinearAccessBit);
  static constexpr bool DontVectorize =
      enum_lt_not_dynamic(Linearize ? MaxSizeAtCompileTime : MaxInnerSizeAtCompileTime, PacketSize);
  static constexpr bool Vectorize =
      !DontVectorize && bool(Flags & PacketAccessBit) && functor_traits<Func>::PacketAccess;
  using Loop = find_coeff_loop<Evaluator, Func, Linearize, Vectorize>;
  template <bool ForwardLinearAccess = Linearize, std::enable_if_t<!ForwardLinearAccess, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
                                                        Index& inner) {
    Evaluator eval(xpr);
    Loop::run(eval, func, res, outer, inner);
  }
  template <bool ForwardLinearAccess = Linearize, std::enable_if_t<ForwardLinearAccess, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
                                                        Index& inner) {
    // where possible, use the linear loop and back-calculate the outer and inner indices
    Index index = 0;
    run(xpr, func, res, index);
    outer = index / xpr.innerSize();
    inner = index % xpr.innerSize();
  }
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& index) {
    Evaluator eval(xpr);
    Loop::run(eval, func, res, index);
  }
 };
 template <typename Derived, typename IndexType, typename Func>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
                                                                       IndexType* rowPtr, IndexType* colPtr) {
  eigen_assert(mat.rows() > 0 && mat.cols() > 0 && "you are using an empty matrix");
  using Scalar = typename DenseBase<Derived>::Scalar;
  using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
  Index outer = 0;
  Index inner = 0;
  Scalar res = mat.coeff(0, 0);
  FindCoeffImpl::run(mat.derived(), func, res, outer, inner);
  *rowPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? outer : inner);
  if (colPtr) *colPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? inner : outer);
  return res;
 }
 template <typename Derived, typename IndexType, typename Func>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
                                                                       IndexType* indexPtr) {
  eigen_assert(mat.size() > 0 && "you are using an empty matrix");
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  using Scalar = typename DenseBase<Derived>::Scalar;
  using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
  Index index = 0;
  Scalar res = mat.coeff(0);
  FindCoeffImpl::run(mat.derived(), func, res, index);
  *indexPtr = internal::convert_index<IndexType>(index);
  return res;
 }
 }  // namespace internal
 /** \fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
 * \returns the minimum of all coefficients of *this and puts in *row and *col its location.
 *
 * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
 *
 * In case \c *this contains NaN, NaNPropagation determines the behavior:
 *   NaNPropagation == PropagateFast : undefined
 *   NaNPropagation == PropagateNaN : result is NaN
 *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
 * \warning the matrix must be not empty, otherwise an assertion is triggered.
 *
 * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
 */
 template <typename Derived>
 template <int NaNPropagation, typename IndexType>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* rowPtr,
                                                                                          IndexType* colPtr) const {
  using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
  Func func;
  return internal::findCoeff(derived(), func, rowPtr, colPtr);
 }
 /** \returns the minimum of all coefficients of *this and puts in *index its location.
 *
 * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
 *
 * In case \c *this contains NaN, NaNPropagation determines the behavior:
 *   NaNPropagation == PropagateFast : undefined
 *   NaNPropagation == PropagateNaN : result is NaN
 *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
 * \warning the matrix must be not empty, otherwise an assertion is triggered.
 *
 * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(),
 * DenseBase::minCoeff()
 */
 template <typename Derived>
 template <int NaNPropagation, typename IndexType>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* indexPtr) const {
  using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
  Func func;
  return internal::findCoeff(derived(), func, indexPtr);
 }
 /** \fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const
 * \returns the maximum of all coefficients of *this and puts in *row and *col its location.
 *
 * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
 *
 * In case \c *this contains NaN, NaNPropagation determines the behavior:
 *   NaNPropagation == PropagateFast : undefined
 *   NaNPropagation == PropagateNaN : result is NaN
 *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
 * \warning the matrix must be not empty, otherwise an assertion is triggered.
 *
 * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
 */
 template <typename Derived>
 template <int NaNPropagation, typename IndexType>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* rowPtr,
                                                                                          IndexType* colPtr) const {
  using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
  Func func;
  return internal::findCoeff(derived(), func, rowPtr, colPtr);
 }
 /** \returns the maximum of all coefficients of *this and puts in *index its location.
 *
 * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
 *
 * In case \c *this contains NaN, NaNPropagation determines the behavior:
 *   NaNPropagation == PropagateFast : undefined
 *   NaNPropagation == PropagateNaN : result is NaN
 *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
 * \warning the matrix must be not empty, otherwise an assertion is triggered.
 *
 * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(),
 * DenseBase::maxCoeff()
 */
 template <typename Derived>
 template <int NaNPropagation, typename IndexType>
 EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* indexPtr) const {
  using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
  Func func;
  return internal::findCoeff(derived(), func, indexPtr);
 }
 }  // namespace Eigen
 #endif  // EIGEN_FIND_COEFF_H
--- a/Eigen/src/Core/ForceAlignedAccess.h
+++ b/Eigen/src/Core/ForceAlignedAccess.h
@@ -10,9 +10,6 @@
 #ifndef EIGEN_FORCEALIGNEDACCESS_H
 #define EIGEN_FORCEALIGNEDACCESS_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 /** \class ForceAlignedAccess
@@ -30,51 +27,66 @@ namespace Eigen {
 namespace internal {
 template<typename ExpressionType>
-struct traits<ForceAlignedAccess<ExpressionType>> : public traits<ExpressionType> {};
+struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
-}  // namespace internal
+{};
 }
-template <typename ExpressionType>
+template<typename ExpressionType> class ForceAlignedAccess
-class ForceAlignedAccess : public internal::dense_xpr_base<ForceAlignedAccess<ExpressionType>>::type {
+  : public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
 {
  public:
    typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
    EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+    EIGEN_DEVICE_FUNC inline Index rows() const { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+    EIGEN_DEVICE_FUNC inline Index cols() const { return m_expression.cols(); }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+    EIGEN_DEVICE_FUNC inline Index outerStride() const { return m_expression.outerStride(); }
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
+    EIGEN_DEVICE_FUNC inline Index innerStride() const { return m_expression.innerStride(); }
-  EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const {
+    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const
    {
      return m_expression.coeff(row, col);
    }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col) {
+    EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col)
    {
      return m_expression.const_cast_derived().coeffRef(row, col);
    }
-  EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const { return m_expression.coeff(index); }
+    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const
    {
      return m_expression.coeff(index);
    }
-  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index) { return m_expression.const_cast_derived().coeffRef(index); }
+    EIGEN_DEVICE_FUNC 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 {
+    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) {
+    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 {
+    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) {
+    inline void writePacket(Index index, const PacketScalar& x)
    {
      m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
    }
@@ -91,7 +103,9 @@ class ForceAlignedAccess : public internal::dense_xpr_base<ForceAlignedAccess<Ex
  * \sa forceAlignedAccessIf(),class ForceAlignedAccess
  */
 template<typename Derived>
-inline const ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess() const {
+inline const ForceAlignedAccess<Derived>
 MatrixBase<Derived>::forceAlignedAccess() const
 {
  return ForceAlignedAccess<Derived>(derived());
 }
@@ -99,7 +113,9 @@ inline const ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess
  * \sa forceAlignedAccessIf(), class ForceAlignedAccess
  */
 template<typename Derived>
-inline ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess() {
+inline ForceAlignedAccess<Derived>
 MatrixBase<Derived>::forceAlignedAccess()
 {
  return ForceAlignedAccess<Derived>(derived());
 }
@@ -108,8 +124,9 @@ inline ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess() {
  */
 template<typename Derived>
 template<bool Enable>
-inline add_const_on_value_type_t<std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&>>
+inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type
-MatrixBase<Derived>::forceAlignedAccessIf() const {
+MatrixBase<Derived>::forceAlignedAccessIf() const
 {
  return derived();  // FIXME This should not work but apparently is never used
 }
@@ -118,7 +135,9 @@ MatrixBase<Derived>::forceAlignedAccessIf() const {
  */
 template<typename Derived>
 template<bool Enable>
-inline std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> MatrixBase<Derived>::forceAlignedAccessIf() {
+inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type
 MatrixBase<Derived>::forceAlignedAccessIf()
 {
  return derived();  // FIXME This should not work but apparently is never used
 }
--- a/Eigen/src/Core/Fuzzy.h
+++ b/Eigen/src/Core/Fuzzy.h
@@ -11,62 +11,76 @@
 #ifndef EIGEN_FUZZY_H
 #define EIGEN_FUZZY_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
-namespace internal {
+namespace internal
 {
 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
-struct isApprox_selector {
+struct isApprox_selector
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) {
+{
  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
  {
    typename internal::nested_eval<Derived,2>::type nested(x);
    typename internal::nested_eval<OtherDerived,2>::type otherNested(y);
-    return (nested.matrix() - otherNested.matrix()).cwiseAbs2().sum() <=
+    return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
           prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
  }
 };
 template<typename Derived, typename OtherDerived>
-struct isApprox_selector<Derived, OtherDerived, true> {
+struct isApprox_selector<Derived, OtherDerived, true>
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) {
+{
  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const OtherDerived& y, const 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 {
+struct isMuchSmallerThan_object_selector
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) {
+{
  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
  {
    return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
  }
 };
 template<typename Derived, typename OtherDerived>
-struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> {
+struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) {
+{
  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const OtherDerived&, const 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 {
+struct isMuchSmallerThan_scalar_selector
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const typename Derived::RealScalar& y,
+{
-                                    const typename Derived::RealScalar& prec) {
+  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
  {
    return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
  }
 };
 template<typename Derived>
-struct isMuchSmallerThan_scalar_selector<Derived, true> {
+struct isMuchSmallerThan_scalar_selector<Derived, true>
-  EIGEN_DEVICE_FUNC static bool run(const Derived& x, const typename Derived::RealScalar&,
+{
-                                    const typename Derived::RealScalar&) {
+  EIGEN_DEVICE_FUNC
  static bool run(const Derived& x, const typename Derived::RealScalar&, const 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.
  *
@@ -86,8 +100,11 @@ struct isMuchSmallerThan_scalar_selector<Derived, true> {
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(const DenseBase<OtherDerived>& other,
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(
-                                                    const RealScalar& prec) const {
+  const DenseBase<OtherDerived>& other,
  const RealScalar& prec
 ) const
 {
  return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
 }
@@ -105,8 +122,11 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(const DenseBase<OtherDerived
  * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
  */
 template<typename Derived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(const typename NumTraits<Scalar>::Real& other,
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
-                                                             const RealScalar& prec) const {
+  const typename NumTraits<Scalar>::Real& other,
  const RealScalar& prec
 ) const
 {
  return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
 }
@@ -122,8 +142,11 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(const typename NumT
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(const DenseBase<OtherDerived>& other,
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
-                                                             const RealScalar& prec) const {
+  const DenseBase<OtherDerived>& other,
  const RealScalar& prec
 ) const
 {
  return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
 }
--- a/Eigen/src/Core/GeneralProduct.h
+++ b/Eigen/src/Core/GeneralProduct.h
@@ -11,33 +11,23 @@
 #ifndef EIGEN_GENERAL_PRODUCT_H
 #define EIGEN_GENERAL_PRODUCT_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
-enum { Large = 2, Small = 3 };
+enum {
-
+  Large = 2,
-// Define the threshold value to fallback from the generic matrix-matrix product
+  Small = 3
-// implementation (heavy) to the lightweight coeff-based product one.
+};
 // See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
 // in products/GeneralMatrixMatrix.h for more details.
 // TODO This threshold should also be used in the compile-time selector below.
 #ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
 // This default value has been obtained on a Haswell architecture.
 #define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
 #endif
 namespace internal {
-template <int Rows, int Cols, int Depth>
+template<int Rows, int Cols, int Depth> struct product_type_selector;
 struct product_type_selector;
-template <int Size, int MaxSize>
+template<int Size, int MaxSize> struct product_size_category
-struct product_size_category {
+{
  enum {
-#ifndef EIGEN_GPU_COMPILE_PHASE
+    #ifndef EIGEN_CUDA_ARCH
-    is_large = MaxSize == Dynamic || Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
+    is_large = MaxSize == Dynamic ||
               Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
               (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
    #else
    is_large = 0,
@@ -48,17 +38,19 @@ struct product_size_category {
  };
 };
-template <typename Lhs, typename Rhs>
+template<typename Lhs, typename Rhs> struct product_type
-struct product_type {
+{
-  typedef remove_all_t<Lhs> Lhs_;
+  typedef typename remove_all<Lhs>::type _Lhs;
-  typedef remove_all_t<Rhs> Rhs_;
+  typedef typename remove_all<Rhs>::type _Rhs;
  enum {
-    MaxRows = traits<Lhs_>::MaxRowsAtCompileTime,
+    MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,
-    Rows = traits<Lhs_>::RowsAtCompileTime,
+    Rows    = traits<_Lhs>::RowsAtCompileTime,
-    MaxCols = traits<Rhs_>::MaxColsAtCompileTime,
+    MaxCols = traits<_Rhs>::MaxColsAtCompileTime,
-    Cols = traits<Rhs_>::ColsAtCompileTime,
+    Cols    = traits<_Rhs>::ColsAtCompileTime,
-    MaxDepth = min_size_prefer_fixed(traits<Lhs_>::MaxColsAtCompileTime, traits<Rhs_>::MaxRowsAtCompileTime),
+    MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,
-    Depth = min_size_prefer_fixed(traits<Lhs_>::ColsAtCompileTime, traits<Rhs_>::RowsAtCompileTime)
+                                           traits<_Rhs>::MaxRowsAtCompileTime),
    Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,
                                        traits<_Rhs>::RowsAtCompileTime)
  };
  // the splitting into different lines of code here, introducing the _select enums and the typedef below,
@@ -72,9 +64,13 @@ struct product_type {
  typedef product_type_selector<rows_select, cols_select, depth_select> selector;
 public:
-  enum { value = selector::ret, ret = selector::ret };
+  enum {
    value = selector::ret,
    ret = selector::ret
  };
 #ifdef EIGEN_DEBUG_PRODUCT
-  static void debug() {
+  static void debug()
  {
      EIGEN_DEBUG_VAR(Rows);
      EIGEN_DEBUG_VAR(Cols);
      EIGEN_DEBUG_VAR(Depth);
@@ -90,102 +86,30 @@ struct product_type {
 * 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>
+template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
-struct product_type_selector<M, N, 1> {
+template<int M>         struct product_type_selector<M, 1, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
-  enum { ret = OuterProduct };
+template<int N>         struct product_type_selector<1, N, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
-};
+template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
-template <int M>
+template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
-struct product_type_selector<M, 1, 1> {
+template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
-  enum { ret = LazyCoeffBasedProductMode };
+template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
-};
+template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
-template <int N>
+template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
-struct product_type_selector<1, N, 1> {
+template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
-  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 <int Depth>
+template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
-struct product_type_selector<1, 1, Depth> {
+template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
-  enum { ret = InnerProduct };
+template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
-};
+template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
-template <>
+template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
-struct product_type_selector<1, 1, 1> {
+template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
-  enum { ret = InnerProduct };
+template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
-};
+template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
-template <>
+template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
-struct product_type_selector<Small, 1, Small> {
+template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
-  enum { ret = CoeffBasedProductMode };
+template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = CoeffBasedProductMode }; };
-};
+template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
 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 = CoeffBasedProductMode };
 };
 template <>
 struct product_type_selector<Small, Large, Small> {
  enum { ret = CoeffBasedProductMode };
 };
 template <>
 struct product_type_selector<Large, Large, Small> {
  enum { ret = GemmProduct };
 };
 } // end namespace internal
@@ -224,129 +148,141 @@ struct gemv_dense_selector;
 namespace internal {
-template <typename Scalar, int Size, int MaxSize, bool Cond>
+template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
 struct gemv_static_vector_if;
 template<typename Scalar,int Size,int MaxSize>
-struct gemv_static_vector_if<Scalar, Size, MaxSize, false> {
+struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Scalar* data() {
+{
-    eigen_internal_assert(false && "should never be called");
+  EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
    return 0;
  }
 };
 template<typename Scalar,int Size>
-struct gemv_static_vector_if<Scalar, Size, Dynamic, true> {
+struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Scalar* data() { return 0; }
+{
  EIGEN_STRONG_INLINE Scalar* data() { return 0; }
 };
 template<typename Scalar,int Size,int MaxSize>
-struct gemv_static_vector_if<Scalar, Size, MaxSize, true> {
+struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
 {
  enum {
    ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
    PacketSize      = internal::packet_traits<Scalar>::size
  };
  #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
-  internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize), 0, AlignedMax> m_data;
+  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;
-  EIGEN_STRONG_INLINE constexpr Scalar* data() { return m_data.array; }
+  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.
-  internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize) + EIGEN_MAX_ALIGN_BYTES, 0> m_data;
+  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
-  EIGEN_STRONG_INLINE constexpr Scalar* data() {
+  EIGEN_STRONG_INLINE Scalar* data() {
-    return reinterpret_cast<Scalar*>((std::uintptr_t(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES - 1))) +
+    return ForceAlignment
-                                     EIGEN_MAX_ALIGN_BYTES);
+            ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
            : m_data.array;
  }
  #endif
 };
 // The vector is on the left => transposition
 template<int StorageOrder, bool BlasCompatible>
-struct gemv_dense_selector<OnTheLeft, StorageOrder, BlasCompatible> {
+struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
 {
  template<typename Lhs, typename Rhs, typename Dest>
-  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
+  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
  {
    Transpose<Dest> destT(dest);
    enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
-    gemv_dense_selector<OnTheRight, OtherStorageOrder, BlasCompatible>::run(rhs.transpose(), lhs.transpose(), destT,
+    gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
-                                                                            alpha);
+      ::run(rhs.transpose(), lhs.transpose(), destT, alpha);
  }
 };
-template <>
+template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
-struct gemv_dense_selector<OnTheRight, ColMajor, true> {
+{
  template<typename Lhs, typename Rhs, typename Dest>
-  static inline void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
+  static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
  {
    typedef typename Lhs::Scalar   LhsScalar;
    typedef typename Rhs::Scalar   RhsScalar;
    typedef typename Dest::Scalar  ResScalar;
    typedef typename Dest::RealScalar  RealScalar;
    typedef internal::blas_traits<Lhs> LhsBlasTraits;
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef internal::blas_traits<Rhs> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
-    typedef Map<Matrix<ResScalar, Dynamic, 1>, plain_enum_min(AlignedMax, internal::packet_traits<ResScalar>::size)>
+    typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
        MappedDest;
    ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
    ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
-    ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
+    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
                                  * RhsBlasTraits::extractScalarFactor(rhs);
    // make sure Dest is a compile-time vector type (bug 1166)
-    typedef std::conditional_t<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr> ActualDest;
+    typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
    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 = (ActualDest::InnerStrideAtCompileTime==1),
      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
-      MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime != 0)
+      MightCannotUseDest = (!EvalToDestAtCompileTime) || ComplexByReal
    };
    typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
    typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
    RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
-    if (!MightCannotUseDest) {
+    if(!MightCannotUseDest)
    {
      // shortcut if we are sure to be able to use dest directly,
      // this ease the compiler to generate cleaner and more optimzized code for most common cases
-      general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
+      general_matrix_vector_product
-                                    RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
+          <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
-                                                                                    LhsMapper(actualLhs.data(),
+          actualLhs.rows(), actualLhs.cols(),
-                                                                                              actualLhs.outerStride()),
+          LhsMapper(actualLhs.data(), actualLhs.outerStride()),
-                                                                                    RhsMapper(actualRhs.data(),
+          RhsMapper(actualRhs.data(), actualRhs.innerStride()),
-                                                                                              actualRhs.innerStride()),
+          dest.data(), 1,
-                                                                                    dest.data(), 1, compatibleAlpha);
+          compatibleAlpha);
-    } else {
+    }
-      gemv_static_vector_if<ResScalar, ActualDest::SizeAtCompileTime, ActualDest::MaxSizeAtCompileTime,
+    else
-                            MightCannotUseDest>
+    {
-          static_dest;
+      gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
-      const bool alphaIsCompatible = (!ComplexByReal) || (numext::is_exactly_zero(numext::imag(actualAlpha)));
+      const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
      const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
      ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
                                                    evalToDest ? dest.data() : static_dest.data());
-      if (!evalToDest) {
+      if(!evalToDest)
      {
        #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        constexpr int Size = Dest::SizeAtCompileTime;
        Index size = dest.size();
        EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        #endif
-        if (!alphaIsCompatible) {
+        if(!alphaIsCompatible)
        {
          MappedDest(actualDestPtr, dest.size()).setZero();
          compatibleAlpha = RhsScalar(1);
-        } else
+        }
        else
          MappedDest(actualDestPtr, dest.size()) = dest;
      }
-      general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
+      general_matrix_vector_product
-                                    RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
+          <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
-                                                                                    LhsMapper(actualLhs.data(),
+          actualLhs.rows(), actualLhs.cols(),
-                                                                                              actualLhs.outerStride()),
+          LhsMapper(actualLhs.data(), actualLhs.outerStride()),
-                                                                                    RhsMapper(actualRhs.data(),
+          RhsMapper(actualRhs.data(), actualRhs.innerStride()),
-                                                                                              actualRhs.innerStride()),
+          actualDestPtr, 1,
-                                                                                    actualDestPtr, 1, compatibleAlpha);
+          compatibleAlpha);
-      if (!evalToDest) {
+      if (!evalToDest)
      {
        if(!alphaIsCompatible)
          dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
        else
@@ -356,10 +292,11 @@ struct gemv_dense_selector<OnTheRight, ColMajor, true> {
  }
 };
-template <>
+template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
-struct gemv_dense_selector<OnTheRight, RowMajor, true> {
+{
  template<typename Lhs, typename Rhs, typename Dest>
-  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
+  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
  {
    typedef typename Lhs::Scalar   LhsScalar;
    typedef typename Rhs::Scalar   RhsScalar;
    typedef typename Dest::Scalar  ResScalar;
@@ -368,31 +305,28 @@ struct gemv_dense_selector<OnTheRight, RowMajor, true> {
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef internal::blas_traits<Rhs> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
-    typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+    typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
-    std::add_const_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
+    typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
-    std::add_const_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);
+    typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
-    ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
+    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
                                  * RhsBlasTraits::extractScalarFactor(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 =
+      DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1
          ActualRhsTypeCleaned::InnerStrideAtCompileTime == 1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime == 0
    };
-    gemv_static_vector_if<RhsScalar, ActualRhsTypeCleaned::SizeAtCompileTime,
+    gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
                          ActualRhsTypeCleaned::MaxSizeAtCompileTime, !DirectlyUseRhs>
        static_rhs;
-    ei_declare_aligned_stack_constructed_variable(
+    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
        RhsScalar, actualRhsPtr, actualRhs.size(),
        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
-    if (!DirectlyUseRhs) {
+    if(!DirectlyUseRhs)
    {
      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
      constexpr int Size = ActualRhsTypeCleaned::SizeAtCompileTime;
      Index size = actualRhs.size();
      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
      #endif
@@ -401,36 +335,36 @@ struct gemv_dense_selector<OnTheRight, RowMajor, true> {
    typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
    typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
-    general_matrix_vector_product<Index, LhsScalar, LhsMapper, RowMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
+    general_matrix_vector_product
-                                  RhsMapper, RhsBlasTraits::NeedToConjugate>::
+        <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
-        run(actualLhs.rows(), actualLhs.cols(), LhsMapper(actualLhs.data(), actualLhs.outerStride()),
+        actualLhs.rows(), actualLhs.cols(),
-            RhsMapper(actualRhsPtr, 1), dest.data(),
+        LhsMapper(actualLhs.data(), actualLhs.outerStride()),
-            dest.col(0).innerStride(),  // NOTE  if dest is not a vector at compile-time, then dest.innerStride() might
+        RhsMapper(actualRhsPtr, 1),
-                                        // be wrong. (bug 1166)
+        dest.data(), dest.col(0).innerStride(), //NOTE  if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
        actualAlpha);
  }
 };
-template <>
+template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
-struct gemv_dense_selector<OnTheRight, ColMajor, false> {
+{
  template<typename Lhs, typename Rhs, typename Dest>
-  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
+  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
-    EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
+  {
-                        EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
+    EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
-    // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory,
+    // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
    // otherwise use a temp
    typename nested_eval<Rhs,1>::type actual_rhs(rhs);
    const Index size = rhs.rows();
-    for (Index k = 0; k < size; ++k) dest += (alpha * actual_rhs.coeff(k)) * lhs.col(k);
+    for(Index k=0; k<size; ++k)
      dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
  }
 };
-template <>
+template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
-struct gemv_dense_selector<OnTheRight, RowMajor, false> {
+{
  template<typename Lhs, typename Rhs, typename Dest>
-  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
+  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
-    EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
+  {
-                        EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
+    EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
    typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
    const Index rows = dest.rows();
    for(Index i=0; i<rows; ++i)
@@ -452,23 +386,24 @@ struct gemv_dense_selector<OnTheRight, RowMajor, false> {
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived> MatrixBase<Derived>::operator*(
+EIGEN_DEVICE_FUNC inline const Product<Derived, OtherDerived>
-    const MatrixBase<OtherDerived>& other) const {
+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 ||
+    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
-                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
+                   || 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(
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
      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)
@@ -493,19 +428,20 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived> Matri
  */
 template<typename Derived>
 template<typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived, LazyProduct>
+EIGEN_DEVICE_FUNC const Product<Derived,OtherDerived,LazyProduct>
-MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived>& other) const {
+MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
 {
  enum {
-    ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
+    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
-                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
+                   || 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(
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
      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)
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -14,22 +14,22 @@
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 #define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
-  /** \returns an expression of the coefficient-wise DOC_OP of \a x                                             \
+  /** \returns an expression of the coefficient-wise DOC_OP of \a x
-                                                                                                              \ \
+
-    DOC_DETAILS                                                                                                 \
+    DOC_DETAILS
-                                                                                                              \ \
+
-    \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp   \
+    \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
    */ \
  template<typename Derived> \
-  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> NAME(     \
+  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
-      const Eigen::ArrayBase<Derived>& x);
+  NAME(const Eigen::ArrayBase<Derived>& x);
 #else
 #define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
  template<typename Derived> \
-  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(NAME)(    \
+  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
-      const Eigen::ArrayBase<Derived>& x) {                                                                     \
+  (NAME)(const Eigen::ArrayBase<Derived>& x) { \
    return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
  }
@@ -38,20 +38,21 @@
 #define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
  \
  template<typename Derived> \
-  struct NAME##_retval<ArrayBase<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> > {                                                                    \
+  struct NAME##_impl<ArrayBase<Derived> > \
-    static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) {  \
+  { \
    static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
    { \
      return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
    } \
  };
-// IWYU pragma: private
+namespace Eigen
-#include "./InternalHeaderCheck.h"
+{
 namespace Eigen {
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
@@ -65,64 +66,32 @@ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos, scalar_acos_op, arc - consine,\sa ArrayBa
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh, scalar_asinh_op, inverse hyperbolic sine,\sa ArrayBase::asinh)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh, scalar_acosh_op, inverse hyperbolic cosine,\sa ArrayBase::acosh)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh, scalar_atanh_op, inverse hyperbolic tangent,\sa ArrayBase::atanh)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic, scalar_logistic_op, logistic function,\sa ArrayBase::logistic)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma, scalar_lgamma_op,
                                 natural logarithm of the gamma function,\sa ArrayBase::lgamma)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri, scalar_ndtri_op, inverse normal distribution function,\sa ArrayBase::ndtri)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp2, scalar_exp2_op, exponential,\sa ArrayBase::exp2)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1, scalar_expm1_op, exponential of a value minus 1,\sa ArrayBase::expm1)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10, scalar_log10_op, base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2, scalar_log2_op, base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2, scalar_abs2_op,
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
-                                 squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg, scalar_arg_op, complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(carg, scalar_carg_op,
                                 complex argument, \sa ArrayBase::carg DOXCOMMA MatrixBase::cwiseCArg)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cbrt, scalar_cbrt_op, cube root,\sa ArrayBase::cbrt DOXCOMMA MatrixBase::cwiseCbrt)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square, scalar_square_op,
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
                                 square(power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint, scalar_rint_op,
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
-                                 nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round, scalar_round_op,
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
-                                 nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
-EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
-    floor, scalar_floor_op, nearest integer not greater than the given value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
    ceil, scalar_ceil_op, nearest integer not less than the given value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(trunc, scalar_trunc_op,
                                 nearest integer not greater in magnitude than the given value,\sa Eigen::trunc DOXCOMMA
                                     ArrayBase::trunc)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
    isnan, scalar_isnan_op, not -a - number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
    isinf, scalar_isinf_op, infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite, scalar_isfinite_op,
                                 finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)
 template <typename Derived, typename ScalarExponent>
 using GlobalUnaryPowReturnType = std::enable_if_t<
    !internal::is_arithmetic<typename NumTraits<Derived>::Real>::value &&
        internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
    CwiseUnaryOp<internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>, const Derived> >;
  /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
    *
- * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given
+    * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression (\c Derived::Scalar).
 * expression (\c Derived::Scalar).
    *
    * \sa ArrayBase::pow()
    *
@@ -130,14 +99,20 @@ using GlobalUnaryPowReturnType = std::enable_if_t<
    */
 #ifdef EIGEN_PARSED_BY_DOXYGEN
  template<typename Derived,typename ScalarExponent>
-EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(const Eigen::ArrayBase<Derived>& x,
+  inline const CwiseBinaryOp<internal::scalar_pow_op<Derived::Scalar,ScalarExponent>,Derived,Constant<ScalarExponent> >
-                                                                                     const ScalarExponent& exponent);
+  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
 #else
  template<typename Derived,typename ScalarExponent>
-EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(const Eigen::ArrayBase<Derived>& x,
+  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,typename Derived::Scalar,ScalarExponent),
-                                                                                     const ScalarExponent& exponent) {
+          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type
-  return GlobalUnaryPowReturnType<Derived, ScalarExponent>(
+  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
-      x.derived(), internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>(exponent));
+    return x.derived().pow(exponent);
  }
  template<typename Derived>
  inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename Derived::Scalar,pow)
  pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
    return x.derived().pow(exponent);
  }
 #endif
@@ -153,21 +128,20 @@ EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent>
    * \relates ArrayBase
    */
  template<typename Derived,typename ExponentDerived>
-inline const Eigen::CwiseBinaryOp<
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
-    Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived,
+  pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents) 
-    const ExponentDerived>
+  {
-pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents) {
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
-  return Eigen::CwiseBinaryOp<
+      x.derived(),
-      Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived,
+      exponents.derived()
-      const ExponentDerived>(x.derived(), exponents.derived());
+    );
  }
  /** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
    *
    * This function computes the coefficient-wise power between a scalar and an array of exponents.
    *
- * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression
+    * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
 * (\c Derived::Scalar).
    *
    * Example: \include Cwise_scalar_power_array.cpp
    * Output: \verbinclude Cwise_scalar_power_array.out
@@ -178,53 +152,36 @@ pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>&
    */
 #ifdef EIGEN_PARSED_BY_DOXYGEN
  template<typename Scalar,typename Derived>
-inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar, Derived::Scalar>, Constant<Scalar>, Derived> pow(
+  inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
-    const Scalar& x, const Eigen::ArrayBase<Derived>& x);
+  pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
 #else
  template<typename Scalar, typename Derived>
-EIGEN_DEVICE_FUNC inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(
+  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar),
-    typename internal::promote_scalar_arg<typename Derived::Scalar EIGEN_COMMA Scalar EIGEN_COMMA
+          const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type
-                                              EIGEN_SCALAR_BINARY_SUPPORTED(pow, Scalar,
+  pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
-                                                                            typename Derived::Scalar)>::type,
+  {
-    Derived, pow) pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow)(
-  typedef
+            typename internal::plain_constant_type<Derived,Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
-      typename internal::promote_scalar_arg<typename Derived::Scalar, Scalar,
+  }
-                                            EIGEN_SCALAR_BINARY_SUPPORTED(pow, Scalar, typename Derived::Scalar)>::type
+
-          PromotedScalar;
+  template<typename Derived>
-  return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar, Derived, pow)(
+  inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)
-      typename internal::plain_constant_type<Derived, PromotedScalar>::type(
+  pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
-          exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)),
+  {
-      exponents.derived());
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)(
      typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
  }
 #endif
 /** \returns an expression of the coefficient-wise atan2(\a x, \a y). \a x and \a y must be of the same type.
 *
 * This function computes the coefficient-wise atan2().
 *
 * \sa ArrayBase::atan2()
 *
 * \relates ArrayBase
 */
 template <typename LhsDerived, typename RhsDerived>
 inline const std::enable_if_t<
    std::is_same<typename LhsDerived::Scalar, typename RhsDerived::Scalar>::value,
    Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>,
                         const LhsDerived, const RhsDerived> >
 atan2(const Eigen::ArrayBase<LhsDerived>& x, const Eigen::ArrayBase<RhsDerived>& exponents) {
  return Eigen::CwiseBinaryOp<
      Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived,
      const RhsDerived>(x.derived(), exponents.derived());
 }
-namespace internal {
+  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(abs2,scalar_abs2_op)
-}  // namespace internal
+  }
-}  // namespace Eigen
+}
-// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random,
+// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
 // internal::isApprox...)
 #endif // EIGEN_GLOBAL_FUNCTIONS_H
--- a/Eigen/src/Core/IO.h
+++ b/Eigen/src/Core/IO.h
@@ -11,13 +11,11 @@
 #ifndef EIGEN_IO_H
 #define EIGEN_IO_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 enum { DontAlignCols = 1 };
-enum { StreamPrecision = -1, FullPrecision = -2 };
+enum { StreamPrecision = -1,
       FullPrecision = -2 };
 namespace internal {
 template<typename Derived>
@@ -30,46 +28,42 @@ std::ostream& print_matrix(std::ostream& s, const Derived& _m, const IOFormat& f
  * \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
+  *  - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
- * FullPrecision. The default is the special value \c StreamPrecision which means to use the stream's own precision
+  *                 The default is the special value \c StreamPrecision which means to use the
- * setting, as set for instance using \c cout.precision(3). The other special value \c FullPrecision means that the
+  *                 stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
- * number of digits will be computed to match the full precision of each floating-point type.
+  *                 \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
- *  - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c
+  *                 type.
- * DontAlignCols which allows to disable the alignment of columns, resulting in faster code.
+  *  - \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
 *  - \b fill character printed to fill the empty space in aligned columns
  *
  * Example: \include IOFormat.cpp
  * Output: \verbinclude IOFormat.out
  *
  * \sa DenseBase::format(), class WithFormat
  */
-struct IOFormat {
+struct IOFormat
 {
  /** Default constructor, see class IOFormat for the meaning of the parameters */
-  IOFormat(int _precision = StreamPrecision, int _flags = 0, const std::string& _coeffSeparator = " ",
+  IOFormat(int _precision = StreamPrecision, int _flags = 0,
-           const std::string& _rowSeparator = "\n", const std::string& _rowPrefix = "",
+    const std::string& _coeffSeparator = " ",
-           const std::string& _rowSuffix = "", const std::string& _matPrefix = "", const std::string& _matSuffix = "",
+    const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
-           const char _fill = ' ')
+    const std::string& _matPrefix="", const std::string& _matSuffix="")
-      : matPrefix(_matPrefix),
+  : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
-        matSuffix(_matSuffix),
+    rowSpacer(""), coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
-        rowPrefix(_rowPrefix),
+  {
        rowSuffix(_rowSuffix),
        rowSeparator(_rowSeparator),
        rowSpacer(""),
        coeffSeparator(_coeffSeparator),
        fill(_fill),
        precision(_precision),
        flags(_flags) {
    // TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline
    // don't add rowSpacer if columns are not to be aligned
-    if ((flags & DontAlignCols)) return;
+    if((flags & DontAlignCols))
-    int i = int(matPrefix.length()) - 1;
+      return;
-    while (i >= 0 && matPrefix[i] != '\n') {
+    int i = int(matSuffix.length())-1;
    while (i>=0 && matSuffix[i]!='\n')
    {
      rowSpacer += ' ';
      i--;
    }
@@ -77,7 +71,6 @@ struct IOFormat {
  std::string matPrefix, matSuffix;
  std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
  std::string coeffSeparator;
  char fill;
  int precision;
  int flags;
 };
@@ -98,11 +91,16 @@ struct IOFormat {
  * \sa DenseBase::format(), class IOFormat
  */
 template<typename ExpressionType>
-class WithFormat {
+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) {
+    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);
    }
@@ -115,47 +113,50 @@ namespace internal {
 // NOTE: This helper is kept for backward compatibility with previous code specializing
 //       this internal::significant_decimals_impl structure. In the future we should directly
-//       call max_digits10().
+//       call digits10() which has been introduced in July 2016 in 3.3.
 template<typename Scalar>
-struct significant_decimals_impl {
+struct significant_decimals_impl
-  static inline int run() { return NumTraits<Scalar>::max_digits10(); }
+{
  static inline int run()
  {
    return NumTraits<Scalar>::digits10();
  }
 };
 /** \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) {
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
-  using internal::is_same;
+{
-
+  if(_m.size() == 0)
-  if (_m.size() == 0) {
+  {
    s << fmt.matPrefix << fmt.matSuffix;
    return s;
  }
  typename Derived::Nested m = _m;
  typedef typename Derived::Scalar Scalar;
  typedef std::conditional_t<is_same<Scalar, char>::value || is_same<Scalar, unsigned char>::value ||
                                 is_same<Scalar, numext::int8_t>::value || is_same<Scalar, numext::uint8_t>::value,
                             int,
                             std::conditional_t<is_same<Scalar, std::complex<char> >::value ||
                                                    is_same<Scalar, std::complex<unsigned char> >::value ||
                                                    is_same<Scalar, std::complex<numext::int8_t> >::value ||
                                                    is_same<Scalar, std::complex<numext::uint8_t> >::value,
                                                std::complex<int>, const Scalar&> >
      PrintType;
  Index width = 0;
  std::streamsize explicit_precision;
-  if (fmt.precision == StreamPrecision) {
+  if(fmt.precision == StreamPrecision)
  {
    explicit_precision = 0;
-  } else if (fmt.precision == FullPrecision) {
+  }
-    if (NumTraits<Scalar>::IsInteger) {
+  else if(fmt.precision == FullPrecision)
  {
    if (NumTraits<Scalar>::IsInteger)
    {
      explicit_precision = 0;
-    } else {
+    }
    else
    {
      explicit_precision = significant_decimals_impl<Scalar>::run();
    }
-  } else {
+  }
  else
  {
    explicit_precision = fmt.precision;
  }
@@ -163,44 +164,38 @@ std::ostream& print_matrix(std::ostream& s, const Derived& _m, const IOFormat& f
  if(explicit_precision) old_precision = s.precision(explicit_precision);
  bool align_cols = !(fmt.flags & DontAlignCols);
-  if (align_cols) {
+  if(align_cols)
  {
    // compute the largest width
    for(Index j = 0; j < m.cols(); ++j)
-      for (Index i = 0; i < m.rows(); ++i) {
+      for(Index i = 0; i < m.rows(); ++i)
      {
        std::stringstream sstr;
        sstr.copyfmt(s);
-        sstr << static_cast<PrintType>(m.coeff(i, j));
+        sstr << m.coeff(i,j);
        width = std::max<Index>(width, Index(sstr.str().length()));
      }
  }
  std::streamsize old_width = s.width();
  char old_fill_character = s.fill();
  s << fmt.matPrefix;
-  for (Index i = 0; i < m.rows(); ++i) {
+  for(Index i = 0; i < m.rows(); ++i)
-    if (i) s << fmt.rowSpacer;
+  {
    if (i)
      s << fmt.rowSpacer;
    s << fmt.rowPrefix;
-    if (width) {
+    if(width) s.width(width);
-      s.fill(fmt.fill);
+    s << m.coeff(i, 0);
-      s.width(width);
+    for(Index j = 1; j < m.cols(); ++j)
-    }
+    {
    s << static_cast<PrintType>(m.coeff(i, 0));
    for (Index j = 1; j < m.cols(); ++j) {
      s << fmt.coeffSeparator;
-      if (width) {
+      if (width) s.width(width);
-        s.fill(fmt.fill);
+      s << m.coeff(i, j);
        s.width(width);
      }
      s << static_cast<PrintType>(m.coeff(i, j));
    }
    s << fmt.rowSuffix;
-    if (i < m.rows() - 1) s << fmt.rowSeparator;
+    if( i < m.rows() - 1)
      s << fmt.rowSeparator;
  }
  s << fmt.matSuffix;
  if(explicit_precision) s.precision(old_precision);
  if (width) {
    s.fill(old_fill_character);
    s.width(old_width);
  }
  return s;
 }
@@ -213,21 +208,18 @@ std::ostream& print_matrix(std::ostream& s, const Derived& _m, const IOFormat& f
  * 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
+  * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
 * parameters.
  *
  * \sa DenseBase::format()
  */
 template<typename Derived>
-std::ostream& operator<<(std::ostream& s, const DenseBase<Derived>& m) {
+std::ostream & operator <<
 (std::ostream & s,
 const DenseBase<Derived> & m)
 {
  return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
 }
 template <typename Derived>
 std::ostream& operator<<(std::ostream& s, const DiagonalBase<Derived>& m) {
  return internal::print_matrix(s, m.derived(), EIGEN_DEFAULT_IO_FORMAT);
 }
 } // end namespace Eigen
 #endif // EIGEN_IO_H
--- a/Eigen/src/Core/IndexedView.h
+++ b/Eigen/src/Core/IndexedView.h
@@ -1,321 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_INDEXED_VIEW_H
 #define EIGEN_INDEXED_VIEW_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 template <typename XprType, typename RowIndices, typename ColIndices>
 struct traits<IndexedView<XprType, RowIndices, ColIndices>> : traits<XprType> {
  enum {
    RowsAtCompileTime = int(IndexedViewHelper<RowIndices>::SizeAtCompileTime),
    ColsAtCompileTime = int(IndexedViewHelper<ColIndices>::SizeAtCompileTime),
    MaxRowsAtCompileTime = RowsAtCompileTime,
    MaxColsAtCompileTime = ColsAtCompileTime,
    XprTypeIsRowMajor = (int(traits<XprType>::Flags) & RowMajorBit) != 0,
    IsRowMajor = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1)   ? 1
                 : (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
                                                                            : XprTypeIsRowMajor,
    RowIncr = int(IndexedViewHelper<RowIndices>::IncrAtCompileTime),
    ColIncr = int(IndexedViewHelper<ColIndices>::IncrAtCompileTime),
    InnerIncr = IsRowMajor ? ColIncr : RowIncr,
    OuterIncr = IsRowMajor ? RowIncr : ColIncr,
    HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
    XprInnerStride = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time<XprType>::ret)
                                                  : int(outer_stride_at_compile_time<XprType>::ret),
    XprOuterstride = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType>::ret)
                                                  : int(inner_stride_at_compile_time<XprType>::ret),
    InnerSize = XprTypeIsRowMajor ? ColsAtCompileTime : RowsAtCompileTime,
    IsBlockAlike = InnerIncr == 1 && OuterIncr == 1,
    IsInnerPannel = HasSameStorageOrderAsXprType &&
                    is_same<AllRange<InnerSize>, std::conditional_t<XprTypeIsRowMajor, ColIndices, RowIndices>>::value,
    InnerStrideAtCompileTime =
        InnerIncr < 0 || InnerIncr == DynamicIndex || XprInnerStride == Dynamic || InnerIncr == Undefined
            ? Dynamic
            : XprInnerStride * InnerIncr,
    OuterStrideAtCompileTime =
        OuterIncr < 0 || OuterIncr == DynamicIndex || XprOuterstride == Dynamic || OuterIncr == Undefined
            ? Dynamic
            : XprOuterstride * OuterIncr,
    ReturnAsScalar = is_single_range<RowIndices>::value && is_single_range<ColIndices>::value,
    ReturnAsBlock = (!ReturnAsScalar) && IsBlockAlike,
    ReturnAsIndexedView = (!ReturnAsScalar) && (!ReturnAsBlock),
    // FIXME we deal with compile-time strides if and only if we have DirectAccessBit flag,
    // but this is too strict regarding negative strides...
    DirectAccessMask = (int(InnerIncr) != Undefined && int(OuterIncr) != Undefined && InnerIncr >= 0 && OuterIncr >= 0)
                           ? DirectAccessBit
                           : 0,
    FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
    FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
    Flags = (traits<XprType>::Flags & (HereditaryBits | DirectAccessMask)) | FlagsLvalueBit | FlagsRowMajorBit |
            FlagsLinearAccessBit
  };
  typedef Block<XprType, RowsAtCompileTime, ColsAtCompileTime, IsInnerPannel> BlockType;
 };
 template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind, bool DirectAccess>
 class IndexedViewImpl;
 }  // namespace internal
 /** \class IndexedView
 * \ingroup Core_Module
 *
 * \brief Expression of a non-sequential sub-matrix defined by arbitrary sequences of row and column indices
 *
 * \tparam XprType the type of the expression in which we are taking the intersections of sub-rows and sub-columns
 * \tparam RowIndices the type of the object defining the sequence of row indices
 * \tparam ColIndices the type of the object defining the sequence of column indices
 *
 * This class represents an expression of a sub-matrix (or sub-vector) defined as the intersection
 * of sub-sets of rows and columns, that are themself defined by generic sequences of row indices \f$
 * \{r_0,r_1,..r_{m-1}\} \f$ and column indices \f$ \{c_0,c_1,..c_{n-1} \}\f$. Let \f$ A \f$  be the nested matrix, then
 * the resulting matrix \f$ B \f$ has \c m rows and \c n columns, and its entries are given by: \f$ B(i,j) = A(r_i,c_j)
 * \f$.
 *
 * The \c RowIndices and \c ColIndices types must be compatible with the following API:
 * \code
 * <integral type> operator[](Index) const;
 * Index size() const;
 * \endcode
 *
 * Typical supported types thus include:
 *  - std::vector<int>
 *  - std::valarray<int>
 *  - std::array<int>
 *  - Eigen::ArrayXi
 *  - decltype(ArrayXi::LinSpaced(...))
 *  - Any view/expressions of the previous types
 *  - Eigen::ArithmeticSequence
 *  - Eigen::internal::AllRange     (helper for Eigen::placeholders::all)
 *  - Eigen::internal::SingleRange  (helper for single index)
 *  - etc.
 *
 * In typical usages of %Eigen, this class should never be used directly. It is the return type of
 * DenseBase::operator()(const RowIndices&, const ColIndices&).
 *
 * \sa class Block
 */
 template <typename XprType, typename RowIndices, typename ColIndices>
 class IndexedView
    : public internal::IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind,
                                       (internal::traits<IndexedView<XprType, RowIndices, ColIndices>>::Flags &
                                        DirectAccessBit) != 0> {
 public:
  typedef typename internal::IndexedViewImpl<
      XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind,
      (internal::traits<IndexedView<XprType, RowIndices, ColIndices>>::Flags & DirectAccessBit) != 0>
      Base;
  EIGEN_GENERIC_PUBLIC_INTERFACE(IndexedView)
  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedView)
  template <typename T0, typename T1>
  IndexedView(XprType& xpr, const T0& rowIndices, const T1& colIndices) : Base(xpr, rowIndices, colIndices) {}
 };
 namespace internal {
 // Generic API dispatcher
 template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind, bool DirectAccess>
 class IndexedViewImpl : public internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices>>::type {
 public:
  typedef typename internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices>>::type Base;
  typedef typename internal::ref_selector<XprType>::non_const_type MatrixTypeNested;
  typedef internal::remove_all_t<XprType> NestedExpression;
  typedef typename XprType::Scalar Scalar;
  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedViewImpl)
  template <typename T0, typename T1>
  IndexedViewImpl(XprType& xpr, const T0& rowIndices, const T1& colIndices)
      : m_xpr(xpr), m_rowIndices(rowIndices), m_colIndices(colIndices) {}
  /** \returns number of rows */
  Index rows() const { return IndexedViewHelper<RowIndices>::size(m_rowIndices); }
  /** \returns number of columns */
  Index cols() const { return IndexedViewHelper<ColIndices>::size(m_colIndices); }
  /** \returns the nested expression */
  const internal::remove_all_t<XprType>& nestedExpression() const { return m_xpr; }
  /** \returns the nested expression */
  std::remove_reference_t<XprType>& nestedExpression() { return m_xpr; }
  /** \returns a const reference to the object storing/generating the row indices */
  const RowIndices& rowIndices() const { return m_rowIndices; }
  /** \returns a const reference to the object storing/generating the column indices */
  const ColIndices& colIndices() const { return m_colIndices; }
  constexpr Scalar& coeffRef(Index rowId, Index colId) {
    return nestedExpression().coeffRef(m_rowIndices[rowId], m_colIndices[colId]);
  }
  constexpr const Scalar& coeffRef(Index rowId, Index colId) const {
    return nestedExpression().coeffRef(m_rowIndices[rowId], m_colIndices[colId]);
  }
 protected:
  MatrixTypeNested m_xpr;
  RowIndices m_rowIndices;
  ColIndices m_colIndices;
 };
 template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
 class IndexedViewImpl<XprType, RowIndices, ColIndices, StorageKind, true>
    : public IndexedViewImpl<XprType, RowIndices, ColIndices, StorageKind, false> {
 public:
  using Base = internal::IndexedViewImpl<XprType, RowIndices, ColIndices,
                                         typename internal::traits<XprType>::StorageKind, false>;
  using Derived = IndexedView<XprType, RowIndices, ColIndices>;
  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedViewImpl)
  template <typename T0, typename T1>
  IndexedViewImpl(XprType& xpr, const T0& rowIndices, const T1& colIndices) : Base(xpr, rowIndices, colIndices) {}
  Index rowIncrement() const {
    if (traits<Derived>::RowIncr != DynamicIndex && traits<Derived>::RowIncr != Undefined) {
      return traits<Derived>::RowIncr;
    }
    return IndexedViewHelper<RowIndices>::incr(this->rowIndices());
  }
  Index colIncrement() const {
    if (traits<Derived>::ColIncr != DynamicIndex && traits<Derived>::ColIncr != Undefined) {
      return traits<Derived>::ColIncr;
    }
    return IndexedViewHelper<ColIndices>::incr(this->colIndices());
  }
  Index innerIncrement() const { return traits<Derived>::IsRowMajor ? colIncrement() : rowIncrement(); }
  Index outerIncrement() const { return traits<Derived>::IsRowMajor ? rowIncrement() : colIncrement(); }
  std::decay_t<typename XprType::Scalar>* data() {
    Index row_offset = this->rowIndices()[0] * this->nestedExpression().rowStride();
    Index col_offset = this->colIndices()[0] * this->nestedExpression().colStride();
    return this->nestedExpression().data() + row_offset + col_offset;
  }
  const std::decay_t<typename XprType::Scalar>* data() const {
    Index row_offset = this->rowIndices()[0] * this->nestedExpression().rowStride();
    Index col_offset = this->colIndices()[0] * this->nestedExpression().colStride();
    return this->nestedExpression().data() + row_offset + col_offset;
  }
  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept {
    if (traits<Derived>::InnerStrideAtCompileTime != Dynamic) {
      return traits<Derived>::InnerStrideAtCompileTime;
    }
    return innerIncrement() * this->nestedExpression().innerStride();
  }
  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept {
    if (traits<Derived>::OuterStrideAtCompileTime != Dynamic) {
      return traits<Derived>::OuterStrideAtCompileTime;
    }
    return outerIncrement() * this->nestedExpression().outerStride();
  }
 };
 template <typename ArgType, typename RowIndices, typename ColIndices>
 struct unary_evaluator<IndexedView<ArgType, RowIndices, ColIndices>, IndexBased>
    : evaluator_base<IndexedView<ArgType, RowIndices, ColIndices>> {
  typedef IndexedView<ArgType, RowIndices, ColIndices> XprType;
  enum {
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost /* TODO + cost of row/col index */,
    FlagsLinearAccessBit =
        (traits<XprType>::RowsAtCompileTime == 1 || traits<XprType>::ColsAtCompileTime == 1) ? LinearAccessBit : 0,
    FlagsRowMajorBit = traits<XprType>::FlagsRowMajorBit,
    Flags = (evaluator<ArgType>::Flags & (HereditaryBits & ~RowMajorBit /*| LinearAccessBit | DirectAccessBit*/)) |
            FlagsLinearAccessBit | FlagsRowMajorBit,
    Alignment = 0
  };
  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
                 m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
    return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
                 m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
    return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    EIGEN_STATIC_ASSERT_LVALUE(XprType)
    Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
    Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
    eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
                 m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
    return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const {
    Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
    Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
    eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
                 m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
    return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index index) const {
    Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
    Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
    eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
                 m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
    return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
  }
 protected:
  evaluator<ArgType> m_argImpl;
  const XprType& m_xpr;
 };
 // Catch assignments to an IndexedView.
 template <typename ArgType, typename RowIndices, typename ColIndices>
 struct evaluator_assume_aliasing<IndexedView<ArgType, RowIndices, ColIndices>> {
  static const bool value = true;
 };
 }  // end namespace internal
 }  // end namespace Eigen
 #endif  // EIGEN_INDEXED_VIEW_H
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -1,260 +0,0 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2024 Charlie Schlosser <cs.schlosser@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 #ifndef EIGEN_INNER_PRODUCT_EVAL_H
 #define EIGEN_INNER_PRODUCT_EVAL_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen {
 namespace internal {
 // recursively searches for the largest simd type that does not exceed Size, or the smallest if no such type exists
 template <typename Scalar, int Size, typename Packet = typename packet_traits<Scalar>::type,
          bool Stop =
              (unpacket_traits<Packet>::size <= Size) || is_same<Packet, typename unpacket_traits<Packet>::half>::value>
 struct find_inner_product_packet_helper;
 template <typename Scalar, int Size, typename Packet>
 struct find_inner_product_packet_helper<Scalar, Size, Packet, false> {
  using type = typename find_inner_product_packet_helper<Scalar, Size, typename unpacket_traits<Packet>::half>::type;
 };
 template <typename Scalar, int Size, typename Packet>
 struct find_inner_product_packet_helper<Scalar, Size, Packet, true> {
  using type = Packet;
 };
 template <typename Scalar, int Size>
 struct find_inner_product_packet : find_inner_product_packet_helper<Scalar, Size> {};
 template <typename Scalar>
 struct find_inner_product_packet<Scalar, Dynamic> {
  using type = typename packet_traits<Scalar>::type;
 };
 template <typename Lhs, typename Rhs>
 struct inner_product_assert {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Lhs)
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Rhs)
  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Lhs, Rhs)
 #ifndef EIGEN_NO_DEBUG
  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, const Rhs& rhs) {
    eigen_assert((lhs.size() == rhs.size()) && "Inner product: lhs and rhs vectors must have same size");
  }
 #else
  static EIGEN_DEVICE_FUNC void run(const Lhs&, const Rhs&) {}
 #endif
 };
 template <typename Func, typename Lhs, typename Rhs>
 struct inner_product_evaluator {
  static constexpr int LhsFlags = evaluator<Lhs>::Flags;
  static constexpr int RhsFlags = evaluator<Rhs>::Flags;
  static constexpr int SizeAtCompileTime = size_prefer_fixed(Lhs::SizeAtCompileTime, Rhs::SizeAtCompileTime);
  static constexpr int MaxSizeAtCompileTime =
      min_size_prefer_fixed(Lhs::MaxSizeAtCompileTime, Rhs::MaxSizeAtCompileTime);
  static constexpr int LhsAlignment = evaluator<Lhs>::Alignment;
  static constexpr int RhsAlignment = evaluator<Rhs>::Alignment;
  using Scalar = typename Func::result_type;
  using Packet = typename find_inner_product_packet<Scalar, SizeAtCompileTime>::type;
  static constexpr bool Vectorize =
      bool(LhsFlags & RhsFlags & PacketAccessBit) && Func::PacketAccess &&
      ((MaxSizeAtCompileTime == Dynamic) || (unpacket_traits<Packet>::size <= MaxSizeAtCompileTime));
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit inner_product_evaluator(const Lhs& lhs, const Rhs& rhs,
                                                                         Func func = Func())
      : m_func(func), m_lhs(lhs), m_rhs(rhs), m_size(lhs.size()) {
    inner_product_assert<Lhs, Rhs>::run(lhs, rhs);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_size.value(); }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index index) const {
    return m_func.coeff(m_lhs.coeff(index), m_rhs.coeff(index));
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& value, Index index) const {
    return m_func.coeff(value, m_lhs.coeff(index), m_rhs.coeff(index));
  }
  template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_func.packet(m_lhs.template packet<LhsMode, PacketType>(index),
                         m_rhs.template packet<RhsMode, PacketType>(index));
  }
  template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(const PacketType& value, Index index) const {
    return m_func.packet(value, m_lhs.template packet<LhsMode, PacketType>(index),
                         m_rhs.template packet<RhsMode, PacketType>(index));
  }
  const Func m_func;
  const evaluator<Lhs> m_lhs;
  const evaluator<Rhs> m_rhs;
  const variable_if_dynamic<Index, SizeAtCompileTime> m_size;
 };
 template <typename Evaluator, bool Vectorize = Evaluator::Vectorize>
 struct inner_product_impl;
 // scalar loop
 template <typename Evaluator>
 struct inner_product_impl<Evaluator, false> {
  using Scalar = typename Evaluator::Scalar;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
    const Index size = eval.size();
    if (size == 0) return Scalar(0);
    Scalar result = eval.coeff(0);
    for (Index k = 1; k < size; k++) {
      result = eval.coeff(result, k);
    }
    return result;
  }
 };
 // vector loop
 template <typename Evaluator>
 struct inner_product_impl<Evaluator, true> {
  using UnsignedIndex = std::make_unsigned_t<Index>;
  using Scalar = typename Evaluator::Scalar;
  using Packet = typename Evaluator::Packet;
  static constexpr int PacketSize = unpacket_traits<Packet>::size;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
    const UnsignedIndex size = static_cast<UnsignedIndex>(eval.size());
    if (size < PacketSize) return inner_product_impl<Evaluator, false>::run(eval);
    const UnsignedIndex packetEnd = numext::round_down(size, PacketSize);
    const UnsignedIndex quadEnd = numext::round_down(size, 4 * PacketSize);
    const UnsignedIndex numPackets = size / PacketSize;
    const UnsignedIndex numRemPackets = (packetEnd - quadEnd) / PacketSize;
    Packet presult0, presult1, presult2, presult3;
    presult0 = eval.template packet<Packet>(0 * PacketSize);
    if (numPackets >= 2) presult1 = eval.template packet<Packet>(1 * PacketSize);
    if (numPackets >= 3) presult2 = eval.template packet<Packet>(2 * PacketSize);
    if (numPackets >= 4) {
      presult3 = eval.template packet<Packet>(3 * PacketSize);
      for (UnsignedIndex k = 4 * PacketSize; k < quadEnd; k += 4 * PacketSize) {
        presult0 = eval.packet(presult0, k + 0 * PacketSize);
        presult1 = eval.packet(presult1, k + 1 * PacketSize);
        presult2 = eval.packet(presult2, k + 2 * PacketSize);
        presult3 = eval.packet(presult3, k + 3 * PacketSize);
      }
      if (numRemPackets >= 1) presult0 = eval.packet(presult0, quadEnd + 0 * PacketSize);
      if (numRemPackets >= 2) presult1 = eval.packet(presult1, quadEnd + 1 * PacketSize);
      if (numRemPackets == 3) presult2 = eval.packet(presult2, quadEnd + 2 * PacketSize);
      presult2 = padd(presult2, presult3);
    }
    if (numPackets >= 3) presult1 = padd(presult1, presult2);
    if (numPackets >= 2) presult0 = padd(presult0, presult1);
    Scalar result = predux(presult0);
    for (UnsignedIndex k = packetEnd; k < size; k++) {
      result = eval.coeff(result, k);
    }
    return result;
  }
 };
 template <typename Scalar, bool Conj>
 struct conditional_conj;
 template <typename Scalar>
 struct conditional_conj<Scalar, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return numext::conj(a); }
  template <typename Packet>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
    return pconj(a);
  }
 };
 template <typename Scalar>
 struct conditional_conj<Scalar, false> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return a; }
  template <typename Packet>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
    return a;
  }
 };
 template <typename LhsScalar, typename RhsScalar, bool Conj>
 struct scalar_inner_product_op {
  using result_type = typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType;
  using conj_helper = conditional_conj<LhsScalar, Conj>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const LhsScalar& a, const RhsScalar& b) const {
    return (conj_helper::coeff(a) * b);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const result_type& accum, const LhsScalar& a,
                                                          const RhsScalar& b) const {
    return (conj_helper::coeff(a) * b) + accum;
  }
  static constexpr bool PacketAccess = false;
 };
 // Partial specialization for packet access if and only if
 // LhsScalar == RhsScalar == ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType.
 template <typename Scalar, bool Conj>
 struct scalar_inner_product_op<
    Scalar,
    typename std::enable_if<internal::is_same<typename ScalarBinaryOpTraits<Scalar, Scalar>::ReturnType, Scalar>::value,
                            Scalar>::type,
    Conj> {
  using result_type = Scalar;
  using conj_helper = conditional_conj<Scalar, Conj>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a, const Scalar& b) const {
    return pmul(conj_helper::coeff(a), b);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& accum, const Scalar& a, const Scalar& b) const {
    return pmadd(conj_helper::coeff(a), b, accum);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a, const Packet& b) const {
    return pmul(conj_helper::packet(a), b);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& accum, const Packet& a, const Packet& b) const {
    return pmadd(conj_helper::packet(a), b, accum);
  }
  static constexpr bool PacketAccess = packet_traits<Scalar>::HasMul && packet_traits<Scalar>::HasAdd;
 };
 template <typename Lhs, typename Rhs, bool Conj>
 struct default_inner_product_impl {
  using LhsScalar = typename traits<Lhs>::Scalar;
  using RhsScalar = typename traits<Rhs>::Scalar;
  using Op = scalar_inner_product_op<LhsScalar, RhsScalar, Conj>;
  using Evaluator = inner_product_evaluator<Op, Lhs, Rhs>;
  using result_type = typename Evaluator::Scalar;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type run(const MatrixBase<Lhs>& a, const MatrixBase<Rhs>& b) {
    Evaluator eval(a.derived(), b.derived(), Op());
    return inner_product_impl<Evaluator>::run(eval);
  }
 };
 template <typename Lhs, typename Rhs>
 struct dot_impl : default_inner_product_impl<Lhs, Rhs, true> {};
 }  // namespace internal
 }  // namespace Eigen
 #endif  // EIGEN_INNER_PRODUCT_EVAL_H
--- a/Eigen/src/Core/InternalHeaderCheck.h
+++ b/Eigen/src/Core/InternalHeaderCheck.h
@@ -1,3 +0,0 @@
 #ifndef EIGEN_CORE_MODULE_H
 #error "Please include Eigen/Core instead of including headers inside the src directory directly."
 #endif
--- a/Eigen/src/Core/Inverse.h
+++ b/Eigen/src/Core/Inverse.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2014-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -10,21 +10,21 @@
 #ifndef EIGEN_INVERSE_H
 #define EIGEN_INVERSE_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
-template <typename XprType, typename StorageKind>
+template<typename XprType,typename StorageKind> class InverseImpl;
 class InverseImpl;
 namespace internal {
 template<typename XprType>
-struct traits<Inverse<XprType> > : traits<typename XprType::PlainObject> {
+struct traits<Inverse<XprType> >
  : traits<typename XprType::PlainObject>
 {
  typedef typename XprType::PlainObject PlainObject;
  typedef traits<PlainObject> BaseTraits;
-  enum { Flags = BaseTraits::Flags & RowMajorBit };
+  enum {
    Flags = BaseTraits::Flags & RowMajorBit
  };
 };
 } // end namespace internal
@@ -40,19 +40,23 @@ struct traits<Inverse<XprType> > : traits<typename XprType::PlainObject> {
  *
  */
 template<typename XprType>
-class Inverse : public InverseImpl<XprType, typename internal::traits<XprType>::StorageKind> {
+class Inverse : public InverseImpl<XprType,typename internal::traits<XprType>::StorageKind>
 {
 public:
  typedef typename XprType::StorageIndex StorageIndex;
  typedef typename XprType::PlainObject                       PlainObject;
  typedef typename XprType::Scalar                            Scalar;
  typedef typename internal::ref_selector<XprType>::type      XprTypeNested;
-  typedef internal::remove_all_t<XprTypeNested> XprTypeNestedCleaned;
+  typedef typename internal::remove_all<XprTypeNested>::type  XprTypeNestedCleaned;
  typedef typename internal::ref_selector<Inverse>::type Nested;
-  typedef internal::remove_all_t<XprType> NestedExpression;
+  typedef typename internal::remove_all<XprType>::type NestedExpression;
-  explicit EIGEN_DEVICE_FUNC Inverse(const XprType& xpr) : m_xpr(xpr) {}
+  explicit EIGEN_DEVICE_FUNC Inverse(const XprType &xpr)
    : m_xpr(xpr)
  {}
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_xpr.cols(); }
+  EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_xpr.rows(); }
+  EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); }
  EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }
@@ -62,12 +66,14 @@ class Inverse : public InverseImpl<XprType, typename internal::traits<XprType>::
 // Generic API dispatcher
 template<typename XprType, typename StorageKind>
-class InverseImpl : public internal::generic_xpr_base<Inverse<XprType> >::type {
+class InverseImpl
  : public internal::generic_xpr_base<Inverse<XprType> >::type
 {
 public:
  typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;
  typedef typename XprType::Scalar Scalar;
 private:
  Scalar coeff(Index row, Index col) const;
  Scalar coeff(Index i) const;
 };
@@ -85,15 +91,19 @@ namespace internal {
  * \sa class Inverse
  */
 template<typename ArgType>
-struct unary_evaluator<Inverse<ArgType> > : public evaluator<typename Inverse<ArgType>::PlainObject> {
+struct unary_evaluator<Inverse<ArgType> >
  : public evaluator<typename Inverse<ArgType>::PlainObject>
 {
  typedef Inverse<ArgType> InverseType;
  typedef typename InverseType::PlainObject PlainObject;
  typedef evaluator<PlainObject> Base;
  enum { Flags = Base::Flags | EvalBeforeNestingBit };
-  EIGEN_DEVICE_FUNC unary_evaluator(const InverseType& inv_xpr) : m_result(inv_xpr.rows(), inv_xpr.cols()) {
+  unary_evaluator(const InverseType& inv_xpr)
-    internal::construct_at<Base>(this, m_result);
+    : m_result(inv_xpr.rows(), inv_xpr.cols())
  {
    ::new (static_cast<Base*>(this)) Base(m_result);
    internal::call_assignment_no_alias(m_result, inv_xpr);
  }
--- a/Eigen/src/Core/Map.h
+++ b/Eigen/src/Core/Map.h
@@ -11,14 +11,13 @@
 #ifndef EIGEN_MAP_H
 #define EIGEN_MAP_H
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 namespace internal {
 template<typename PlainObjectType, int MapOptions, typename StrideType>
-struct traits<Map<PlainObjectType, MapOptions, StrideType> > : public traits<PlainObjectType> {
+struct traits<Map<PlainObjectType, MapOptions, StrideType> >
  : public traits<PlainObjectType>
 {
  typedef traits<PlainObjectType> TraitsBase;
  enum {
    PlainObjectTypeInnerSize = ((traits<PlainObjectType>::Flags&RowMajorBit)==RowMajorBit)
@@ -37,11 +36,10 @@ struct traits<Map<PlainObjectType, MapOptions, StrideType> > : public traits<Pla
    Flags0 = TraitsBase::Flags & (~NestByRefBit),
    Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
  };
 private:
  enum { Options }; // Expressions don't have Options
 };
-}  // namespace internal
+}
 /** \class Map
  * \ingroup Core_Module
@@ -49,10 +47,11 @@ struct traits<Map<PlainObjectType, MapOptions, StrideType> > : public traits<Pla
  * \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 the pointer alignment in bytes. It can be: \c #Aligned128, \c #Aligned64, \c #Aligned32,
+  * \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
- * \c #Aligned16, \c #Aligned8 or \c #Unaligned. The default is \c #Unaligned. \tparam StrideType optionally specifies
+  *                The default is \c #Unaligned.
- * strides. By default, Map assumes the memory layout of an ordinary, contiguous array. This can be overridden by
+  * \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
- * specifying strides. The type passed here must be a specialization of the Stride template, see examples below.
+  *                   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,
@@ -92,26 +91,32 @@ struct traits<Map<PlainObjectType, MapOptions, StrideType> > : public traits<Pla
  *
  * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
  */
-template <typename PlainObjectType, int MapOptions, typename StrideType>
+template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
-class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
+  : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
 {
  public:
    typedef MapBase<Map> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(Map)
    typedef typename Base::PointerType PointerType;
    typedef PointerType PointerArgType;
-  EIGEN_DEVICE_FUNC inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
+    EIGEN_DEVICE_FUNC
    inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
-  EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
+    EIGEN_DEVICE_FUNC
    inline Index innerStride() const
    {
      return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
    }
-  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
+    EIGEN_DEVICE_FUNC
-    return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+    inline Index outerStride() const
-           : internal::traits<Map>::OuterStrideAtCompileTime != Dynamic
+    {
-               ? Index(internal::traits<Map>::OuterStrideAtCompileTime)
+      return int(StrideType::OuterStrideAtCompileTime) != 0 ? m_stride.outer()
           : int(internal::traits<Map>::OuterStrideAtCompileTime) != Dynamic ? Index(internal::traits<Map>::OuterStrideAtCompileTime)
           : IsVectorAtCompileTime ? (this->size() * innerStride())
-           : int(Flags) & RowMajorBit ? (this->cols() * innerStride())
+           : (int(Flags)&RowMajorBit) ? (this->cols() * innerStride())
           : (this->rows() * innerStride());
    }
@@ -120,8 +125,12 @@ class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
      * \param dataPtr pointer to the array to map
      * \param stride optional Stride object, passing the strides.
      */
-  EIGEN_DEVICE_FUNC explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())
+    EIGEN_DEVICE_FUNC
-      : Base(cast_to_pointer_type(dataPtr)), m_stride(stride) {}
+    explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())
      : Base(cast_to_pointer_type(dataPtr)), m_stride(stride)
    {
      PlainObjectType::Base::_check_template_params();
    }
    /** Constructor in the dynamic-size vector case.
      *
@@ -129,8 +138,12 @@ class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
      * \param size the size of the vector expression
      * \param stride optional Stride object, passing the strides.
      */
-  EIGEN_DEVICE_FUNC inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())
+    EIGEN_DEVICE_FUNC
-      : Base(cast_to_pointer_type(dataPtr), size), m_stride(stride) {}
+    inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())
      : Base(cast_to_pointer_type(dataPtr), size), m_stride(stride)
    {
      PlainObjectType::Base::_check_template_params();
    }
    /** Constructor in the dynamic-size matrix case.
      *
@@ -139,8 +152,12 @@ class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
      * \param cols the number of columns of the matrix expression
      * \param stride optional Stride object, passing the strides.
      */
-  EIGEN_DEVICE_FUNC inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())
+    EIGEN_DEVICE_FUNC
-      : Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride) {}
+    inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())
      : Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride)
    {
      PlainObjectType::Base::_check_template_params();
    }
    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
@@ -148,6 +165,7 @@ class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
    StrideType m_stride;
 };
 } // end namespace Eigen
 #endif // EIGEN_MAP_H
--- a/Eigen/src/Core/MapBase.h
+++ b/Eigen/src/Core/MapBase.h
@@ -15,9 +15,6 @@
      EIGEN_STATIC_ASSERT((int(internal::evaluator<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
                          YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 namespace Eigen { 
 /** \ingroup Core_Module
@@ -37,9 +34,11 @@ namespace Eigen {
  *
  * \sa class Map, class Block
  */
-template <typename Derived>
+template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
-class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Derived>::type {
+  : public internal::dense_xpr_base<Derived>::type
 {
  public:
    typedef typename internal::dense_xpr_base<Derived>::type Base;
    enum {
      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
@@ -52,31 +51,35 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
    typedef typename internal::traits<Derived>::Scalar Scalar;
    typedef typename internal::packet_traits<Scalar>::type PacketScalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef std::conditional_t<bool(internal::is_lvalue<Derived>::value), Scalar*, const Scalar*> PointerType;
+    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::IsVectorAtCompileTime;
  using Base::MaxColsAtCompileTime;
  using Base::MaxRowsAtCompileTime;
  using Base::MaxSizeAtCompileTime;
    using Base::rows;
    using Base::cols;
    using Base::size;
    using Base::coeff;
    using Base::coeffRef;
  using Base::cols;
  using Base::eval;
    using Base::lazyAssign;
-  using Base::rows;
+    using Base::eval;
  using Base::size;
  using Base::colStride;
    using Base::innerStride;
    using Base::outerStride;
    using Base::rowStride;
    using Base::colStride;
    // bug 217 - compile error on ICC 11.1
    using Base::operator=;
@@ -84,9 +87,9 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
    typedef typename Base::CoeffReturnType CoeffReturnType;
    /** \copydoc DenseBase::rows() */
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_rows.value(); }
+    EIGEN_DEVICE_FUNC inline Index rows() const { return m_rows.value(); }
    /** \copydoc DenseBase::cols() */
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_cols.value(); }
+    EIGEN_DEVICE_FUNC inline Index cols() const { return m_cols.value(); }
    /** Returns a pointer to the first coefficient of the matrix or vector.
      *
@@ -94,55 +97,69 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
      *
      * \sa innerStride(), outerStride()
      */
-  EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_data; }
+    EIGEN_DEVICE_FUNC inline const Scalar* data() const { return m_data; }
    /** \copydoc PlainObjectBase::coeff(Index,Index) const */
-  EIGEN_DEVICE_FUNC inline const Scalar& coeff(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeff(Index rowId, Index colId) const
    {
      return m_data[colId * colStride() + rowId * rowStride()];
    }
    /** \copydoc PlainObjectBase::coeff(Index) const */
-  EIGEN_DEVICE_FUNC inline const Scalar& coeff(Index index) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeff(Index index) const
    {
      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
      return m_data[index * innerStride()];
    }
    /** \copydoc PlainObjectBase::coeffRef(Index,Index) const */
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index rowId, Index colId) const
    {
      return this->m_data[colId * colStride() + rowId * rowStride()];
    }
    /** \copydoc PlainObjectBase::coeffRef(Index) const */
-  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
+    EIGEN_DEVICE_FUNC
    inline const Scalar& coeffRef(Index index) const
    {
      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
      return this->m_data[index * innerStride()];
    }
    /** \internal */
    template<int LoadMode>
-  inline PacketScalar packet(Index rowId, Index colId) const {
+    inline PacketScalar packet(Index rowId, Index colId) const
-    return internal::ploadt<PacketScalar, LoadMode>(m_data + (colId * colStride() + rowId * rowStride()));
+    {
      return internal::ploadt<PacketScalar, LoadMode>
               (m_data + (colId * colStride() + rowId * rowStride()));
    }
    /** \internal */
    template<int LoadMode>
-  inline PacketScalar packet(Index index) const {
+    inline PacketScalar packet(Index index) const
    {
      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
      return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
    }
    /** \internal Constructor for fixed size matrices or vectors */
-  EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr)
+    EIGEN_DEVICE_FUNC
-      : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime) {
+    explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
    {
      EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
      checkSanity<Derived>();
    }
    /** \internal Constructor for dynamically sized vectors */
-  EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize)
+    EIGEN_DEVICE_FUNC
    inline MapBase(PointerType dataPtr, Index vecSize)
            : m_data(dataPtr),
              m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),
-        m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime)) {
+              m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime))
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
      eigen_assert(vecSize >= 0);
      eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
@@ -150,10 +167,13 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
    }
    /** \internal Constructor for dynamically sized matrices */
-  EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols)
+    EIGEN_DEVICE_FUNC
-      : m_data(dataPtr), m_rows(rows), m_cols(cols) {
+    inline MapBase(PointerType dataPtr, Index rows, Index cols)
-    eigen_assert((dataPtr == 0) || (rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) &&
+            : m_data(dataPtr), m_rows(rows), m_cols(cols)
-                                    cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
+    {
      eigen_assert( (dataPtr == 0)
              || (   rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
                  && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
      checkSanity<Derived>();
    }
@@ -166,31 +186,22 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
    EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
    template<typename T>
-  EIGEN_DEVICE_FUNC void checkSanity(std::enable_if_t<(internal::traits<T>::Alignment > 0), void*> = 0) const {
+    EIGEN_DEVICE_FUNC
-// Temporary macro to allow scalars to not be properly aligned.  This is while we sort out failures
+    void checkSanity(typename internal::enable_if<(internal::traits<T>::Alignment>0),void*>::type = 0) const
-// in TensorFlow Lite that are currently relying on this UB.
+    {
 #ifndef EIGEN_ALLOW_UNALIGNED_SCALARS
    // Pointer must be aligned to the Scalar type, otherwise we get UB.
    eigen_assert((std::uintptr_t(m_data) % alignof(Scalar) == 0) && "data is not scalar-aligned");
 #endif
 #if EIGEN_MAX_ALIGN_BYTES>0
-    // innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible
+      // innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible value:
    // value:
      const Index minInnerStride = InnerStrideAtCompileTime == Dynamic ? 1 : Index(InnerStrideAtCompileTime);
      EIGEN_ONLY_USED_FOR_DEBUG(minInnerStride);
-    eigen_assert((((std::uintptr_t(m_data) % internal::traits<Derived>::Alignment) == 0) ||
+      eigen_assert((   ((internal::UIntPtr(m_data) % internal::traits<Derived>::Alignment) == 0)
-                  (cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits<Derived>::Alignment) &&
+                    || (cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits<Derived>::Alignment ) && "data is not aligned");
                 "data is not aligned");
 #endif
    }
    template<typename T>
-  EIGEN_DEVICE_FUNC void checkSanity(std::enable_if_t<internal::traits<T>::Alignment == 0, void*> = 0) const {
+    EIGEN_DEVICE_FUNC
-#ifndef EIGEN_ALLOW_UNALIGNED_SCALARS
+    void checkSanity(typename internal::enable_if<internal::traits<T>::Alignment==0,void*>::type = 0) const
-    // Pointer must be aligned to the Scalar type, otherwise we get UB.
+    {}
    eigen_assert((std::uintptr_t(m_data) % alignof(Scalar) == 0) && "data is not scalar-aligned");
 #endif
  }
    PointerType m_data;
    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
@@ -207,11 +218,12 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
  *
  * \sa class Map, class Block
  */
-template <typename Derived>
+template<typename Derived> class MapBase<Derived, WriteAccessors>
-class MapBase<Derived, WriteAccessors> : public MapBase<Derived, ReadOnlyAccessors> {
+  : public MapBase<Derived, ReadOnlyAccessors>
 {
    typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
  public:
    typedef MapBase<Derived, ReadOnlyAccessors> Base;
    typedef typename Base::Scalar Scalar;
@@ -219,50 +231,64 @@ class MapBase<Derived, WriteAccessors> : public MapBase<Derived, ReadOnlyAccesso
    typedef typename Base::StorageIndex StorageIndex;
    typedef typename Base::PointerType PointerType;
  using Base::coeff;
  using Base::coeffRef;
  using Base::cols;
    using Base::derived;
    using Base::rows;
    using Base::cols;
    using Base::size;
    using Base::coeff;
    using Base::coeffRef;
  using Base::colStride;
    using Base::innerStride;
    using Base::outerStride;
    using Base::rowStride;
    using Base::colStride;
-  typedef std::conditional_t<internal::is_lvalue<Derived>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;
+    typedef typename internal::conditional<
                    internal::is_lvalue<Derived>::value,
                    Scalar,
                    const Scalar
                  >::type ScalarWithConstIfNotLvalue;
-  EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return this->m_data; }
+    EIGEN_DEVICE_FUNC
-  EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() {
+    inline const Scalar* data() const { return this->m_data; }
-    return this->m_data;
+    EIGEN_DEVICE_FUNC
-  }  // no const-cast here so non-const-correct code will give a compile error
+    inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
-  EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col) {
+    EIGEN_DEVICE_FUNC
    inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
    {
      return this->m_data[col * colStride() + row * rowStride()];
    }
-  EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue& coeffRef(Index index) {
+    EIGEN_DEVICE_FUNC
    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& val) {
+    inline void writePacket(Index row, Index col, const PacketScalar& val)
-    internal::pstoret<Scalar, PacketScalar, StoreMode>(this->m_data + (col * colStride() + row * rowStride()), val);
+    {
      internal::pstoret<Scalar, PacketScalar, StoreMode>
               (this->m_data + (col * colStride() + row * rowStride()), val);
    }
    template<int StoreMode>
-  inline void writePacket(Index index, const PacketScalar& val) {
+    inline void writePacket(Index index, const PacketScalar& val)
    {
      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
-    internal::pstoret<Scalar, PacketScalar, StoreMode>(this->m_data + index * innerStride(), val);
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
                (this->m_data + index * innerStride(), val);
    }
    EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}
    EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}
    EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {}
-  EIGEN_DEVICE_FUNC Derived& operator=(const MapBase& other) {
+    EIGEN_DEVICE_FUNC
    Derived& operator=(const MapBase& other)
    {
      ReadOnlyMapBase::Base::operator=(other);
      return derived();
    }
@@ -270,7 +296,6 @@ class MapBase<Derived, WriteAccessors> : public MapBase<Derived, ReadOnlyAccesso
    // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
    // see bugs 821 and 920.
    using ReadOnlyMapBase::Base::operator=;
  protected:
    EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
    EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
--- a/Show More
+++ b/Show More