Fix a previous mistake in moving the 2.0-beta5 in svn for some last-minute

fixes.

.krazy

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

CMakeLists.txt

@@ -1,18 +1,122 @@
 project(Eigen)
+set(EIGEN_VERSION_NUMBER "2.0.52-unstable")
 
-OPTION(BUILD_TESTS "Build tests"  OFF)
-OPTION(BUILD_EXAMPLES "Build examples"  OFF)
+#if the svnversion program is absent, this will leave the SVN_REVISION string empty,
+#but won't stop CMake.
+execute_process(COMMAND svnversion -n ${CMAKE_SOURCE_DIR}
+                OUTPUT_VARIABLE EIGEN_SVNVERSION_OUTPUT)
+
+#we only want EIGEN_SVN_REVISION if it is an actual revision number, not a string like "exported"
+string(REGEX MATCH "^[0-9]+.*" EIGEN_SVN_REVISION "${EIGEN_SVNVERSION_OUTPUT}")
+
+if(EIGEN_SVN_REVISION)
+  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (SVN revision ${EIGEN_SVN_REVISION})")
+else(EIGEN_SVN_REVISION)
+  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
+endif(EIGEN_SVN_REVISION)
+
+cmake_minimum_required(VERSION 2.6.2)
+
+include(CheckCXXCompilerFlag)
+
+set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
+
+option(EIGEN_BUILD_TESTS "Build tests" OFF)
+option(EIGEN_BUILD_DEMOS "Build demos" OFF)
+if(NOT WIN32)
+  option(EIGEN_BUILD_LIB "Build the binary shared library" OFF)
+endif(NOT WIN32)
+option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
+
+if(EIGEN_BUILD_LIB)
+  option(EIGEN_TEST_LIB "Build the unit tests using the library (disable -pedantic)" OFF)
+endif(EIGEN_BUILD_LIB)
 
 set(CMAKE_INCLUDE_CURRENT_DIR ON)
 
 if(CMAKE_COMPILER_IS_GNUCXX)
-   if (CMAKE_SYSTEM_NAME MATCHES Linux)
-     set ( CMAKE_C_FLAGS     "${CMAKE_C_FLAGS} -Wno-long-long -ansi -Wundef -Wcast-align -Werror-implicit-function-declaration -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -Wmissing-format-attribute -fno-common")
-     set ( CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wnon-virtual-dtor -Wno-long-long -ansi -Wundef -Wcast-align -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -fno-exceptions -fno-check-new -fno-common")
-   endif (CMAKE_SYSTEM_NAME MATCHES Linux)
-endif (CMAKE_COMPILER_IS_GNUCXX)
+  if(CMAKE_SYSTEM_NAME MATCHES Linux)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wnon-virtual-dtor -Wno-long-long -ansi -Wundef -Wcast-align -Wchar-subscripts -Wall -W -Wpointer-arith -Wwrite-strings -Wformat-security -fno-exceptions -fno-check-new -fno-common -fstrict-aliasing")
 
-include_directories( ${CMAKE_SOURCE_DIR} ${CMAKE_BINARY_DIR} )
+    check_cxx_compiler_flag("-Wextra" COMPILER_SUPPORT_WEXTRA)
+    if(COMPILER_SUPPORT_WEXTRA)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wextra")
+    endif()
 
-add_subdirectory(src)
-add_subdirectory(test)
+    if(NOT EIGEN_TEST_LIB)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -pedantic")
+    endif(NOT EIGEN_TEST_LIB)
+
+    option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
+    if(EIGEN_TEST_SSE2)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2")
+      message("Enabling SSE2 in tests/examples")
+    endif(EIGEN_TEST_SSE2)
+
+    option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF)
+    if(EIGEN_TEST_SSE3)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3")
+      message("Enabling SSE3 in tests/examples")
+    endif(EIGEN_TEST_SSE3)
+
+    option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF)
+    if(EIGEN_TEST_SSSE3)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3")
+      message("Enabling SSSE3 in tests/examples")
+    endif(EIGEN_TEST_SSSE3)
+
+    option(EIGEN_TEST_ALTIVEC "Enable/Disable altivec in tests/examples" OFF)
+    if(EIGEN_TEST_ALTIVEC)
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec")
+      message("Enabling AltiVec in tests/examples")
+    endif(EIGEN_TEST_ALTIVEC)
+
+  endif(CMAKE_SYSTEM_NAME MATCHES Linux)
+endif(CMAKE_COMPILER_IS_GNUCXX)
+
+if(MSVC)
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ")
+
+  option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
+  if(EIGEN_TEST_SSE2)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
+    message("Enabling SSE2 in tests/examples")
+  endif(EIGEN_TEST_SSE2)
+endif(MSVC)
+
+option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
+if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
+  add_definitions(-DEIGEN_DONT_VECTORIZE=1)
+  message("Disabling vectorization in tests/examples")
+endif(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
+
+include_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})
+
+set(INCLUDE_INSTALL_DIR
+    "${CMAKE_INSTALL_PREFIX}/include/eigen2"
+    CACHE PATH
+    "The directory where we install the header files"
+    FORCE)
+
+add_subdirectory(Eigen)
+
+add_subdirectory(doc)
+
+if(EIGEN_BUILD_TESTS)
+  include(CTest)
+  add_subdirectory(test)
+endif(EIGEN_BUILD_TESTS)
+
+add_subdirectory(unsupported)
+
+if(EIGEN_BUILD_DEMOS)
+  add_subdirectory(demos)
+endif(EIGEN_BUILD_DEMOS)
+
+if(EIGEN_BUILD_BTL)
+  add_subdirectory(bench/btl)
+endif(EIGEN_BUILD_BTL)
+
+if(EIGEN_BUILD_TESTS)
+  ei_testing_print_summary()
+endif(EIGEN_BUILD_TESTS)

COPYING

@@ -0,0 +1,674 @@
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+propagate that work, subject to this License.  You are not responsible
+for enforcing compliance by third parties with this License.
+
+  An "entity transaction" is a transaction transferring control of an
+organization, or substantially all assets of one, or subdividing an
+organization, or merging organizations.  If propagation of a covered
+work results from an entity transaction, each party to that
+transaction who receives a copy of the work also receives whatever
+licenses to the work the party's predecessor in interest had or could
+give under the previous paragraph, plus a right to possession of the
+Corresponding Source of the work from the predecessor in interest, if
+the predecessor has it or can get it with reasonable efforts.
+
+  You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License.  For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+  11. Patents.
+
+  A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based.  The
+work thus licensed is called the contributor's "contributor version".
+
+  A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version.  For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+  Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+  In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement).  To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+  If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients.  "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+  If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+  A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License.  You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
+to the third party based on the extent of your activity of conveying
+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
+patent license (a) in connection with copies of the covered work
+conveyed by you (or copies made from those copies), or (b) primarily
+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+  Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+  12. No Surrender of Others' Freedom.
+
+  If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License.  If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all.  For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+  13. Use with the GNU Affero General Public License.
+
+  Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
+combined work, and to convey the resulting work.  The terms of this
+License will continue to apply to the part which is the covered work,
+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+  14. Revised Versions of this License.
+
+  The Free Software Foundation may publish revised and/or new versions of
+the GNU 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
+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation.  If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
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+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM 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 PROGRAM (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 PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state 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 program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program 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 General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

COPYING.LESSER

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

CTestConfig.cmake

@@ -0,0 +1,13 @@
+## This file should be placed in the root directory of your project.
+## Then modify the CMakeLists.txt file in the root directory of your
+## project to incorporate the testing dashboard.
+## # The following are required to uses Dart and the Cdash dashboard
+##   ENABLE_TESTING()
+##   INCLUDE(Dart)
+set(CTEST_PROJECT_NAME "Eigen")
+set(CTEST_NIGHTLY_START_TIME "05:00:00 UTC")
+
+set(CTEST_DROP_METHOD "http")
+set(CTEST_DROP_SITE "www.cdash.org")
+set(CTEST_DROP_LOCATION "/CDashPublic/submit.php?project=Eigen")
+set(CTEST_DROP_SITE_CDASH TRUE)

Doxyfile

@@ -0,0 +1,281 @@
+# Doxyfile 1.5.3
+
+#---------------------------------------------------------------------------
+# Project related configuration options
+#---------------------------------------------------------------------------
+DOXYFILE_ENCODING      = UTF-8
+PROJECT_NAME           = Eigen
+PROJECT_NUMBER         = 2.0
+OUTPUT_DIRECTORY       = ./
+CREATE_SUBDIRS         = NO
+OUTPUT_LANGUAGE        = English
+BRIEF_MEMBER_DESC      = YES
+REPEAT_BRIEF           = YES
+ABBREVIATE_BRIEF       = "The $name class" \
+                         "The $name widget" \
+                         "The $name file" \
+                         is \
+                         provides \
+                         specifies \
+                         contains \
+                         represents \
+                         a \
+                         an \
+                         the
+ALWAYS_DETAILED_SEC    = NO
+INLINE_INHERITED_MEMB  = NO
+FULL_PATH_NAMES        = NO
+STRIP_FROM_PATH        = 
+STRIP_FROM_INC_PATH    = 
+SHORT_NAMES            = NO
+JAVADOC_AUTOBRIEF      = NO
+QT_AUTOBRIEF           = NO
+MULTILINE_CPP_IS_BRIEF = NO
+DETAILS_AT_TOP         = NO
+INHERIT_DOCS           = YES
+SEPARATE_MEMBER_PAGES  = NO
+TAB_SIZE               = 8
+ALIASES                = 
+OPTIMIZE_OUTPUT_FOR_C  = NO
+OPTIMIZE_OUTPUT_JAVA   = NO
+BUILTIN_STL_SUPPORT    = NO
+CPP_CLI_SUPPORT        = NO
+DISTRIBUTE_GROUP_DOC   = NO
+SUBGROUPING            = YES
+#---------------------------------------------------------------------------
+# Build related configuration options
+#---------------------------------------------------------------------------
+EXTRACT_ALL            = NO
+EXTRACT_PRIVATE        = NO
+EXTRACT_STATIC         = NO
+EXTRACT_LOCAL_CLASSES  = NO
+EXTRACT_LOCAL_METHODS  = NO
+EXTRACT_ANON_NSPACES   = NO
+HIDE_UNDOC_MEMBERS     = YES
+HIDE_UNDOC_CLASSES     = YES
+HIDE_FRIEND_COMPOUNDS  = YES
+HIDE_IN_BODY_DOCS      = NO
+INTERNAL_DOCS          = NO
+CASE_SENSE_NAMES       = YES
+HIDE_SCOPE_NAMES       = YES
+SHOW_INCLUDE_FILES     = YES
+INLINE_INFO            = YES
+SORT_MEMBER_DOCS       = YES
+SORT_BRIEF_DOCS        = NO
+SORT_BY_SCOPE_NAME     = NO
+GENERATE_TODOLIST      = YES
+GENERATE_TESTLIST      = YES
+GENERATE_BUGLIST       = YES
+GENERATE_DEPRECATEDLIST= YES
+ENABLED_SECTIONS       = 
+MAX_INITIALIZER_LINES  = 30
+SHOW_USED_FILES        = YES
+SHOW_DIRECTORIES       = NO
+FILE_VERSION_FILTER    = 
+#---------------------------------------------------------------------------
+# configuration options related to warning and progress messages
+#---------------------------------------------------------------------------
+QUIET                  = NO
+WARNINGS               = YES
+WARN_IF_UNDOCUMENTED   = YES
+WARN_IF_DOC_ERROR      = YES
+WARN_NO_PARAMDOC       = NO
+WARN_FORMAT            = "$file:$line: $text"
+WARN_LOGFILE           = 
+#---------------------------------------------------------------------------
+# configuration options related to the input files
+#---------------------------------------------------------------------------
+INPUT                  = ./
+INPUT_ENCODING         = UTF-8
+FILE_PATTERNS          = *.c \
+                         *.cc \
+                         *.cxx \
+                         *.cpp \
+                         *.c++ \
+                         *.d \
+                         *.java \
+                         *.ii \
+                         *.ixx \
+                         *.ipp \
+                         *.i++ \
+                         *.inl \
+                         *.h \
+                         *.hh \
+                         *.hxx \
+                         *.hpp \
+                         *.h++ \
+                         *.idl \
+                         *.odl \
+                         *.cs \
+                         *.php \
+                         *.php3 \
+                         *.inc \
+                         *.m \
+                         *.mm \
+                         *.dox \
+                         *.py \
+                         *.C \
+                         *.CC \
+                         *.C++ \
+                         *.II \
+                         *.I++ \
+                         *.H \
+                         *.HH \
+                         *.H++ \
+                         *.CS \
+                         *.PHP \
+                         *.PHP3 \
+                         *.M \
+                         *.MM \
+                         *.PY
+RECURSIVE              = NO
+EXCLUDE                = 
+EXCLUDE_SYMLINKS       = NO
+EXCLUDE_PATTERNS       = 
+EXCLUDE_SYMBOLS        = 
+EXAMPLE_PATH           = doc/examples/
+EXAMPLE_PATTERNS       = *
+EXAMPLE_RECURSIVE      = NO
+IMAGE_PATH             = 
+INPUT_FILTER           = 
+FILTER_PATTERNS        = 
+FILTER_SOURCE_FILES    = NO
+#---------------------------------------------------------------------------
+# configuration options related to source browsing
+#---------------------------------------------------------------------------
+SOURCE_BROWSER         = NO
+INLINE_SOURCES         = NO
+STRIP_CODE_COMMENTS    = YES
+REFERENCED_BY_RELATION = YES
+REFERENCES_RELATION    = YES
+REFERENCES_LINK_SOURCE = YES
+USE_HTAGS              = NO
+VERBATIM_HEADERS       = YES
+#---------------------------------------------------------------------------
+# configuration options related to the alphabetical class index
+#---------------------------------------------------------------------------
+ALPHABETICAL_INDEX     = NO
+COLS_IN_ALPHA_INDEX    = 5
+IGNORE_PREFIX          = 
+#---------------------------------------------------------------------------
+# configuration options related to the HTML output
+#---------------------------------------------------------------------------
+GENERATE_HTML          = YES
+HTML_OUTPUT            = html
+HTML_FILE_EXTENSION    = .html
+HTML_HEADER            = 
+HTML_FOOTER            = 
+HTML_STYLESHEET        = 
+HTML_ALIGN_MEMBERS     = YES
+GENERATE_HTMLHELP      = NO
+HTML_DYNAMIC_SECTIONS  = NO
+CHM_FILE               = 
+HHC_LOCATION           = 
+GENERATE_CHI           = NO
+BINARY_TOC             = NO
+TOC_EXPAND             = NO
+DISABLE_INDEX          = NO
+ENUM_VALUES_PER_LINE   = 4
+GENERATE_TREEVIEW      = NO
+TREEVIEW_WIDTH         = 250
+#---------------------------------------------------------------------------
+# configuration options related to the LaTeX output
+#---------------------------------------------------------------------------
+GENERATE_LATEX         = YES
+LATEX_OUTPUT           = latex
+LATEX_CMD_NAME         = latex
+MAKEINDEX_CMD_NAME     = makeindex
+COMPACT_LATEX          = NO
+PAPER_TYPE             = a4wide
+EXTRA_PACKAGES         = 
+LATEX_HEADER           = 
+PDF_HYPERLINKS         = NO
+USE_PDFLATEX           = NO
+LATEX_BATCHMODE        = NO
+LATEX_HIDE_INDICES     = NO
+#---------------------------------------------------------------------------
+# configuration options related to the RTF output
+#---------------------------------------------------------------------------
+GENERATE_RTF           = NO
+RTF_OUTPUT             = rtf
+COMPACT_RTF            = NO
+RTF_HYPERLINKS         = NO
+RTF_STYLESHEET_FILE    = 
+RTF_EXTENSIONS_FILE    = 
+#---------------------------------------------------------------------------
+# configuration options related to the man page output
+#---------------------------------------------------------------------------
+GENERATE_MAN           = NO
+MAN_OUTPUT             = man
+MAN_EXTENSION          = .3
+MAN_LINKS              = NO
+#---------------------------------------------------------------------------
+# configuration options related to the XML output
+#---------------------------------------------------------------------------
+GENERATE_XML           = NO
+XML_OUTPUT             = xml
+XML_SCHEMA             = 
+XML_DTD                = 
+XML_PROGRAMLISTING     = YES
+#---------------------------------------------------------------------------
+# configuration options for the AutoGen Definitions output
+#---------------------------------------------------------------------------
+GENERATE_AUTOGEN_DEF   = NO
+#---------------------------------------------------------------------------
+# configuration options related to the Perl module output
+#---------------------------------------------------------------------------
+GENERATE_PERLMOD       = NO
+PERLMOD_LATEX          = NO
+PERLMOD_PRETTY         = YES
+PERLMOD_MAKEVAR_PREFIX = 
+#---------------------------------------------------------------------------
+# Configuration options related to the preprocessor   
+#---------------------------------------------------------------------------
+ENABLE_PREPROCESSING   = YES
+MACRO_EXPANSION        = NO
+EXPAND_ONLY_PREDEF     = NO
+SEARCH_INCLUDES        = YES
+INCLUDE_PATH           = 
+INCLUDE_FILE_PATTERNS  = 
+PREDEFINED             = 
+EXPAND_AS_DEFINED      = 
+SKIP_FUNCTION_MACROS   = YES
+#---------------------------------------------------------------------------
+# Configuration::additions related to external references   
+#---------------------------------------------------------------------------
+TAGFILES               = 
+GENERATE_TAGFILE       = 
+ALLEXTERNALS           = NO
+EXTERNAL_GROUPS        = YES
+PERL_PATH              = /usr/bin/perl
+#---------------------------------------------------------------------------
+# Configuration options related to the dot tool   
+#---------------------------------------------------------------------------
+CLASS_DIAGRAMS         = YES
+MSCGEN_PATH            = 
+HIDE_UNDOC_RELATIONS   = YES
+HAVE_DOT               = YES
+CLASS_GRAPH            = YES
+COLLABORATION_GRAPH    = YES
+GROUP_GRAPHS           = YES
+UML_LOOK               = NO
+TEMPLATE_RELATIONS     = NO
+INCLUDE_GRAPH          = YES
+INCLUDED_BY_GRAPH      = YES
+CALL_GRAPH             = NO
+CALLER_GRAPH           = NO
+GRAPHICAL_HIERARCHY    = YES
+DIRECTORY_GRAPH        = YES
+DOT_IMAGE_FORMAT       = png
+DOT_PATH               = 
+DOTFILE_DIRS           = 
+DOT_GRAPH_MAX_NODES    = 50
+MAX_DOT_GRAPH_DEPTH    = 1000
+DOT_TRANSPARENT        = NO
+DOT_MULTI_TARGETS      = NO
+GENERATE_LEGEND        = YES
+DOT_CLEANUP            = YES
+#---------------------------------------------------------------------------
+# Configuration::additions related to the search engine   
+#---------------------------------------------------------------------------
+SEARCHENGINE           = NO

Eigen/Array

@@ -0,0 +1,45 @@
+#ifndef EIGEN_ARRAY_MODULE_H
+#define EIGEN_ARRAY_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup Array_Module Array module
+  * This module provides several handy features to manipulate matrices as simple array of values.
+  * In addition to listed classes, it defines various methods of the Cwise interface
+  * (accessible from MatrixBase::cwise()), including:
+  *  - matrix-scalar sum,
+  *  - coeff-wise comparison operators,
+  *  - sin, cos, sqrt, pow, exp, log, square, cube, inverse (reciprocal).
+  *
+  * This module also provides various MatrixBase methods, including:
+  *  - boolean reductions: \ref MatrixBase::all() "all", \ref MatrixBase::any() "any", \ref MatrixBase::count() "count",
+  *  - \ref MatrixBase::Random() "random matrix initialization",
+  *  - a \ref MatrixBase::select() "select" function mimicking the trivariate ?: operator,
+  *  - \ref MatrixBase::colwise() "column-wise" and \ref MatrixBase::rowwise() "row-wise" reductions,
+  *  - \ref MatrixBase::reverse() "matrix reverse",
+  *  - \ref MatrixBase::lpNorm() "generic matrix norm".
+  *
+  * \code
+  * #include <Eigen/Array>
+  * \endcode
+  */
+
+#include "src/Array/CwiseOperators.h"
+#include "src/Array/Functors.h"
+#include "src/Array/BooleanRedux.h"
+#include "src/Array/Select.h"
+#include "src/Array/PartialRedux.h"
+#include "src/Array/Random.h"
+#include "src/Array/Norms.h"
+#include "src/Array/Replicate.h"
+#include "src/Array/Reverse.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_ARRAY_MODULE_H

Eigen/CMakeLists.txt

@@ -0,0 +1,28 @@
+set(Eigen_HEADERS Core LU Cholesky QR Geometry Sparse Array SVD LeastSquares QtAlignedMalloc StdVector)
+
+if(EIGEN_BUILD_LIB)
+    set(Eigen_SRCS
+      src/Core/CoreInstantiations.cpp
+      src/Cholesky/CholeskyInstantiations.cpp
+      src/QR/QrInstantiations.cpp
+    )
+
+    add_library(Eigen2 SHARED ${Eigen_SRCS})
+
+    install(TARGETS Eigen2
+            RUNTIME DESTINATION bin
+            LIBRARY DESTINATION lib
+            ARCHIVE DESTINATION lib)
+endif(EIGEN_BUILD_LIB)
+
+if(CMAKE_COMPILER_IS_GNUCXX)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -g1 -O2")
+    set(CMAKE_CXX_FLAGS_RELWITHDEBINFO "${CMAKE_CXX_FLAGS_RELWITHDEBINFO} -g1 -O2")
+endif(CMAKE_COMPILER_IS_GNUCXX)
+
+install(FILES
+  ${Eigen_HEADERS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel
+  )
+
+add_subdirectory(src)

Eigen/Cholesky

@@ -0,0 +1,65 @@
+#ifndef EIGEN_CHOLESKY_MODULE_H
+#define EIGEN_CHOLESKY_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module
+#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2)
+  #ifndef EIGEN_HIDE_HEAVY_CODE
+  #define EIGEN_HIDE_HEAVY_CODE
+  #endif
+#elif defined EIGEN_HIDE_HEAVY_CODE
+  #undef EIGEN_HIDE_HEAVY_CODE
+#endif
+
+namespace Eigen {
+
+/** \defgroup Cholesky_Module Cholesky module
+  *
+  * \nonstableyet
+  *
+  * This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
+  * Those decompositions are accessible via the following MatrixBase methods:
+  *  - MatrixBase::llt(),
+  *  - MatrixBase::ldlt()
+  *
+  * \code
+  * #include <Eigen/Cholesky>
+  * \endcode
+  */
+
+#include "src/Array/CwiseOperators.h"
+#include "src/Array/Functors.h"
+#include "src/Cholesky/LLT.h"
+#include "src/Cholesky/LDLT.h"
+
+} // namespace Eigen
+
+#define EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(MATRIXTYPE,PREFIX) \
+  PREFIX template class LLT<MATRIXTYPE>; \
+  PREFIX template class LDLT<MATRIXTYPE>
+
+#define EIGEN_CHOLESKY_MODULE_INSTANTIATE(PREFIX) \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix2f,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix2d,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix3f,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix3d,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix4f,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(Matrix4d,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(MatrixXf,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(MatrixXd,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(MatrixXcf,PREFIX); \
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE_TYPE(MatrixXcd,PREFIX)
+
+#ifdef EIGEN_EXTERN_INSTANTIATIONS
+
+namespace Eigen {
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE(extern);
+} // namespace Eigen
+#endif
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_CHOLESKY_MODULE_H

Eigen/Core

@@ -0,0 +1,186 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CORE_H
+#define EIGEN_CORE_H
+
+// first thing Eigen does: prevent MSVC from committing suicide
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+#ifdef _MSC_VER
+  #include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled
+  #if (_MSC_VER >= 1500) // 2008 or later
+    // Remember that usage of defined() in a #define is undefined by the standard.
+    // a user reported that in 64-bit mode, MSVC doesn't care to define _M_IX86_FP.
+    #if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(_M_X64)
+      #define EIGEN_SSE2_ON_MSVC_2008_OR_LATER
+    #endif
+  #endif
+#endif
+
+#ifdef __GNUC__
+  #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__>=x && __GNUC_MINOR__>=y) || __GNUC__>x)
+#else
+  #define EIGEN_GNUC_AT_LEAST(x,y) 0
+#endif
+
+// Remember that usage of defined() in a #define is undefined by the standard
+#if (defined __SSE2__) && ( (!defined __GNUC__) || EIGEN_GNUC_AT_LEAST(4,2) )
+  #define EIGEN_SSE2_BUT_NOT_OLD_GCC
+#endif
+
+#ifdef EIGEN_DONT_ALIGN
+  #define EIGEN_DONT_VECTORIZE
+#endif
+
+#ifndef EIGEN_DONT_VECTORIZE
+  #if defined (EIGEN_SSE2_BUT_NOT_OLD_GCC) || defined(EIGEN_SSE2_ON_MSVC_2008_OR_LATER)
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_SSE
+    #include <emmintrin.h>
+    #include <xmmintrin.h>
+    #ifdef __SSE3__
+      #include <pmmintrin.h>
+    #endif
+    #ifdef __SSSE3__
+      #include <tmmintrin.h>
+    #endif
+  #elif defined __ALTIVEC__
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_ALTIVEC
+    #include <altivec.h>
+    // We need to #undef all these ugly tokens defined in <altivec.h>
+    // => use __vector instead of vector
+    #undef bool
+    #undef vector
+    #undef pixel
+  #endif
+#endif
+
+#include <cstdlib>
+#include <cmath>
+#include <complex>
+#include <cassert>
+#include <functional>
+#include <iostream>
+#include <cstring>
+#include <string>
+#include <limits>
+
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(EIGEN_NO_EXCEPTIONS)
+  #define EIGEN_EXCEPTIONS
+#endif
+
+#ifdef EIGEN_EXCEPTIONS
+  #include <new>
+#endif
+
+// this needs to be done after all possible windows C header includes and before any Eigen source includes
+// (system C++ includes are supposed to be able to deal with this already):
+// windows.h defines min and max macros which would make Eigen fail to compile.
+#if defined(min) || defined(max)
+#error The preprocessor symbols 'min' or 'max' are defined. If you are compiling on Windows, do #define NOMINMAX to prevent windows.h from defining these symbols.
+#endif
+
+namespace Eigen {
+
+/** \defgroup Core_Module Core module
+  * This is the main module of Eigen providing dense matrix and vector support
+  * (both fixed and dynamic size) with all the features corresponding to a BLAS library
+  * and much more...
+  *
+  * \code
+  * #include <Eigen/Core>
+  * \endcode
+  */
+
+#include "src/Core/util/Macros.h"
+#include "src/Core/util/Constants.h"
+#include "src/Core/util/ForwardDeclarations.h"
+#include "src/Core/util/Meta.h"
+#include "src/Core/util/XprHelper.h"
+#include "src/Core/util/StaticAssert.h"
+#include "src/Core/util/Memory.h"
+
+#include "src/Core/NumTraits.h"
+#include "src/Core/MathFunctions.h"
+#include "src/Core/GenericPacketMath.h"
+
+#if defined EIGEN_VECTORIZE_SSE
+  #include "src/Core/arch/SSE/PacketMath.h"
+  #include "src/Core/arch/SSE/MathFunctions.h"
+#elif defined EIGEN_VECTORIZE_ALTIVEC
+  #include "src/Core/arch/AltiVec/PacketMath.h"
+#endif
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
+#endif
+
+#include "src/Core/Functors.h"
+#include "src/Core/MatrixBase.h"
+#include "src/Core/Coeffs.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/MatrixStorage.h"
+#include "src/Core/NestByValue.h"
+#include "src/Core/ReturnByValue.h"
+#include "src/Core/Flagged.h"
+#include "src/Core/Matrix.h"
+#include "src/Core/Cwise.h"
+#include "src/Core/CwiseBinaryOp.h"
+#include "src/Core/CwiseUnaryOp.h"
+#include "src/Core/CwiseNullaryOp.h"
+#include "src/Core/Dot.h"
+#include "src/Core/DiagonalProduct.h"
+#include "src/Core/SolveTriangular.h"
+#include "src/Core/MapBase.h"
+#include "src/Core/Map.h"
+#include "src/Core/Block.h"
+#include "src/Core/Minor.h"
+#include "src/Core/Transpose.h"
+#include "src/Core/DiagonalMatrix.h"
+#include "src/Core/Diagonal.h"
+#include "src/Core/Redux.h"
+#include "src/Core/Visitor.h"
+#include "src/Core/Fuzzy.h"
+#include "src/Core/IO.h"
+#include "src/Core/Swap.h"
+#include "src/Core/CommaInitializer.h"
+#include "src/Core/Part.h"
+#include "src/Core/Product.h"
+#include "src/Core/products/GeneralMatrixMatrix.h"
+#include "src/Core/products/GeneralMatrixVector.h"
+#include "src/Core/products/SelfadjointMatrixVector.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_CORE_H

Eigen/Geometry

@@ -0,0 +1,56 @@
+#ifndef EIGEN_GEOMETRY_MODULE_H
+#define EIGEN_GEOMETRY_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+#include "Array"
+#include <limits>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+namespace Eigen {
+
+/** \defgroup Geometry_Module Geometry module
+  *
+  * \nonstableyet
+  *
+  * This module provides support for:
+  *  - fixed-size homogeneous transformations
+  *  - translation, scaling, 2D and 3D rotations
+  *  - quaternions
+  *  - \ref MatrixBase::cross() "cross product"
+  *  - \ref MatrixBase::unitOrthogonal() "orthognal vector generation"
+  *  - some linear components: parametrized-lines and hyperplanes
+  *
+  * \code
+  * #include <Eigen/Geometry>
+  * \endcode
+  */
+
+#include "src/Geometry/OrthoMethods.h"
+#include "src/Geometry/Homogeneous.h"
+#include "src/Geometry/RotationBase.h"
+#include "src/Geometry/Rotation2D.h"
+#include "src/Geometry/Quaternion.h"
+#include "src/Geometry/AngleAxis.h"
+#include "src/Geometry/EulerAngles.h"
+#include "src/Geometry/Transform.h"
+#include "src/Geometry/Translation.h"
+#include "src/Geometry/Scaling.h"
+#include "src/Geometry/Hyperplane.h"
+#include "src/Geometry/ParametrizedLine.h"
+#include "src/Geometry/AlignedBox.h"
+
+#if defined EIGEN_VECTORIZE_SSE
+  #include "src/Geometry/arch/Geometry_SSE.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_GEOMETRY_MODULE_H

Eigen/LU

@@ -0,0 +1,30 @@
+#ifndef EIGEN_LU_MODULE_H
+#define EIGEN_LU_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup LU_Module LU module
+  * This module includes %LU decomposition and related notions such as matrix inversion and determinant.
+  * This module defines the following MatrixBase methods:
+  *  - MatrixBase::inverse()
+  *  - MatrixBase::determinant()
+  *
+  * \code
+  * #include <Eigen/LU>
+  * \endcode
+  */
+
+#include "src/LU/LU.h"
+#include "src/LU/PartialLU.h"
+#include "src/LU/Determinant.h"
+#include "src/LU/Inverse.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_LU_MODULE_H

Eigen/LeastSquares

@@ -0,0 +1,27 @@
+#ifndef EIGEN_REGRESSION_MODULE_H
+#define EIGEN_REGRESSION_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+#include "QR"
+#include "Geometry"
+
+namespace Eigen {
+
+/** \defgroup LeastSquares_Module LeastSquares module
+  * This module provides linear regression and related features.
+  *
+  * \code
+  * #include <Eigen/LeastSquares>
+  * \endcode
+  */
+
+#include "src/LeastSquares/LeastSquares.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_REGRESSION_MODULE_H

Eigen/QR

@@ -0,0 +1,73 @@
+#ifndef EIGEN_QR_MODULE_H
+#define EIGEN_QR_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+#include "Cholesky"
+
+// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module
+#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2)
+  #ifndef EIGEN_HIDE_HEAVY_CODE
+  #define EIGEN_HIDE_HEAVY_CODE
+  #endif
+#elif defined EIGEN_HIDE_HEAVY_CODE
+  #undef EIGEN_HIDE_HEAVY_CODE
+#endif
+
+namespace Eigen {
+
+/** \defgroup QR_Module QR module
+  *
+  * \nonstableyet
+  *
+  * This module mainly provides QR decomposition and an eigen value solver.
+  * This module also provides some MatrixBase methods, including:
+  *  - MatrixBase::qr(),
+  *  - MatrixBase::eigenvalues(),
+  *  - MatrixBase::operatorNorm()
+  *
+  * \code
+  * #include <Eigen/QR>
+  * \endcode
+  */
+
+#include "src/QR/QR.h"
+#include "src/QR/Tridiagonalization.h"
+#include "src/QR/EigenSolver.h"
+#include "src/QR/SelfAdjointEigenSolver.h"
+#include "src/QR/HessenbergDecomposition.h"
+
+// declare all classes for a given matrix type
+#define EIGEN_QR_MODULE_INSTANTIATE_TYPE(MATRIXTYPE,PREFIX) \
+  PREFIX template class QR<MATRIXTYPE>; \
+  PREFIX template class Tridiagonalization<MATRIXTYPE>; \
+  PREFIX template class HessenbergDecomposition<MATRIXTYPE>; \
+  PREFIX template class SelfAdjointEigenSolver<MATRIXTYPE>
+
+// removed because it does not support complex yet
+//  PREFIX template class EigenSolver<MATRIXTYPE>
+
+// declare all class for all types
+#define EIGEN_QR_MODULE_INSTANTIATE(PREFIX) \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix2f,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix2d,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix3f,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix3d,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix4f,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(Matrix4d,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(MatrixXf,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(MatrixXd,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(MatrixXcf,PREFIX); \
+  EIGEN_QR_MODULE_INSTANTIATE_TYPE(MatrixXcd,PREFIX)
+
+#ifdef EIGEN_EXTERN_INSTANTIATIONS
+  EIGEN_QR_MODULE_INSTANTIATE(extern);
+#endif // EIGEN_EXTERN_INSTANTIATIONS
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_QR_MODULE_H

Eigen/QtAlignedMalloc

@@ -0,0 +1,29 @@
+
+#ifndef EIGEN_QTMALLOC_MODULE_H
+#define EIGEN_QTMALLOC_MODULE_H
+
+#include "Core"
+
+#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
+
+inline void *qMalloc(size_t size)
+{
+  return Eigen::ei_aligned_malloc(size);
+}
+
+inline void qFree(void *ptr)
+{
+  Eigen::ei_aligned_free(ptr);
+}
+
+inline void *qRealloc(void *ptr, size_t size)
+{
+  void* newPtr = Eigen::ei_aligned_malloc(size);
+  memcpy(newPtr, ptr, size);
+  Eigen::ei_aligned_free(ptr);
+  return newPtr;
+}
+
+#endif
+
+#endif // EIGEN_QTMALLOC_MODULE_H

Eigen/SVD

@@ -0,0 +1,29 @@
+#ifndef EIGEN_SVD_MODULE_H
+#define EIGEN_SVD_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+namespace Eigen {
+
+/** \defgroup SVD_Module SVD module
+  *
+  * \nonstableyet
+  *
+  * This module provides SVD decomposition for (currently) real matrices.
+  * This decomposition is accessible via the following MatrixBase method:
+  *  - MatrixBase::svd()
+  *
+  * \code
+  * #include <Eigen/SVD>
+  * \endcode
+  */
+
+#include "src/SVD/SVD.h"
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_SVD_MODULE_H

Eigen/Sparse

@@ -0,0 +1,133 @@
+#ifndef EIGEN_SPARSE_MODULE_H
+#define EIGEN_SPARSE_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableMSVCWarnings.h"
+
+#include <vector>
+#include <map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+
+#ifdef EIGEN_GOOGLEHASH_SUPPORT
+  #include <google/dense_hash_map>
+#endif
+
+#ifdef EIGEN_CHOLMOD_SUPPORT
+  extern "C" {
+    #include "cholmod.h"
+  }
+#endif
+
+#ifdef EIGEN_TAUCS_SUPPORT
+  // taucs.h declares a lot of mess
+  #define isnan
+  #define finite
+  #define isinf
+  extern "C" {
+    #include "taucs.h"
+  }
+  #undef isnan
+  #undef finite
+  #undef isinf
+
+  #ifdef min
+    #undef min
+  #endif
+  #ifdef max
+    #undef max
+  #endif
+  #ifdef complex
+    #undef complex
+  #endif
+#endif
+
+#ifdef EIGEN_SUPERLU_SUPPORT
+  typedef int int_t;
+  #include "slu_Cnames.h"
+  #include "supermatrix.h"
+  #include "slu_util.h"
+
+  namespace SuperLU_S {
+  #include "slu_sdefs.h"
+  }
+  namespace SuperLU_D {
+  #include "slu_ddefs.h"
+  }
+  namespace SuperLU_C {
+  #include "slu_cdefs.h"
+  }
+  namespace SuperLU_Z {
+  #include "slu_zdefs.h"
+  }
+  namespace Eigen { struct SluMatrix; }
+#endif
+
+#ifdef EIGEN_UMFPACK_SUPPORT
+  #include "umfpack.h"
+#endif
+
+namespace Eigen {
+
+/** \defgroup Sparse_Module Sparse module
+  *
+  * \nonstableyet
+  *
+  * See the \ref TutorialSparse "Sparse tutorial"
+  *
+  * \code
+  * #include <Eigen/QR>
+  * \endcode
+  */
+
+#include "src/Sparse/SparseUtil.h"
+#include "src/Sparse/SparseMatrixBase.h"
+#include "src/Sparse/CompressedStorage.h"
+#include "src/Sparse/AmbiVector.h"
+#include "src/Sparse/RandomSetter.h"
+#include "src/Sparse/SparseBlock.h"
+#include "src/Sparse/SparseMatrix.h"
+#include "src/Sparse/DynamicSparseMatrix.h"
+#include "src/Sparse/MappedSparseMatrix.h"
+#include "src/Sparse/SparseVector.h"
+#include "src/Sparse/CoreIterators.h"
+#include "src/Sparse/SparseTranspose.h"
+#include "src/Sparse/SparseCwise.h"
+#include "src/Sparse/SparseCwiseUnaryOp.h"
+#include "src/Sparse/SparseCwiseBinaryOp.h"
+#include "src/Sparse/SparseDot.h"
+#include "src/Sparse/SparseAssign.h"
+#include "src/Sparse/SparseRedux.h"
+#include "src/Sparse/SparseFuzzy.h"
+#include "src/Sparse/SparseFlagged.h"
+#include "src/Sparse/SparseProduct.h"
+#include "src/Sparse/SparseDiagonalProduct.h"
+#include "src/Sparse/SparseTriangular.h"
+#include "src/Sparse/TriangularSolver.h"
+#include "src/Sparse/SparseLLT.h"
+#include "src/Sparse/SparseLDLT.h"
+#include "src/Sparse/SparseLU.h"
+
+#ifdef EIGEN_CHOLMOD_SUPPORT
+# include "src/Sparse/CholmodSupport.h"
+#endif
+
+#ifdef EIGEN_TAUCS_SUPPORT
+# include "src/Sparse/TaucsSupport.h"
+#endif
+
+#ifdef EIGEN_SUPERLU_SUPPORT
+# include "src/Sparse/SuperLUSupport.h"
+#endif
+
+#ifdef EIGEN_UMFPACK_SUPPORT
+# include "src/Sparse/UmfPackSupport.h"
+#endif
+
+} // namespace Eigen
+
+#include "src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_SPARSE_MODULE_H

Eigen/StdVector

@@ -0,0 +1,167 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STDVECTOR_MODULE_H
+#define EIGEN_STDVECTOR_MODULE_H
+
+#include "Core"
+#include <vector>
+
+namespace Eigen {
+
+// This one is needed to prevent reimplementing the whole std::vector.
+template <class T>
+class aligned_allocator_indirection : public aligned_allocator<T>
+{
+public:
+  typedef size_t    size_type;
+  typedef ptrdiff_t difference_type;
+  typedef T*        pointer;
+  typedef const T*  const_pointer;
+  typedef T&        reference;
+  typedef const T&  const_reference;
+  typedef T         value_type;
+
+  template<class U>
+  struct rebind
+  {
+    typedef aligned_allocator_indirection<U> other;
+  };
+
+  aligned_allocator_indirection() throw() {}
+  aligned_allocator_indirection(const aligned_allocator_indirection& ) throw() : aligned_allocator<T>() {}
+  aligned_allocator_indirection(const aligned_allocator<T>& ) throw() {}
+  template<class U>
+  aligned_allocator_indirection(const aligned_allocator_indirection<U>& ) throw() {}
+  template<class U>
+  aligned_allocator_indirection(const aligned_allocator<U>& ) throw() {}
+  ~aligned_allocator_indirection() throw() {}
+};
+
+#ifdef _MSC_VER
+
+  // sometimes, MSVC detects, at compile time, that the argument x
+  // in std::vector::resize(size_t s,T x) won't be aligned and generate an error
+  // even if this function is never called. Whence this little wrapper.
+  #define EIGEN_WORKAROUND_MSVC_STD_VECTOR(T) Eigen::ei_workaround_msvc_std_vector<T>
+  template<typename T> struct ei_workaround_msvc_std_vector : public T
+  {
+    inline ei_workaround_msvc_std_vector() : T() {}
+    inline ei_workaround_msvc_std_vector(const T& other) : T(other) {}
+    inline operator T& () { return *static_cast<T*>(this); }
+    inline operator const T& () const { return *static_cast<const T*>(this); }
+    template<typename OtherT>
+    inline T& operator=(const OtherT& other)
+    { T::operator=(other); return *this; }
+    inline ei_workaround_msvc_std_vector& operator=(const ei_workaround_msvc_std_vector& other)
+    { T::operator=(other); return *this; }
+  };
+
+#else
+
+  #define EIGEN_WORKAROUND_MSVC_STD_VECTOR(T) T
+
+#endif
+
+}
+
+namespace std {
+
+#define EIGEN_STD_VECTOR_SPECIALIZATION_BODY \
+  public:  \
+    typedef T value_type; \
+    typedef typename vector_base::allocator_type allocator_type; \
+    typedef typename vector_base::size_type size_type;  \
+    typedef typename vector_base::iterator iterator;  \
+    typedef typename vector_base::const_iterator const_iterator;  \
+    explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {}  \
+    template<typename InputIterator> \
+    vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \
+    : vector_base(first, last, a) {} \
+    vector(const vector& c) : vector_base(c) {}  \
+    explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \
+    vector(iterator start, iterator end) : vector_base(start, end) {}  \
+    vector& operator=(const vector& x) {  \
+      vector_base::operator=(x);  \
+      return *this;  \
+    }
+
+template<typename T>
+class vector<T,Eigen::aligned_allocator<T> >
+  : public vector<EIGEN_WORKAROUND_MSVC_STD_VECTOR(T),
+                  Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STD_VECTOR(T)> >
+{
+  typedef vector<EIGEN_WORKAROUND_MSVC_STD_VECTOR(T),
+                 Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STD_VECTOR(T)> > vector_base;
+  EIGEN_STD_VECTOR_SPECIALIZATION_BODY
+
+  void resize(size_type new_size)
+  { resize(new_size, T()); }
+
+#if defined(_VECTOR_)
+  // workaround MSVC std::vector implementation
+  void resize(size_type new_size, const value_type& x)
+  {
+    if (vector_base::size() < new_size)
+      vector_base::_Insert_n(vector_base::end(), new_size - vector_base::size(), x);
+    else if (new_size < vector_base::size())
+      vector_base::erase(vector_base::begin() + new_size, vector_base::end());
+  }
+  void push_back(const value_type& x)
+  { vector_base::push_back(x); } 
+  using vector_base::insert;  
+  iterator insert(const_iterator position, const value_type& x)
+  { return vector_base::insert(position,x); }
+  void insert(const_iterator position, size_type new_size, const value_type& x)
+  { vector_base::insert(position, new_size, x); }
+#elif defined(_GLIBCXX_VECTOR) && EIGEN_GNUC_AT_LEAST(4,1)
+  // workaround GCC std::vector implementation
+  // Note that before gcc-4.1 we already have: std::vector::resize(size_type,const T&),
+  // no no need to workaround !
+  void resize(size_type new_size, const value_type& x)
+  {
+    if (new_size < vector_base::size())
+      vector_base::_M_erase_at_end(this->_M_impl._M_start + new_size);
+    else
+      vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);
+  }
+#elif defined(_GLIBCXX_VECTOR)
+  using vector_base::resize;
+#else
+  // default implementation which should always work.
+  void resize(size_type new_size, const value_type& x)
+  {
+    if (new_size < vector_base::size())
+      vector_base::erase(vector_base::begin() + new_size, vector_base::end());
+    else if (new_size > vector_base::size())
+      vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);
+  }
+#endif
+
+};
+
+}
+
+#endif // EIGEN_STDVECTOR_MODULE_H

Eigen/src/Array/BooleanRedux.h

@@ -0,0 +1,145 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ALLANDANY_H
+#define EIGEN_ALLANDANY_H
+
+template<typename Derived, int UnrollCount>
+struct ei_all_unroller
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static bool run(const Derived &mat)
+  {
+    return ei_all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
+  }
+};
+
+template<typename Derived>
+struct ei_all_unroller<Derived, 1>
+{
+  inline static bool run(const Derived &mat) { return mat.coeff(0, 0); }
+};
+
+template<typename Derived>
+struct ei_all_unroller<Derived, Dynamic>
+{
+  inline static bool run(const Derived &) { return false; }
+};
+
+template<typename Derived, int UnrollCount>
+struct ei_any_unroller
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static bool run(const Derived &mat)
+  {
+    return ei_any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
+  }
+};
+
+template<typename Derived>
+struct ei_any_unroller<Derived, 1>
+{
+  inline static bool run(const Derived &mat) { return mat.coeff(0, 0); }
+};
+
+template<typename Derived>
+struct ei_any_unroller<Derived, Dynamic>
+{
+  inline static bool run(const Derived &) { return false; }
+};
+
+/** \array_module
+  * 
+  * \returns true if all coefficients are true
+  *
+  * \addexample CwiseAll \label How to check whether a point is inside a box (using operator< and all())
+  *
+  * Example: \include MatrixBase_all.cpp
+  * Output: \verbinclude MatrixBase_all.out
+  *
+  * \sa MatrixBase::any(), Cwise::operator<()
+  */
+template<typename Derived>
+inline bool MatrixBase<Derived>::all() const
+{
+  const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
+                      <= EIGEN_UNROLLING_LIMIT;
+  if(unroll)
+    return ei_all_unroller<Derived,
+                           unroll ? int(SizeAtCompileTime) : Dynamic
+     >::run(derived());
+  else
+  {
+    for(int j = 0; j < cols(); ++j)
+      for(int i = 0; i < rows(); ++i)
+        if (!coeff(i, j)) return false;
+    return true;
+  }
+}
+
+/** \array_module
+  * 
+  * \returns true if at least one coefficient is true
+  *
+  * \sa MatrixBase::all()
+  */
+template<typename Derived>
+inline bool MatrixBase<Derived>::any() const
+{
+  const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
+                      <= EIGEN_UNROLLING_LIMIT;
+  if(unroll)
+    return ei_any_unroller<Derived,
+                           unroll ? int(SizeAtCompileTime) : Dynamic
+           >::run(derived());
+  else
+  {
+    for(int j = 0; j < cols(); ++j)
+      for(int i = 0; i < rows(); ++i)
+        if (coeff(i, j)) return true;
+    return false;
+  }
+}
+
+/** \array_module
+  * 
+  * \returns the number of coefficients which evaluate to true
+  *
+  * \sa MatrixBase::all(), MatrixBase::any()
+  */
+template<typename Derived>
+inline int MatrixBase<Derived>::count() const
+{
+  return this->cast<bool>().cast<int>().sum();
+}
+
+#endif // EIGEN_ALLANDANY_H

Eigen/src/Array/CMakeLists.txt

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

Eigen/src/Array/CwiseOperators.h

@@ -0,0 +1,453 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAY_CWISE_OPERATORS_H
+#define EIGEN_ARRAY_CWISE_OPERATORS_H
+
+// -- unary operators --
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise square root of *this.
+  *
+  * Example: \include Cwise_sqrt.cpp
+  * Output: \verbinclude Cwise_sqrt.out
+  *
+  * \sa pow(), square()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_sqrt_op)
+Cwise<ExpressionType>::sqrt() const
+{
+  return _expression();
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise exponential of *this.
+  *
+  * Example: \include Cwise_exp.cpp
+  * Output: \verbinclude Cwise_exp.out
+  *
+  * \sa pow(), log(), sin(), cos()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_exp_op)
+Cwise<ExpressionType>::exp() const
+{
+  return _expression();
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise logarithm of *this.
+  *
+  * Example: \include Cwise_log.cpp
+  * Output: \verbinclude Cwise_log.out
+  *
+  * \sa exp()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_log_op)
+Cwise<ExpressionType>::log() const
+{
+  return _expression();
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise cosine of *this.
+  *
+  * Example: \include Cwise_cos.cpp
+  * Output: \verbinclude Cwise_cos.out
+  *
+  * \sa sin(), exp(), EIGEN_FAST_MATH
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_cos_op)
+Cwise<ExpressionType>::cos() const
+{
+  return _expression();
+}
+
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise sine of *this.
+  *
+  * Example: \include Cwise_sin.cpp
+  * Output: \verbinclude Cwise_sin.out
+  *
+  * \sa cos(), exp(), EIGEN_FAST_MATH
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_sin_op)
+Cwise<ExpressionType>::sin() const
+{
+  return _expression();
+}
+
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise power of *this to the given exponent.
+  *
+  * Example: \include Cwise_pow.cpp
+  * Output: \verbinclude Cwise_pow.out
+  *
+  * \sa exp(), log()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_pow_op)
+Cwise<ExpressionType>::pow(const Scalar& exponent) const
+{
+  return EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_pow_op)(_expression(), ei_scalar_pow_op<Scalar>(exponent));
+}
+
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise inverse of *this.
+  *
+  * Example: \include Cwise_inverse.cpp
+  * Output: \verbinclude Cwise_inverse.out
+  *
+  * \sa operator/(), operator*()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_inverse_op)
+Cwise<ExpressionType>::inverse() const
+{
+  return _expression();
+}
+
+/** \array_module
+  *
+  * \returns an expression of the coefficient-wise square of *this.
+  *
+  * Example: \include Cwise_square.cpp
+  * Output: \verbinclude Cwise_square.out
+  *
+  * \sa operator/(), operator*(), abs2()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_square_op)
+Cwise<ExpressionType>::square() const
+{
+  return _expression();
+}
+
+/** \array_module
+  *
+  * \returns an expression of the coefficient-wise cube of *this.
+  *
+  * Example: \include Cwise_cube.cpp
+  * Output: \verbinclude Cwise_cube.out
+  *
+  * \sa square(), pow()
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_cube_op)
+Cwise<ExpressionType>::cube() const
+{
+  return _expression();
+}
+
+
+// -- binary operators --
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \< operator of *this and \a other
+  *
+  * Example: \include Cwise_less.cpp
+  * Output: \verbinclude Cwise_less.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), operator>(), operator<=()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)
+Cwise<ExpressionType>::operator<(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)(_expression(), other.derived());
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \<= operator of *this and \a other
+  *
+  * Example: \include Cwise_less_equal.cpp
+  * Output: \verbinclude Cwise_less_equal.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), operator>=(), operator<()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)
+Cwise<ExpressionType>::operator<=(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)(_expression(), other.derived());
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \> operator of *this and \a other
+  *
+  * Example: \include Cwise_greater.cpp
+  * Output: \verbinclude Cwise_greater.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), operator>=(), operator<()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)
+Cwise<ExpressionType>::operator>(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)(_expression(), other.derived());
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \>= operator of *this and \a other
+  *
+  * Example: \include Cwise_greater_equal.cpp
+  * Output: \verbinclude Cwise_greater_equal.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), operator>(), operator<=()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)
+Cwise<ExpressionType>::operator>=(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)(_expression(), other.derived());
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise == operator of *this and \a other
+  *
+  * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+  * generally a far better idea to use a fuzzy comparison as provided by MatrixBase::isApprox() and
+  * MatrixBase::isMuchSmallerThan().
+  *
+  * Example: \include Cwise_equal_equal.cpp
+  * Output: \verbinclude Cwise_equal_equal.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), MatrixBase::isApprox(), MatrixBase::isMuchSmallerThan()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)
+Cwise<ExpressionType>::operator==(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)(_expression(), other.derived());
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise != operator of *this and \a other
+  *
+  * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+  * generally a far better idea to use a fuzzy comparison as provided by MatrixBase::isApprox() and
+  * MatrixBase::isMuchSmallerThan().
+  *
+  * Example: \include Cwise_not_equal.cpp
+  * Output: \verbinclude Cwise_not_equal.out
+  *
+  * \sa MatrixBase::all(), MatrixBase::any(), MatrixBase::isApprox(), MatrixBase::isMuchSmallerThan()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline const EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)
+Cwise<ExpressionType>::operator!=(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)(_expression(), other.derived());
+}
+
+// comparisons to scalar value
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \< operator of *this and a scalar \a s
+  *
+  * \sa operator<(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)
+Cwise<ExpressionType>::operator<(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \<= operator of *this and a scalar \a s
+  *
+  * \sa operator<=(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)
+Cwise<ExpressionType>::operator<=(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \> operator of *this and a scalar \a s
+  *
+  * \sa operator>(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)
+Cwise<ExpressionType>::operator>(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise \>= operator of *this and a scalar \a s
+  *
+  * \sa operator>=(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)
+Cwise<ExpressionType>::operator>=(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise == operator of *this and a scalar \a s
+  *
+  * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+  * generally a far better idea to use a fuzzy comparison as provided by MatrixBase::isApprox() and
+  * MatrixBase::isMuchSmallerThan().
+  *
+  * \sa operator==(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)
+Cwise<ExpressionType>::operator==(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+/** \array_module
+  * 
+  * \returns an expression of the coefficient-wise != operator of *this and a scalar \a s
+  *
+  * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+  * generally a far better idea to use a fuzzy comparison as provided by MatrixBase::isApprox() and
+  * MatrixBase::isMuchSmallerThan().
+  *
+  * \sa operator!=(const MatrixBase<OtherDerived> &) const
+  */
+template<typename ExpressionType>
+inline const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)
+Cwise<ExpressionType>::operator!=(Scalar s) const
+{
+  return EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)(_expression(),
+            typename ExpressionType::ConstantReturnType(_expression().rows(), _expression().cols(), s));
+}
+
+// scalar addition
+
+/** \array_module
+  *
+  * \returns an expression of \c *this with each coeff incremented by the constant \a scalar
+  *
+  * Example: \include Cwise_plus.cpp
+  * Output: \verbinclude Cwise_plus.out
+  *
+  * \sa operator+=(), operator-()
+  */
+template<typename ExpressionType>
+inline const typename Cwise<ExpressionType>::ScalarAddReturnType
+Cwise<ExpressionType>::operator+(const Scalar& scalar) const
+{
+  return typename Cwise<ExpressionType>::ScalarAddReturnType(m_matrix, ei_scalar_add_op<Scalar>(scalar));
+}
+
+/** \array_module
+  *
+  * Adds the given \a scalar to each coeff of this expression.
+  *
+  * Example: \include Cwise_plus_equal.cpp
+  * Output: \verbinclude Cwise_plus_equal.out
+  *
+  * \sa operator+(), operator-=()
+  */
+template<typename ExpressionType>
+inline ExpressionType& Cwise<ExpressionType>::operator+=(const Scalar& scalar)
+{
+  return m_matrix.const_cast_derived() = *this + scalar;
+}
+
+/** \array_module
+  *
+  * \returns an expression of \c *this with each coeff decremented by the constant \a scalar
+  *
+  * Example: \include Cwise_minus.cpp
+  * Output: \verbinclude Cwise_minus.out
+  *
+  * \sa operator+(), operator-=()
+  */
+template<typename ExpressionType>
+inline const typename Cwise<ExpressionType>::ScalarAddReturnType
+Cwise<ExpressionType>::operator-(const Scalar& scalar) const
+{
+  return *this + (-scalar);
+}
+
+/** \array_module
+  *
+  * Substracts the given \a scalar from each coeff of this expression.
+  *
+  * Example: \include Cwise_minus_equal.cpp
+  * Output: \verbinclude Cwise_minus_equal.out
+  *
+  * \sa operator+=(), operator-()
+  */
+
+template<typename ExpressionType>
+inline ExpressionType& Cwise<ExpressionType>::operator-=(const Scalar& scalar)
+{
+  return m_matrix.const_cast_derived() = *this - scalar;
+}
+
+#endif // EIGEN_ARRAY_CWISE_OPERATORS_H

Eigen/src/Array/Functors.h

@@ -0,0 +1,329 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAY_FUNCTORS_H
+#define EIGEN_ARRAY_FUNCTORS_H
+
+/** \internal
+  * \array_module
+  *
+  * \brief Template functor to add a scalar to a fixed other one
+  *
+  * \sa class CwiseUnaryOp, Array::operator+
+  */
+/* If you wonder why doing the ei_pset1() in packetOp() is an optimization check ei_scalar_multiple_op */
+template<typename Scalar>
+struct ei_scalar_add_op {
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  inline ei_scalar_add_op(const ei_scalar_add_op& other) : m_other(other.m_other) { }
+  inline ei_scalar_add_op(const Scalar& other) : m_other(other) { }
+  inline Scalar operator() (const Scalar& a) const { return a + m_other; }
+  inline const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_padd(a, ei_pset1(m_other)); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_add_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = ei_packet_traits<Scalar>::size>1 }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the square root of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::sqrt()
+  */
+template<typename Scalar> struct ei_scalar_sqrt_op EIGEN_EMPTY_STRUCT {
+  inline const Scalar operator() (const Scalar& a) const { return ei_sqrt(a); }
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return ei_psqrt(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_sqrt_op<Scalar> >
+{ enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = ei_packet_traits<Scalar>::HasSqrt
+  };
+};
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the exponential of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::exp()
+  */
+template<typename Scalar> struct ei_scalar_exp_op EIGEN_EMPTY_STRUCT {
+  inline const Scalar operator() (const Scalar& a) const { return ei_exp(a); }
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return ei_pexp(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_exp_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = ei_packet_traits<Scalar>::HasExp }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the logarithm of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::log()
+  */
+template<typename Scalar> struct ei_scalar_log_op EIGEN_EMPTY_STRUCT {
+  inline const Scalar operator() (const Scalar& a) const { return ei_log(a); }
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return ei_plog(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_log_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = ei_packet_traits<Scalar>::HasLog }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the cosine of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::cos()
+  */
+template<typename Scalar> struct ei_scalar_cos_op EIGEN_EMPTY_STRUCT {
+  inline Scalar operator() (const Scalar& a) const { return ei_cos(a); }
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return ei_pcos(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_cos_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = ei_packet_traits<Scalar>::HasCos && EIGEN_FAST_MATH
+  };
+};
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the sine of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::sin()
+  */
+template<typename Scalar> struct ei_scalar_sin_op EIGEN_EMPTY_STRUCT {
+  inline const Scalar operator() (const Scalar& a) const { return ei_sin(a); }
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return ei_psin(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_sin_op<Scalar> >
+{
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = ei_packet_traits<Scalar>::HasSin && EIGEN_FAST_MATH
+  };
+};
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to raise a scalar to a power
+  *
+  * \sa class CwiseUnaryOp, Cwise::pow
+  */
+template<typename Scalar>
+struct ei_scalar_pow_op {
+  // FIXME default copy constructors seems bugged with std::complex<>
+  inline ei_scalar_pow_op(const ei_scalar_pow_op& other) : m_exponent(other.m_exponent) { }
+  inline ei_scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
+  inline Scalar operator() (const Scalar& a) const { return ei_pow(a, m_exponent); }
+  const Scalar m_exponent;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_pow_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the inverse of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::inverse()
+  */
+template<typename Scalar>
+struct ei_scalar_inverse_op {
+  inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
+  template<typename PacketScalar>
+  inline const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pdiv(ei_pset1(Scalar(1)),a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_inverse_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = int(ei_packet_traits<Scalar>::size)>1 }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the square of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::square()
+  */
+template<typename Scalar>
+struct ei_scalar_square_op {
+  inline Scalar operator() (const Scalar& a) const { return a*a; }
+  template<typename PacketScalar>
+  inline const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pmul(a,a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_square_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = int(ei_packet_traits<Scalar>::size)>1 }; };
+
+/** \internal
+  *
+  * \array_module
+  *
+  * \brief Template functor to compute the cube of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::cube()
+  */
+template<typename Scalar>
+struct ei_scalar_cube_op {
+  inline Scalar operator() (const Scalar& a) const { return a*a*a; }
+  template<typename PacketScalar>
+  inline const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pmul(a,ei_pmul(a,a)); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_cube_op<Scalar> >
+{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = int(ei_packet_traits<Scalar>::size)>1 }; };
+
+// default ei_functor_traits for STL functors:
+
+template<typename T>
+struct ei_functor_traits<std::multiplies<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::divides<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::plus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::minus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::negate<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::logical_or<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::logical_and<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::logical_not<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::greater<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::less<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::greater_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::less_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::not_equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::binder2nd<T> >
+{ enum { Cost = ei_functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::binder1st<T> >
+{ enum { Cost = ei_functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::unary_negate<T> >
+{ enum { Cost = 1 + ei_functor_traits<T>::Cost, PacketAccess = false }; };
+
+template<typename T>
+struct ei_functor_traits<std::binary_negate<T> >
+{ enum { Cost = 1 + ei_functor_traits<T>::Cost, PacketAccess = false }; };
+
+#ifdef EIGEN_STDEXT_SUPPORT
+
+template<typename T0,typename T1>
+struct ei_functor_traits<std::project1st<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct ei_functor_traits<std::project2nd<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct ei_functor_traits<std::select2nd<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct ei_functor_traits<std::select1st<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct ei_functor_traits<std::unary_compose<T0,T1> >
+{ enum { Cost = ei_functor_traits<T0>::Cost + ei_functor_traits<T1>::Cost, PacketAccess = false }; };
+
+template<typename T0,typename T1,typename T2>
+struct ei_functor_traits<std::binary_compose<T0,T1,T2> >
+{ enum { Cost = ei_functor_traits<T0>::Cost + ei_functor_traits<T1>::Cost + ei_functor_traits<T2>::Cost, PacketAccess = false }; };
+
+#endif // EIGEN_STDEXT_SUPPORT
+
+#endif // EIGEN_ARRAY_FUNCTORS_H

Eigen/src/Array/Norms.h

@@ -0,0 +1,80 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAY_NORMS_H
+#define EIGEN_ARRAY_NORMS_H
+
+template<typename Derived, int p>
+struct ei_lpNorm_selector
+{
+  typedef typename NumTraits<typename ei_traits<Derived>::Scalar>::Real RealScalar;
+  inline static RealScalar run(const MatrixBase<Derived>& m)
+  {
+    return ei_pow(m.cwise().abs().cwise().pow(p).sum(), RealScalar(1)/p);
+  }
+};
+
+template<typename Derived>
+struct ei_lpNorm_selector<Derived, 1>
+{
+  inline static typename NumTraits<typename ei_traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.cwise().abs().sum();
+  }
+};
+
+template<typename Derived>
+struct ei_lpNorm_selector<Derived, 2>
+{
+  inline static typename NumTraits<typename ei_traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.norm();
+  }
+};
+
+template<typename Derived>
+struct ei_lpNorm_selector<Derived, Infinity>
+{
+  inline static typename NumTraits<typename ei_traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  {
+    return m.cwise().abs().maxCoeff();
+  }
+};
+
+/** \array_module
+  * 
+  * \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
+  *          of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^p\infty \f$
+  *          norm, that is the maximum of the absolute values of the coefficients of *this.
+  *
+  * \sa norm()
+  */
+template<typename Derived>
+template<int p>
+inline typename NumTraits<typename ei_traits<Derived>::Scalar>::Real MatrixBase<Derived>::lpNorm() const
+{
+  return ei_lpNorm_selector<Derived, p>::run(*this);
+}
+
+#endif // EIGEN_ARRAY_NORMS_H

Eigen/src/Array/PartialRedux.h

@@ -0,0 +1,378 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PARTIAL_REDUX_H
+#define EIGEN_PARTIAL_REDUX_H
+
+/** \array_module \ingroup Array_Module
+  *
+  * \class PartialReduxExpr
+  *
+  * \brief Generic expression of a partially reduxed matrix
+  *
+  * \param MatrixType the type of the matrix we are applying the redux operation
+  * \param MemberOp type of the member functor
+  * \param Direction indicates the direction of the redux (Vertical or Horizontal)
+  *
+  * This class represents an expression of a partial redux operator of a matrix.
+  * It is the return type of PartialRedux functions,
+  * and most of the time this is the only way it is used.
+  *
+  * \sa class PartialRedux
+  */
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr;
+
+template<typename MatrixType, typename MemberOp, int Direction>
+struct ei_traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+{
+  typedef typename MemberOp::result_type Scalar;
+  typedef typename MatrixType::Scalar InputScalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_cleantype<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
+    Flags = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
+    TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime
+  };
+  #if EIGEN_GNUC_AT_LEAST(3,4)
+  typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
+  #else
+  typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
+  #endif
+  enum {
+    CoeffReadCost = TraversalSize * ei_traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
+  };
+};
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr : ei_no_assignment_operator,
+  public MatrixBase<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(PartialReduxExpr)
+    typedef typename ei_traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
+    typedef typename ei_traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
+
+    PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
+      : m_matrix(mat), m_functor(func) {}
+
+    int rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
+    int cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
+
+    const Scalar coeff(int i, int j) const
+    {
+      if (Direction==Vertical)
+        return m_functor(m_matrix.col(j));
+      else
+        return m_functor(m_matrix.row(i));
+    }
+
+  protected:
+    const MatrixTypeNested m_matrix;
+    const MemberOp m_functor;
+};
+
+#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST)                           \
+  template <typename ResultType>                                    \
+  struct ei_member_##MEMBER EIGEN_EMPTY_STRUCT {                    \
+    typedef ResultType result_type;                                 \
+    template<typename Scalar, int Size> struct Cost                 \
+    { enum { value = COST }; };                                     \
+    template<typename Derived>                                      \
+    inline ResultType operator()(const MatrixBase<Derived>& mat) const     \
+    { return mat.MEMBER(); } \
+  }
+
+EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
+
+
+/** \internal */
+template <typename BinaryOp, typename Scalar>
+struct ei_member_redux {
+  typedef typename ei_result_of<
+                     BinaryOp(Scalar)
+                   >::type  result_type;
+  template<typename _Scalar, int Size> struct Cost
+  { enum { value = (Size-1) * ei_functor_traits<BinaryOp>::Cost }; };
+  ei_member_redux(const BinaryOp func) : m_functor(func) {}
+  template<typename Derived>
+  inline result_type operator()(const MatrixBase<Derived>& mat) const
+  { return mat.redux(m_functor); }
+  const BinaryOp m_functor;
+};
+
+/** \array_module \ingroup Array_Module
+  *
+  * \class PartialRedux
+  *
+  * \brief Pseudo expression providing partial reduction operations
+  *
+  * \param ExpressionType the type of the object on which to do partial reductions
+  * \param Direction indicates the direction of the redux (Vertical or Horizontal)
+  *
+  * This class represents a pseudo expression with partial reduction features.
+  * It is the return type of MatrixBase::colwise() and MatrixBase::rowwise()
+  * and most of the time this is the only way it is used.
+  *
+  * Example: \include MatrixBase_colwise.cpp
+  * Output: \verbinclude MatrixBase_colwise.out
+  *
+  * \sa MatrixBase::colwise(), MatrixBase::rowwise(), class PartialReduxExpr
+  */
+template<typename ExpressionType, int Direction> class PartialRedux
+{
+  public:
+
+    typedef typename ei_traits<ExpressionType>::Scalar Scalar;
+    typedef typename ei_meta_if<ei_must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, const ExpressionType&>::ret ExpressionTypeNested;
+
+    template<template<typename _Scalar> class Functor> struct ReturnType
+    {
+      typedef PartialReduxExpr<ExpressionType,
+                               Functor<typename ei_traits<ExpressionType>::Scalar>,
+                               Direction
+                              > Type;
+    };
+
+    template<typename BinaryOp> struct ReduxReturnType
+    {
+      typedef PartialReduxExpr<ExpressionType,
+                               ei_member_redux<BinaryOp,typename ei_traits<ExpressionType>::Scalar>,
+                               Direction
+                              > Type;
+    };
+
+    inline PartialRedux(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+    /** \internal */
+    inline const ExpressionType& _expression() const { return m_matrix; }
+
+    template<typename BinaryOp>
+    const typename ReduxReturnType<BinaryOp>::Type
+    redux(const BinaryOp& func = BinaryOp()) const;
+
+    /** \returns a row (or column) vector expression of the smallest coefficient
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_minCoeff.cpp
+      * Output: \verbinclude PartialRedux_minCoeff.out
+      *
+      * \sa MatrixBase::minCoeff() */
+    const typename ReturnType<ei_member_minCoeff>::Type minCoeff() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the largest coefficient
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_maxCoeff.cpp
+      * Output: \verbinclude PartialRedux_maxCoeff.out
+      *
+      * \sa MatrixBase::maxCoeff() */
+    const typename ReturnType<ei_member_maxCoeff>::Type maxCoeff() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the squared norm
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_squaredNorm.cpp
+      * Output: \verbinclude PartialRedux_squaredNorm.out
+      *
+      * \sa MatrixBase::squaredNorm() */
+    const typename ReturnType<ei_member_squaredNorm>::Type squaredNorm() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the norm
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_norm.cpp
+      * Output: \verbinclude PartialRedux_norm.out
+      *
+      * \sa MatrixBase::norm() */
+    const typename ReturnType<ei_member_norm>::Type norm() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the sum
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_sum.cpp
+      * Output: \verbinclude PartialRedux_sum.out
+      *
+      * \sa MatrixBase::sum() */
+    const typename ReturnType<ei_member_sum>::Type sum() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * whether \b all coefficients of each respective column (or row) are \c true.
+      *
+      * \sa MatrixBase::all() */
+    const typename ReturnType<ei_member_all>::Type all() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * whether \b at \b least one coefficient of each respective column (or row) is \c true.
+      *
+      * \sa MatrixBase::any() */
+    const typename ReturnType<ei_member_any>::Type any() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression representing
+      * the number of \c true coefficients of each respective column (or row).
+      *
+      * Example: \include PartialRedux_count.cpp
+      * Output: \verbinclude PartialRedux_count.out
+      *
+      * \sa MatrixBase::count() */
+    const PartialReduxExpr<ExpressionType, ei_member_count<int>, Direction> count() const
+    { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the product
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_prod.cpp
+      * Output: \verbinclude PartialRedux_prod.out
+      *
+      * \sa MatrixBase::prod() */
+    const typename ReturnType<ei_member_prod>::Type prod() const
+    { return _expression(); }
+
+
+    /** \returns a matrix expression
+      * where each column (or row) are reversed.
+      *
+      * Example: \include PartialRedux_reverse.cpp
+      * Output: \verbinclude PartialRedux_reverse.out
+      *
+      * \sa MatrixBase::reverse() */
+    const Reverse<ExpressionType, Direction> reverse() const
+    {
+      return Reverse<ExpressionType, Direction>( _expression() );
+    }
+
+    const Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1>
+    replicate(int factor) const;
+
+    template<int Factor>
+    const Replicate<ExpressionType,(Direction==Vertical?Factor:1),(Direction==Horizontal?Factor:1)>
+    replicate(int factor = Factor) const;
+
+/////////// Geometry module ///////////
+
+    const Homogeneous<ExpressionType,Direction> homogeneous() const;
+
+    typedef typename ExpressionType::PlainMatrixType CrossReturnType;
+    template<typename OtherDerived>
+    const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
+
+    enum {
+      HNormalized_Size = Direction==Vertical ? ei_traits<ExpressionType>::RowsAtCompileTime
+                                             : ei_traits<ExpressionType>::ColsAtCompileTime,
+      HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
+    };
+    typedef Block<ExpressionType,
+                  Direction==Vertical   ? int(HNormalized_SizeMinusOne)
+                                        : int(ei_traits<ExpressionType>::RowsAtCompileTime),
+                  Direction==Horizontal ? int(HNormalized_SizeMinusOne)
+                                        : int(ei_traits<ExpressionType>::ColsAtCompileTime)>
+            HNormalized_Block;
+    typedef Block<ExpressionType,
+                  Direction==Vertical   ? 1 : int(ei_traits<ExpressionType>::RowsAtCompileTime),
+                  Direction==Horizontal ? 1 : int(ei_traits<ExpressionType>::ColsAtCompileTime)>
+            HNormalized_Factors;
+    typedef CwiseBinaryOp<ei_scalar_quotient_op<typename ei_traits<ExpressionType>::Scalar>,
+                NestByValue<HNormalized_Block>,
+                NestByValue<Replicate<NestByValue<HNormalized_Factors>,
+                  Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
+                  Direction==Horizontal ? HNormalized_SizeMinusOne : 1> > >
+            HNormalizedReturnType;
+
+    const HNormalizedReturnType hnormalized() const;
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \array_module
+  *
+  * \returns a PartialRedux wrapper of *this providing additional partial reduction operations
+  *
+  * Example: \include MatrixBase_colwise.cpp
+  * Output: \verbinclude MatrixBase_colwise.out
+  *
+  * \sa rowwise(), class PartialRedux
+  */
+template<typename Derived>
+inline const PartialRedux<Derived,Vertical>
+MatrixBase<Derived>::colwise() const
+{
+  return derived();
+}
+
+/** \array_module
+  *
+  * \returns a PartialRedux wrapper of *this providing additional partial reduction operations
+  *
+  * Example: \include MatrixBase_rowwise.cpp
+  * Output: \verbinclude MatrixBase_rowwise.out
+  *
+  * \sa colwise(), class PartialRedux
+  */
+template<typename Derived>
+inline const PartialRedux<Derived,Horizontal>
+MatrixBase<Derived>::rowwise() const
+{
+  return derived();
+}
+
+/** \returns a row or column vector expression of \c *this reduxed by \a func
+  *
+  * The template parameter \a BinaryOp is the type of the functor
+  * of the custom redux operator. Note that func must be an associative operator.
+  *
+  * \sa class PartialRedux, MatrixBase::colwise(), MatrixBase::rowwise()
+  */
+template<typename ExpressionType, int Direction>
+template<typename BinaryOp>
+const typename PartialRedux<ExpressionType,Direction>::template ReduxReturnType<BinaryOp>::Type
+PartialRedux<ExpressionType,Direction>::redux(const BinaryOp& func) const
+{
+  return typename ReduxReturnType<BinaryOp>::Type(_expression(), func);
+}
+
+#endif // EIGEN_PARTIAL_REDUX_H

Eigen/src/Array/Random.h

@@ -0,0 +1,156 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_RANDOM_H
+#define EIGEN_RANDOM_H
+
+template<typename Scalar> struct ei_scalar_random_op EIGEN_EMPTY_STRUCT {
+  inline ei_scalar_random_op(void) {}
+  inline const Scalar operator() (int, int) const { return ei_random<Scalar>(); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_random_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };
+
+/** \array_module
+  * 
+  * \returns a random matrix (not an expression, the matrix is immediately evaluated).
+  *
+  * 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 ei_random() should be used
+  * instead.
+  *
+  * \addexample RandomExample \label How to create a matrix with random coefficients
+  *
+  * Example: \include MatrixBase_random_int_int.cpp
+  * Output: \verbinclude MatrixBase_random_int_int.out
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(int), MatrixBase::Random()
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::Random(int rows, int cols)
+{
+  return NullaryExpr(rows, cols, ei_scalar_random_op<Scalar>());
+}
+
+/** \array_module
+  * 
+  * \returns a random vector (not an expression, the vector is immediately evaluated).
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so ei_random() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_random_int.cpp
+  * Output: \verbinclude MatrixBase_random_int.out
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(int,int), MatrixBase::Random()
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::Random(int size)
+{
+  return NullaryExpr(size, ei_scalar_random_op<Scalar>());
+}
+
+/** \array_module
+  * 
+  * \returns a fixed-size random matrix or vector
+  * (not an expression, the matrix is immediately evaluated).
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_random.cpp
+  * Output: \verbinclude MatrixBase_random.out
+  *
+  * \sa MatrixBase::setRandom(), MatrixBase::Random(int,int), MatrixBase::Random(int)
+  */
+template<typename Derived>
+inline const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::Random()
+{
+  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_random_op<Scalar>());
+}
+
+/** \array_module
+  * 
+  * Sets all coefficients in this expression to random values.
+  *
+  * Example: \include MatrixBase_setRandom.cpp
+  * Output: \verbinclude MatrixBase_setRandom.out
+  *
+  * \sa class CwiseNullaryOp, setRandom(int), setRandom(int,int)
+  */
+template<typename Derived>
+inline Derived& MatrixBase<Derived>::setRandom()
+{
+  return *this = Random(rows(), cols());
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to random values.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setRandom_int.cpp
+  * Output: \verbinclude Matrix_setRandom_int.out
+  *
+  * \sa MatrixBase::setRandom(), setRandom(int,int), class CwiseNullaryOp, MatrixBase::Random()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setRandom(int size)
+{
+  resize(size);
+  return setRandom();
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to random values.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setRandom_int_int.cpp
+  * Output: \verbinclude Matrix_setRandom_int_int.out
+  *
+  * \sa MatrixBase::setRandom(), setRandom(int), class CwiseNullaryOp, MatrixBase::Random()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setRandom(int rows, int cols)
+{
+  resize(rows, cols);
+  return setRandom();
+}
+
+#endif // EIGEN_RANDOM_H

Eigen/src/Array/Replicate.h

@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REPLICATE_H
+#define EIGEN_REPLICATE_H
+
+/** \nonstableyet
+  * \class Replicate
+  *
+  * \brief Expression of the multiple replication of a matrix or vector
+  *
+  * \param MatrixType the type of the object we are replicating
+  *
+  * This class represents an expression of the multiple replication of a matrix or vector.
+  * It is the return type of MatrixBase::replicate() and most of the time
+  * this is the only way it is used.
+  *
+  * \sa MatrixBase::replicate()
+  */
+template<typename MatrixType,int RowFactor,int ColFactor>
+struct ei_traits<Replicate<MatrixType,RowFactor,ColFactor> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
+                  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
+    ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
+                  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
+    RowsAtCompileTime = RowFactor==Dynamic || MatrixType::RowsAtCompileTime==Dynamic
+                      ? Dynamic
+                      : RowFactor * MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = ColFactor==Dynamic || MatrixType::ColsAtCompileTime==Dynamic
+                      ? Dynamic
+                      : ColFactor * MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = RowsAtCompileTime,
+    MaxColsAtCompileTime = ColsAtCompileTime,
+    Flags = _MatrixTypeNested::Flags & HereditaryBits,
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
+  : public MatrixBase<Replicate<MatrixType,RowFactor,ColFactor> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Replicate)
+
+    inline Replicate(const MatrixType& matrix)
+      : m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)
+    {
+      ei_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);
+    }
+
+    inline Replicate(const MatrixType& matrix, int rowFactor, int colFactor)
+      : m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)
+    {}
+
+    inline int rows() const { return m_matrix.rows() * m_rowFactor.value(); }
+    inline int cols() const { return m_matrix.cols() * m_colFactor.value(); }
+
+    inline Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row%m_matrix.rows(), col%m_matrix.cols());
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+    const ei_int_if_dynamic<RowFactor> m_rowFactor;
+    const ei_int_if_dynamic<ColFactor> m_colFactor;
+};
+
+/** \nonstableyet
+  * \return an expression of the replication of \c *this
+  *
+  * Example: \include MatrixBase_replicate.cpp
+  * Output: \verbinclude MatrixBase_replicate.out
+  *
+  * \sa PartialRedux::replicate(), MatrixBase::replicate(int,int), class Replicate
+  */
+template<typename Derived>
+template<int RowFactor, int ColFactor>
+inline const Replicate<Derived,RowFactor,ColFactor>
+MatrixBase<Derived>::replicate() const
+{
+  return derived();
+}
+
+/** \nonstableyet
+  * \return an expression of the replication of \c *this
+  *
+  * Example: \include MatrixBase_replicate_int_int.cpp
+  * Output: \verbinclude MatrixBase_replicate_int_int.out
+  *
+  * \sa PartialRedux::replicate(), MatrixBase::replicate<int,int>(), class Replicate
+  */
+template<typename Derived>
+inline const Replicate<Derived,Dynamic,Dynamic>
+MatrixBase<Derived>::replicate(int rowFactor,int colFactor) const
+{
+  return Replicate<Derived,Dynamic,Dynamic>(derived(),rowFactor,colFactor);
+}
+
+/** \nonstableyet
+  * \return an expression of the replication of each column (or row) of \c *this
+  *
+  * Example: \include DirectionWise_replicate_int.cpp
+  * Output: \verbinclude DirectionWise_replicate_int.out
+  *
+  * \sa PartialRedux::replicate(), MatrixBase::replicate(), class Replicate
+  */
+template<typename ExpressionType, int Direction>
+const Replicate<ExpressionType,(Direction==Vertical?Dynamic:1),(Direction==Horizontal?Dynamic:1)>
+PartialRedux<ExpressionType,Direction>::replicate(int factor) const
+{
+  return Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1>
+          (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+}
+
+/** \nonstableyet
+  * \return an expression of the replication of each column (or row) of \c *this
+  *
+  * Example: \include DirectionWise_replicate.cpp
+  * Output: \verbinclude DirectionWise_replicate.out
+  *
+  * \sa PartialRedux::replicate(int), MatrixBase::replicate(), class Replicate
+  */
+template<typename ExpressionType, int Direction>
+template<int Factor>
+const Replicate<ExpressionType,(Direction==Vertical?Factor:1),(Direction==Horizontal?Factor:1)>
+PartialRedux<ExpressionType,Direction>::replicate(int factor) const
+{
+  return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
+          (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+}
+
+#endif // EIGEN_REPLICATE_H

Eigen/src/Array/Reverse.h

@@ -0,0 +1,202 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REVERSE_H
+#define EIGEN_REVERSE_H
+
+/** \array_module \ingroup Array_Module
+  *
+  * \class Reverse
+  *
+  * \brief Expression of the reverse of a vector or matrix
+  *
+  * \param MatrixType the type of the object of which we are taking the reverse
+  *
+  * This class represents an expression of the reverse of a vector.
+  * It is the return type of MatrixBase::reverse() and PartialRedux::reverse()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::reverse(), PartialRedux::reverse()
+  */
+template<typename MatrixType, int Direction>
+struct ei_traits<Reverse<MatrixType, Direction> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+
+    // let's enable LinearAccess only with vectorization because of the product overhead
+    LinearAccess = ( (Direction==BothDirections) && (int(_MatrixTypeNested::Flags)&PacketAccessBit) )
+                 ? LinearAccessBit : 0,
+
+    Flags = (int(_MatrixTypeNested::Flags) & (HereditaryBits | PacketAccessBit | LinearAccess))
+          | (int(_MatrixTypeNested::Flags)&UpperTriangularBit ? LowerTriangularBit : 0)
+          | (int(_MatrixTypeNested::Flags)&LowerTriangularBit ? UpperTriangularBit : 0),
+
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename PacketScalar, bool ReversePacket> struct ei_reverse_packet_cond
+{
+  static inline PacketScalar run(const PacketScalar& x) { return ei_preverse(x); }
+};
+template<typename PacketScalar> struct ei_reverse_packet_cond<PacketScalar,false>
+{
+  static inline PacketScalar run(const PacketScalar& x) { return x; }
+};
+
+template<typename MatrixType, int Direction> class Reverse
+  : public MatrixBase<Reverse<MatrixType, Direction> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Reverse)
+
+  protected:
+    enum {
+      PacketSize = ei_packet_traits<Scalar>::size,
+      IsRowMajor = Flags & RowMajorBit,
+      IsColMajor = !IsRowMajor,
+      ReverseRow = (Direction == Vertical)   || (Direction == BothDirections),
+      ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
+      OffsetRow  = ReverseRow && IsColMajor ? PacketSize : 1,
+      OffsetCol  = ReverseCol && IsRowMajor ? PacketSize : 1,
+      ReversePacket = (Direction == BothDirections)
+                    || ((Direction == Vertical)   && IsColMajor)
+                    || ((Direction == Horizontal) && IsRowMajor)
+    };
+    typedef ei_reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;
+  public:
+
+    inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
+
+    inline int rows() const { return m_matrix.rows(); }
+    inline int cols() const { return m_matrix.cols(); }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(ReverseRow ? m_matrix.rows() - row - 1 : row,
+                                                    ReverseCol ? m_matrix.cols() - col - 1 : col);
+    }
+
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(ReverseRow ? m_matrix.rows() - row - 1 : row,
+                            ReverseCol ? m_matrix.cols() - col - 1 : col);
+    }
+
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(m_matrix.size() - index - 1);
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(m_matrix.size() - index - 1);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int row, int col) const
+    {
+      return reverse_packet::run(m_matrix.template packet<LoadMode>(
+                                    ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+                                    ReverseCol ? m_matrix.cols() - col - OffsetCol : col));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(
+                                      ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
+                                      ReverseCol ? m_matrix.cols() - col - OffsetCol : col,
+                                      reverse_packet::run(x));
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int index) const
+    {
+      return ei_preverse(m_matrix.template packet<LoadMode>( m_matrix.size() - index - PacketSize ));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(m_matrix.size() - index - PacketSize, ei_preverse(x));
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \returns an expression of the reverse of *this.
+  *
+  * Example: \include MatrixBase_reverse.cpp
+  * Output: \verbinclude MatrixBase_reverse.out
+  *
+  */
+template<typename Derived>
+inline Reverse<Derived, BothDirections>
+MatrixBase<Derived>::reverse()
+{
+  return derived();
+}
+
+/** This is the const version of reverse(). */
+template<typename Derived>
+inline const Reverse<Derived, BothDirections>
+MatrixBase<Derived>::reverse() const
+{
+  return derived();
+}
+
+/** This is the "in place" version of reverse: it reverses \c *this.
+  *
+  * In most cases it is probably better to simply use the reversed expression
+  * of a matrix. However, when reversing the matrix data itself is really needed,
+  * then this "in-place" version is probably the right choice because it provides
+  * the following additional features:
+  *  - less error prone: doing the same operation with .reverse() requires special care:
+  *    \code m = m.reverse().eval(); \endcode
+  *  - no temporary object is created (currently there is one created but could be avoided using swap)
+  *  - it allows future optimizations (cache friendliness, etc.)
+  *
+  * \sa reverse() */
+template<typename Derived>
+inline void MatrixBase<Derived>::reverseInPlace()
+{
+  derived() = derived().reverse().eval();
+}
+
+
+#endif // EIGEN_REVERSE_H

Eigen/src/Array/Select.h

@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SELECT_H
+#define EIGEN_SELECT_H
+
+/** \array_module \ingroup Array_Module
+  *
+  * \class Select
+  *
+  * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
+  *
+  * \param ConditionMatrixType the type of the \em condition expression which must be a boolean matrix
+  * \param ThenMatrixType the type of the \em then expression
+  * \param ElseMatrixType the type of the \em else expression
+  *
+  * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+  * It is the return type of MatrixBase::select() and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::select(const MatrixBase<ThenDerived>&, const MatrixBase<ElseDerived>&) const
+  */
+
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+struct ei_traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+{
+  typedef typename ei_traits<ThenMatrixType>::Scalar Scalar;
+  typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
+  typedef typename ThenMatrixType::Nested ThenMatrixNested;
+  typedef typename ElseMatrixType::Nested ElseMatrixNested;
+  enum {
+    RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
+    Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & HereditaryBits,
+	CoeffReadCost = ei_traits<typename ei_cleantype<ConditionMatrixNested>::type>::CoeffReadCost
+	+ EIGEN_ENUM_MAX(ei_traits<typename ei_cleantype<ThenMatrixNested>::type>::CoeffReadCost,
+	                 ei_traits<typename ei_cleantype<ElseMatrixNested>::type>::CoeffReadCost)
+  };
+};
+
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+class Select : ei_no_assignment_operator,
+  public MatrixBase<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Select)
+
+    Select(const ConditionMatrixType& conditionMatrix,
+           const ThenMatrixType& thenMatrix,
+           const ElseMatrixType& elseMatrix)
+      : m_condition(conditionMatrix), m_then(thenMatrix), m_else(elseMatrix)
+    {
+      ei_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
+      ei_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
+    }
+
+    int rows() const { return m_condition.rows(); }
+    int cols() const { return m_condition.cols(); }
+
+    const Scalar coeff(int i, int j) const
+    {
+      if (m_condition.coeff(i,j))
+        return m_then.coeff(i,j);
+      else
+        return m_else.coeff(i,j);
+    }
+    
+    const Scalar coeff(int i) const
+    {
+      if (m_condition.coeff(i))
+        return m_then.coeff(i);
+      else
+        return m_else.coeff(i);
+    }
+
+  protected:
+    const typename ConditionMatrixType::Nested m_condition;
+    const typename ThenMatrixType::Nested m_then;
+    const typename ElseMatrixType::Nested m_else;
+};
+
+
+/** \array_module
+  *
+  * \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
+  * if \c *this(i,j), and \a elseMatrix(i,j) otherwise.
+  *
+  * Example: \include MatrixBase_select.cpp
+  * Output: \verbinclude MatrixBase_select.out
+  *
+  * \sa class Select
+  */
+template<typename Derived>
+template<typename ThenDerived,typename ElseDerived>
+inline const Select<Derived,ThenDerived,ElseDerived>
+MatrixBase<Derived>::select(const MatrixBase<ThenDerived>& thenMatrix,
+                            const MatrixBase<ElseDerived>& elseMatrix) const
+{
+  return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
+}
+
+/** \array_module
+  *
+  * Version of MatrixBase::select(const MatrixBase&, const MatrixBase&) with
+  * the \em else expression being a scalar value.
+  *
+  * \sa MatrixBase::select(const MatrixBase<ThenDerived>&, const MatrixBase<ElseDerived>&) const, class Select
+  */
+template<typename Derived>
+template<typename ThenDerived>
+inline const Select<Derived,ThenDerived, NestByValue<typename ThenDerived::ConstantReturnType> >
+MatrixBase<Derived>::select(const MatrixBase<ThenDerived>& thenMatrix,
+                            typename ThenDerived::Scalar elseScalar) const
+{
+  return Select<Derived,ThenDerived,NestByValue<typename ThenDerived::ConstantReturnType> >(
+    derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
+}
+
+/** \array_module
+  *
+  * Version of MatrixBase::select(const MatrixBase&, const MatrixBase&) with
+  * the \em then expression being a scalar value.
+  *
+  * \sa MatrixBase::select(const MatrixBase<ThenDerived>&, const MatrixBase<ElseDerived>&) const, class Select
+  */
+template<typename Derived>
+template<typename ElseDerived>
+inline const Select<Derived, NestByValue<typename ElseDerived::ConstantReturnType>, ElseDerived >
+MatrixBase<Derived>::select(typename ElseDerived::Scalar thenScalar,
+                            const MatrixBase<ElseDerived>& elseMatrix) const
+{
+  return Select<Derived,NestByValue<typename ElseDerived::ConstantReturnType>,ElseDerived>(
+    derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
+}
+
+#endif // EIGEN_SELECT_H

Eigen/src/CMakeLists.txt

@@ -0,0 +1,9 @@
+ADD_SUBDIRECTORY(Core)
+ADD_SUBDIRECTORY(LU)
+ADD_SUBDIRECTORY(QR)
+ADD_SUBDIRECTORY(SVD)
+ADD_SUBDIRECTORY(Cholesky)
+ADD_SUBDIRECTORY(Array)
+ADD_SUBDIRECTORY(Geometry)
+ADD_SUBDIRECTORY(LeastSquares)
+ADD_SUBDIRECTORY(Sparse)

Eigen/src/Cholesky/CMakeLists.txt

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

Eigen/src/Cholesky/CholeskyInstantiations.cpp

@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_EXTERN_INSTANTIATIONS
+#define EIGEN_EXTERN_INSTANTIATIONS
+#endif
+#include "../../Core"
+#undef EIGEN_EXTERN_INSTANTIATIONS
+
+#include "../../Cholesky"
+
+namespace Eigen {
+  EIGEN_CHOLESKY_MODULE_INSTANTIATE();
+}

Eigen/src/Cholesky/LDLT.h

@@ -0,0 +1,277 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_LDLT_H
+#define EIGEN_LDLT_H
+
+/** \ingroup cholesky_Module
+  *
+  * \class LDLT
+  *
+  * \brief Robust Cholesky decomposition of a matrix
+  *
+  * \param MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
+  *
+  * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
+  * matrix \f$ A \f$ such that \f$ A =  P^TLDL^*P \f$, where P is a permutation matrix, L
+  * is lower triangular with a unit diagonal and D is a diagonal matrix.
+  *
+  * The decomposition uses pivoting to ensure stability, so that L will have
+  * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
+  * on D also stabilizes the computation.
+  *
+  * Remember that Cholesky decompositions are not rank-revealing.  Also, do not use a Cholesky decomposition to determine
+  * whether a system of equations has a solution.
+  *
+  * \sa MatrixBase::ldlt(), class LLT
+  */
+ /* THIS PART OF THE DOX IS CURRENTLY DISABLED BECAUSE INACCURATE BECAUSE OF BUG IN THE DECOMPOSITION CODE
+  * Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
+  * the strict lower part does not have to store correct values.
+  */
+template<typename MatrixType> class LDLT
+{
+  public:
+
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+    typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+    typedef Matrix<int, 1, MatrixType::RowsAtCompileTime> IntRowVectorType;
+
+    LDLT(const MatrixType& matrix)
+      : m_matrix(matrix.rows(), matrix.cols()),
+        m_p(matrix.rows()),
+        m_transpositions(matrix.rows())
+    {
+      compute(matrix);
+    }
+
+    /** \returns the lower triangular matrix L */
+    inline Part<MatrixType, UnitLowerTriangular> matrixL(void) const { return m_matrix; }
+
+    /** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed,
+      * representing the P permutation i.e. the permutation of the rows. For its precise meaning,
+      * see the examples given in the documentation of class LU.
+      */
+    inline const IntColVectorType& permutationP() const
+    {
+      return m_p;
+    }
+
+    /** \returns the coefficients of the diagonal matrix D */
+    inline Diagonal<MatrixType,0> vectorD(void) const { return m_matrix.diagonal(); }
+
+    /** \returns true if the matrix is positive (semidefinite) */
+    inline bool isPositive(void) const { return m_sign == 1; }
+
+    /** \returns true if the matrix is negative (semidefinite) */
+    inline bool isNegative(void) const { return m_sign == -1; }
+
+    template<typename RhsDerived, typename ResDerived>
+    bool solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const;
+
+    template<typename Derived>
+    bool solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+    void compute(const MatrixType& matrix);
+
+  protected:
+    /** \internal
+      * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
+      * The strict upper part is used during the decomposition, the strict lower
+      * part correspond to the coefficients of L (its diagonal is equal to 1 and
+      * is not stored), and the diagonal entries correspond to D.
+      */
+    MatrixType m_matrix;
+    IntColVectorType m_p;
+    IntColVectorType m_transpositions;
+    int m_sign;
+};
+
+/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
+  */
+template<typename MatrixType>
+void LDLT<MatrixType>::compute(const MatrixType& a)
+{
+  ei_assert(a.rows()==a.cols());
+  const int size = a.rows();
+
+  m_matrix = a;
+
+  if (size <= 1) {
+    m_p.setZero();
+    m_transpositions.setZero();
+    m_sign = ei_real(a.coeff(0,0))>0 ? 1:-1;
+    return;
+  }
+
+  RealScalar cutoff = 0, biggest_in_corner;
+
+  // By using a temorary, packet-aligned products are guarenteed. In the LLT
+  // case this is unnecessary because the diagonal is included and will always
+  // have optimal alignment.
+  Matrix<Scalar,MatrixType::RowsAtCompileTime,1> _temporary(size);
+
+  for (int j = 0; j < size; ++j)
+  {
+    // Find largest diagonal element
+    int index_of_biggest_in_corner;
+    biggest_in_corner = m_matrix.diagonal().end(size-j).cwise().abs()
+                       .maxCoeff(&index_of_biggest_in_corner);
+    index_of_biggest_in_corner += j;
+
+    if(j == 0)
+    {
+      // The biggest overall is the point of reference to which further diagonals
+      // are compared; if any diagonal is negligible compared
+      // to the largest overall, the algorithm bails.  This cutoff is suggested
+      // in "Analysis of the Cholesky Decomposition of a Semi-definite Matrix" by
+      // Nicholas J. Higham. Also see "Accuracy and Stability of Numerical
+      // Algorithms" page 217, also by Higham.
+      cutoff = ei_abs(machine_epsilon<Scalar>() * size * biggest_in_corner);
+
+      m_sign = ei_real(m_matrix.diagonal().coeff(index_of_biggest_in_corner)) > 0 ? 1 : -1;
+    }
+
+    // Finish early if the matrix is not full rank.
+    if(biggest_in_corner < cutoff)
+    {
+      for(int i = j; i < size; i++) m_transpositions.coeffRef(i) = i;
+      break;
+    }
+
+    m_transpositions.coeffRef(j) = index_of_biggest_in_corner;
+    if(j != index_of_biggest_in_corner)
+    {
+      m_matrix.row(j).swap(m_matrix.row(index_of_biggest_in_corner));
+      m_matrix.col(j).swap(m_matrix.col(index_of_biggest_in_corner));
+    }
+
+    if (j == 0) {
+      m_matrix.row(0) = m_matrix.row(0).conjugate();
+      m_matrix.col(0).end(size-1) = m_matrix.row(0).end(size-1) / m_matrix.coeff(0,0);
+      continue;
+    }
+
+    RealScalar Djj = ei_real(m_matrix.coeff(j,j) - (m_matrix.row(j).start(j)
+                                                  * m_matrix.col(j).start(j).conjugate()).coeff(0,0));
+    m_matrix.coeffRef(j,j) = Djj;
+
+    // Finish early if the matrix is not full rank.
+    if(ei_abs(Djj) < cutoff)
+    {
+      for(int i = j; i < size; i++) m_transpositions.coeffRef(i) = i;
+      break;
+    }
+
+    int endSize = size - j - 1;
+    if (endSize > 0) {
+      _temporary.end(endSize) = ( m_matrix.block(j+1,0, endSize, j)
+                                * m_matrix.col(j).start(j).conjugate() ).lazy();
+
+      m_matrix.row(j).end(endSize) = m_matrix.row(j).end(endSize).conjugate()
+                                   - _temporary.end(endSize).transpose();
+
+      m_matrix.col(j).end(endSize) = m_matrix.row(j).end(endSize) / Djj;
+    }
+  }
+
+  // Reverse applied swaps to get P matrix.
+  for(int k = 0; k < size; ++k) m_p.coeffRef(k) = k;
+  for(int k = size-1; k >= 0; --k) {
+    std::swap(m_p.coeffRef(k), m_p.coeffRef(m_transpositions.coeff(k)));
+  }
+}
+
+/** Computes the solution x of \f$ A x = b \f$ using the current decomposition of A.
+  * The result is stored in \a result
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * In other words, it computes \f$ b = A^{-1} b \f$ with
+  * \f$ P^T{L^{*}}^{-1} D^{-1} L^{-1} P b \f$ from right to left.
+  *
+  * \sa LDLT::solveInPlace(), MatrixBase::ldlt()
+  */
+template<typename MatrixType>
+template<typename RhsDerived, typename ResDerived>
+bool LDLT<MatrixType>
+::solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const
+{
+  const int size = m_matrix.rows();
+  ei_assert(size==b.rows() && "LDLT::solve(): invalid number of rows of the right hand side matrix b");
+  *result = b;
+  return solveInPlace(*result);
+}
+
+/** This is the \em in-place version of solve().
+  *
+  * \param bAndX represents both the right-hand side matrix b and result x.
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * This version avoids a copy when the right hand side matrix b is not
+  * needed anymore.
+  *
+  * \sa LDLT::solve(), MatrixBase::ldlt()
+  */
+template<typename MatrixType>
+template<typename Derived>
+bool LDLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+  const int size = m_matrix.rows();
+  ei_assert(size == bAndX.rows());
+
+  // z = P b
+  for(int i = 0; i < size; ++i) bAndX.row(m_transpositions.coeff(i)).swap(bAndX.row(i));
+
+  // y = L^-1 z
+  matrixL().solveTriangularInPlace(bAndX);
+
+  // w = D^-1 y
+  bAndX = (m_matrix.diagonal().cwise().inverse().asDiagonal() * bAndX).lazy();
+
+  // u = L^-T w
+  m_matrix.adjoint().template part<UnitUpperTriangular>().solveTriangularInPlace(bAndX);
+
+  // x = P^T u
+  for (int i = size-1; i >= 0; --i) bAndX.row(m_transpositions.coeff(i)).swap(bAndX.row(i));
+
+  return true;
+}
+
+/** \cholesky_module
+  * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+  */
+template<typename Derived>
+inline const LDLT<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::ldlt() const
+{
+  return derived();
+}
+
+#endif // EIGEN_LDLT_H

Eigen/src/Cholesky/LLT.h

@@ -0,0 +1,189 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_LLT_H
+#define EIGEN_LLT_H
+
+/** \ingroup cholesky_Module
+  *
+  * \class LLT
+  *
+  * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
+  *
+  * \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
+  *
+  * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
+  * matrix A such that A = LL^* = U^*U, where L is lower triangular.
+  *
+  * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like  D^*D x = b,
+  * for that purpose, we recommend the Cholesky decomposition without square root which is more stable
+  * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
+  * situations like generalised eigen problems with hermitian matrices.
+  *
+  * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
+  * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
+  * has a solution.
+  *
+  * \sa MatrixBase::llt(), class LDLT
+  */
+ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH)
+  * Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
+  * the strict lower part does not have to store correct values.
+  */
+template<typename MatrixType> class LLT
+{
+  private:
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+    enum {
+      PacketSize = ei_packet_traits<Scalar>::size,
+      AlignmentMask = int(PacketSize)-1
+    };
+
+  public:
+
+    LLT(const MatrixType& matrix)
+      : m_matrix(matrix.rows(), matrix.cols())
+    {
+      compute(matrix);
+    }
+
+    /** \returns the lower triangular matrix L */
+    inline Part<MatrixType, LowerTriangular> matrixL(void) const { return m_matrix; }
+
+    template<typename RhsDerived, typename ResDerived>
+    bool solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const;
+
+    template<typename Derived>
+    bool solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+    void compute(const MatrixType& matrix);
+
+  protected:
+    /** \internal
+      * Used to compute and store L
+      * The strict upper part is not used and even not initialized.
+      */
+    MatrixType m_matrix;
+};
+
+/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
+  */
+template<typename MatrixType>
+void LLT<MatrixType>::compute(const MatrixType& a)
+{
+  assert(a.rows()==a.cols());
+  const int size = a.rows();
+  m_matrix.resize(size, size);
+  // The biggest overall is the point of reference to which further diagonals
+  // are compared; if any diagonal is negligible compared
+  // to the largest overall, the algorithm bails.  This cutoff is suggested
+  // in "Analysis of the Cholesky Decomposition of a Semi-definite Matrix" by
+  // Nicholas J. Higham. Also see "Accuracy and Stability of Numerical
+  // Algorithms" page 217, also by Higham.
+  const RealScalar cutoff = machine_epsilon<Scalar>() * size * a.diagonal().cwise().abs().maxCoeff();
+  RealScalar x;
+  x = ei_real(a.coeff(0,0));
+  m_matrix.coeffRef(0,0) = ei_sqrt(x);
+  if(size==1)
+    return;
+  m_matrix.col(0).end(size-1) = a.row(0).end(size-1).adjoint() / ei_real(m_matrix.coeff(0,0));
+  for (int j = 1; j < size; ++j)
+  {
+    x = ei_real(a.coeff(j,j)) - m_matrix.row(j).start(j).squaredNorm();
+    if (ei_abs(x) < cutoff) continue;
+
+    m_matrix.coeffRef(j,j) = x = ei_sqrt(x);
+
+    int endSize = size-j-1;
+    if (endSize>0) {
+      // Note that when all matrix columns have good alignment, then the following
+      // product is guaranteed to be optimal with respect to alignment.
+      m_matrix.col(j).end(endSize) =
+        (m_matrix.block(j+1, 0, endSize, j) * m_matrix.row(j).start(j).adjoint()).lazy();
+
+      // FIXME could use a.col instead of a.row
+      m_matrix.col(j).end(endSize) = (a.row(j).end(endSize).adjoint()
+        - m_matrix.col(j).end(endSize) ) / x;
+    }
+  }
+}
+
+/** Computes the solution x of \f$ A x = b \f$ using the current decomposition of A.
+  * The result is stored in \a result
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * In other words, it computes \f$ b = A^{-1} b \f$ with
+  * \f$ {L^{*}}^{-1} L^{-1} b \f$ from right to left.
+  *
+  * Example: \include LLT_solve.cpp
+  * Output: \verbinclude LLT_solve.out
+  *
+  * \sa LLT::solveInPlace(), MatrixBase::llt()
+  */
+template<typename MatrixType>
+template<typename RhsDerived, typename ResDerived>
+bool LLT<MatrixType>::solve(const MatrixBase<RhsDerived> &b, MatrixBase<ResDerived> *result) const
+{
+  const int size = m_matrix.rows();
+  ei_assert(size==b.rows() && "LLT::solve(): invalid number of rows of the right hand side matrix b");
+  return solveInPlace((*result) = b);
+}
+
+/** This is the \em in-place version of solve().
+  *
+  * \param bAndX represents both the right-hand side matrix b and result x.
+  *
+  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  *
+  * This version avoids a copy when the right hand side matrix b is not
+  * needed anymore.
+  *
+  * \sa LLT::solve(), MatrixBase::llt()
+  */
+template<typename MatrixType>
+template<typename Derived>
+bool LLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+  const int size = m_matrix.rows();
+  ei_assert(size==bAndX.rows());
+  matrixL().solveTriangularInPlace(bAndX);
+  m_matrix.adjoint().template part<UpperTriangular>().solveTriangularInPlace(bAndX);
+  return true;
+}
+
+/** \cholesky_module
+  * \returns the LLT decomposition of \c *this
+  */
+template<typename Derived>
+inline const LLT<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::llt() const
+{
+  return LLT<PlainMatrixType>(derived());
+}
+
+#endif // EIGEN_LLT_H

Eigen/src/Core/Assign.h

@@ -0,0 +1,445 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ASSIGN_H
+#define EIGEN_ASSIGN_H
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template <typename Derived, typename OtherDerived>
+struct ei_assign_traits
+{
+public:
+  enum {
+    DstIsAligned = Derived::Flags & AlignedBit,
+    SrcIsAligned = OtherDerived::Flags & AlignedBit,
+    SrcAlignment = DstIsAligned && SrcIsAligned ? Aligned : Unaligned
+  };
+
+private:
+  enum {
+    InnerSize = int(Derived::Flags)&RowMajorBit
+              ? Derived::ColsAtCompileTime
+              : Derived::RowsAtCompileTime,
+    InnerMaxSize = int(Derived::Flags)&RowMajorBit
+              ? Derived::MaxColsAtCompileTime
+              : Derived::MaxRowsAtCompileTime,
+    PacketSize = ei_packet_traits<typename Derived::Scalar>::size
+  };
+
+  enum {
+    MightVectorize = (int(Derived::Flags) & int(OtherDerived::Flags) & ActualPacketAccessBit)
+                  && ((int(Derived::Flags)&RowMajorBit)==(int(OtherDerived::Flags)&RowMajorBit)),
+    MayInnerVectorize  = MightVectorize && int(InnerSize)!=Dynamic && int(InnerSize)%int(PacketSize)==0
+                       && int(DstIsAligned) && int(SrcIsAligned),
+    MayLinearVectorize = MightVectorize && (int(Derived::Flags) & int(OtherDerived::Flags) & LinearAccessBit),
+    MaySliceVectorize  = MightVectorize && int(InnerMaxSize)>=3*PacketSize /* slice vectorization can be slow, so we only
+      want it if the slices are big, which is indicated by InnerMaxSize rather than InnerSize, think of the case
+      of a dynamic block in a fixed-size matrix */
+  };
+
+public:
+  enum {
+    Vectorization = int(MayInnerVectorize)  ? int(InnerVectorization)
+                  : int(MayLinearVectorize) ? int(LinearVectorization)
+                  : int(MaySliceVectorize)  ? int(SliceVectorization)
+                                            : int(NoVectorization)
+  };
+
+private:
+  enum {
+    UnrollingLimit      = EIGEN_UNROLLING_LIMIT * (int(Vectorization) == int(NoVectorization) ? 1 : int(PacketSize)),
+    MayUnrollCompletely = int(Derived::SizeAtCompileTime) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit),
+    MayUnrollInner      = int(InnerSize * OtherDerived::CoeffReadCost) <= int(UnrollingLimit)
+  };
+
+public:
+  enum {
+    Unrolling = (int(Vectorization) == int(InnerVectorization) || int(Vectorization) == int(NoVectorization))
+              ? (
+                   int(MayUnrollCompletely) ? int(CompleteUnrolling)
+                 : int(MayUnrollInner)      ? int(InnerUnrolling)
+                                            : int(NoUnrolling)
+                )
+              : int(Vectorization) == int(LinearVectorization)
+              ? ( int(MayUnrollCompletely) && int(DstIsAligned) ? int(CompleteUnrolling) : int(NoUnrolling) )
+              : int(NoUnrolling)
+  };
+};
+
+/***************************************************************************
+* Part 2 : meta-unrollers
+***************************************************************************/
+
+/***********************
+*** No vectorization ***
+***********************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct ei_assign_novec_CompleteUnrolling
+{
+  enum {
+    row = int(Derived1::Flags)&RowMajorBit
+        ? Index / int(Derived1::ColsAtCompileTime)
+        : Index % Derived1::RowsAtCompileTime,
+    col = int(Derived1::Flags)&RowMajorBit
+        ? Index % int(Derived1::ColsAtCompileTime)
+        : Index / Derived1::RowsAtCompileTime
+  };
+
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    dst.copyCoeff(row, col, src);
+    ei_assign_novec_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct ei_assign_novec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct ei_assign_novec_InnerUnrolling
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src, int row_or_col)
+  {
+    const bool rowMajor = int(Derived1::Flags)&RowMajorBit;
+    const int row = rowMajor ? row_or_col : Index;
+    const int col = rowMajor ? Index : row_or_col;
+    dst.copyCoeff(row, col, src);
+    ei_assign_novec_InnerUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src, row_or_col);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct ei_assign_novec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &, int) {}
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct ei_assign_innervec_CompleteUnrolling
+{
+  enum {
+    row = int(Derived1::Flags)&RowMajorBit
+        ? Index / int(Derived1::ColsAtCompileTime)
+        : Index % Derived1::RowsAtCompileTime,
+    col = int(Derived1::Flags)&RowMajorBit
+        ? Index % int(Derived1::ColsAtCompileTime)
+        : Index / Derived1::RowsAtCompileTime,
+    SrcAlignment = ei_assign_traits<Derived1,Derived2>::SrcAlignment
+  };
+
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    dst.template copyPacket<Derived2, Aligned, SrcAlignment>(row, col, src);
+    ei_assign_innervec_CompleteUnrolling<Derived1, Derived2,
+      Index+ei_packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct ei_assign_innervec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct ei_assign_innervec_InnerUnrolling
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src, int row_or_col)
+  {
+    const int row = int(Derived1::Flags)&RowMajorBit ? row_or_col : Index;
+    const int col = int(Derived1::Flags)&RowMajorBit ? Index : row_or_col;
+    dst.template copyPacket<Derived2, Aligned, Aligned>(row, col, src);
+    ei_assign_innervec_InnerUnrolling<Derived1, Derived2,
+      Index+ei_packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src, row_or_col);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Stop>
+struct ei_assign_innervec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &, const Derived2 &, int) {}
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Derived1, typename Derived2,
+         int Vectorization = ei_assign_traits<Derived1, Derived2>::Vectorization,
+         int Unrolling = ei_assign_traits<Derived1, Derived2>::Unrolling>
+struct ei_assign_impl;
+
+/***********************
+*** No vectorization ***
+***********************/
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, NoVectorization, NoUnrolling>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const int innerSize = dst.innerSize();
+    const int outerSize = dst.outerSize();
+    for(int j = 0; j < outerSize; ++j)
+      for(int i = 0; i < innerSize; ++i)
+      {
+        if(int(Derived1::Flags)&RowMajorBit)
+          dst.copyCoeff(j, i, src);
+        else
+          dst.copyCoeff(i, j, src);
+      }
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, NoVectorization, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    ei_assign_novec_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+      ::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, NoVectorization, InnerUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const bool rowMajor = int(Derived1::Flags)&RowMajorBit;
+    const int innerSize = rowMajor ? Derived1::ColsAtCompileTime : Derived1::RowsAtCompileTime;
+    const int outerSize = dst.outerSize();
+    for(int j = 0; j < outerSize; ++j)
+      ei_assign_novec_InnerUnrolling<Derived1, Derived2, 0, innerSize>
+        ::run(dst, src, j);
+  }
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, InnerVectorization, NoUnrolling>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const int innerSize = dst.innerSize();
+    const int outerSize = dst.outerSize();
+    const int packetSize = ei_packet_traits<typename Derived1::Scalar>::size;
+    for(int j = 0; j < outerSize; ++j)
+      for(int i = 0; i < innerSize; i+=packetSize)
+      {
+        if(int(Derived1::Flags)&RowMajorBit)
+          dst.template copyPacket<Derived2, Aligned, Aligned>(j, i, src);
+        else
+          dst.template copyPacket<Derived2, Aligned, Aligned>(i, j, src);
+      }
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, InnerVectorization, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    ei_assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+      ::run(dst, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, InnerVectorization, InnerUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const bool rowMajor = int(Derived1::Flags)&RowMajorBit;
+    const int innerSize = rowMajor ? Derived1::ColsAtCompileTime : Derived1::RowsAtCompileTime;
+    const int outerSize = dst.outerSize();
+    for(int j = 0; j < outerSize; ++j)
+      ei_assign_innervec_InnerUnrolling<Derived1, Derived2, 0, innerSize>
+        ::run(dst, src, j);
+  }
+};
+
+/***************************
+*** Linear vectorization ***
+***************************/
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const int size = dst.size();
+    const int packetSize = ei_packet_traits<typename Derived1::Scalar>::size;
+    const int alignedStart = ei_assign_traits<Derived1,Derived2>::DstIsAligned ? 0
+                           : ei_alignmentOffset(&dst.coeffRef(0), size);
+    const int alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
+
+    for(int index = 0; index < alignedStart; ++index)
+      dst.copyCoeff(index, src);
+
+    for(int index = alignedStart; index < alignedEnd; index += packetSize)
+    {
+      dst.template copyPacket<Derived2, Aligned, ei_assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);
+    }
+
+    for(int index = alignedEnd; index < size; ++index)
+      dst.copyCoeff(index, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, LinearVectorization, CompleteUnrolling>
+{
+  EIGEN_STRONG_INLINE static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const int size = Derived1::SizeAtCompileTime;
+    const int packetSize = ei_packet_traits<typename Derived1::Scalar>::size;
+    const int alignedSize = (size/packetSize)*packetSize;
+
+    ei_assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, alignedSize>::run(dst, src);
+    ei_assign_novec_CompleteUnrolling<Derived1, Derived2, alignedSize, size>::run(dst, src);
+  }
+};
+
+/**************************
+*** Slice vectorization ***
+***************************/
+
+template<typename Derived1, typename Derived2>
+struct ei_assign_impl<Derived1, Derived2, SliceVectorization, NoUnrolling>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    const int packetSize = ei_packet_traits<typename Derived1::Scalar>::size;
+    const int packetAlignedMask = packetSize - 1;
+    const int innerSize = dst.innerSize();
+    const int outerSize = dst.outerSize();
+    const int alignedStep = (packetSize - dst.stride() % packetSize) & packetAlignedMask;
+    int alignedStart = ei_assign_traits<Derived1,Derived2>::DstIsAligned ? 0
+                     : ei_alignmentOffset(&dst.coeffRef(0,0), innerSize);
+
+    for(int i = 0; i < outerSize; ++i)
+    {
+      const int alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);
+
+      // do the non-vectorizable part of the assignment
+      for (int index = 0; index<alignedStart ; ++index)
+      {
+        if(Derived1::Flags&RowMajorBit)
+          dst.copyCoeff(i, index, src);
+        else
+          dst.copyCoeff(index, i, src);
+      }
+
+      // do the vectorizable part of the assignment
+      for (int index = alignedStart; index<alignedEnd; index+=packetSize)
+      {
+        if(Derived1::Flags&RowMajorBit)
+          dst.template copyPacket<Derived2, Aligned, Unaligned>(i, index, src);
+        else
+          dst.template copyPacket<Derived2, Aligned, Unaligned>(index, i, src);
+      }
+
+      // do the non-vectorizable part of the assignment
+      for (int index = alignedEnd; index<innerSize ; ++index)
+      {
+        if(Derived1::Flags&RowMajorBit)
+          dst.copyCoeff(i, index, src);
+        else
+          dst.copyCoeff(index, i, src);
+      }
+
+      alignedStart = std::min<int>((alignedStart+alignedStep)%packetSize, innerSize);
+    }
+  }
+};
+
+/***************************************************************************
+* Part 4 : implementation of MatrixBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>
+  ::lazyAssign(const MatrixBase<OtherDerived>& other)
+{
+  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+  EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename OtherDerived::Scalar>::ret),
+    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+  ei_assert(rows() == other.rows() && cols() == other.cols());
+  ei_assign_impl<Derived, OtherDerived>::run(derived(),other.derived());
+  return derived();
+}
+
+template<typename Derived, typename OtherDerived,
+         bool EvalBeforeAssigning = (int(OtherDerived::Flags) & EvalBeforeAssigningBit) != 0,
+         bool NeedToTranspose = Derived::IsVectorAtCompileTime
+                && OtherDerived::IsVectorAtCompileTime
+                && int(Derived::RowsAtCompileTime) == int(OtherDerived::ColsAtCompileTime)
+                && int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime)
+                && int(Derived::SizeAtCompileTime) != 1>
+struct ei_assign_selector;
+
+template<typename Derived, typename OtherDerived>
+struct ei_assign_selector<Derived,OtherDerived,false,false> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
+};
+template<typename Derived, typename OtherDerived>
+struct ei_assign_selector<Derived,OtherDerived,true,false> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.eval()); }
+};
+template<typename Derived, typename OtherDerived>
+struct ei_assign_selector<Derived,OtherDerived,false,true> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose()); }
+};
+template<typename Derived, typename OtherDerived>
+struct ei_assign_selector<Derived,OtherDerived,true,true> {
+  EIGEN_STRONG_INLINE static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose().eval()); }
+};
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>
+  ::operator=(const MatrixBase<OtherDerived>& other)
+{
+  return ei_assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+
+#endif // EIGEN_ASSIGN_H

Eigen/src/Core/Block.h

@@ -0,0 +1,751 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_BLOCK_H
+#define EIGEN_BLOCK_H
+
+/** \class Block
+  *
+  * \brief Expression of a fixed-size or dynamic-size block
+  *
+  * \param MatrixType the type of the object in which we are taking a block
+  * \param BlockRows the number of rows of the block we are taking at compile time (optional)
+  * \param BlockCols the number of columns of the block we are taking at compile time (optional)
+  * \param _PacketAccess allows to enforce aligned loads and stores if set to ForceAligned.
+  *                      The default is AsRequested. This parameter is internaly used by Eigen
+  *                      in expressions such as \code mat.block() += other; \endcode and most of
+  *                      the time this is the only way it is used.
+  * \param _DirectAccessStatus \internal used for partial specialization
+  *
+  * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
+  * type of MatrixBase::block(int,int,int,int) and MatrixBase::block<int,int>(int,int) and
+  * most of the time this is the only way it is used.
+  *
+  * However, if you want to directly maniputate block expressions,
+  * for instance if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * Here is an example illustrating the dynamic case:
+  * \include class_Block.cpp
+  * Output: \verbinclude class_Block.out
+  *
+  * \note Even though this expression has dynamic size, in the case where \a MatrixType
+  * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+  * it does not cause a dynamic memory allocation.
+  *
+  * Here is an example illustrating the fixed-size case:
+  * \include class_FixedBlock.cpp
+  * Output: \verbinclude class_FixedBlock.out
+  *
+  * \sa MatrixBase::block(int,int,int,int), MatrixBase::block(int,int), class VectorBlock
+  */
+template<typename MatrixType, int BlockRows, int BlockCols, int _PacketAccess, int _DirectAccessStatus>
+struct ei_traits<Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectAccessStatus> >
+{
+  typedef typename ei_traits<MatrixType>::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum{
+    RowsAtCompileTime = BlockRows,
+    ColsAtCompileTime = BlockCols,
+    MaxRowsAtCompileTime = RowsAtCompileTime == 1 ? 1
+      : (BlockRows==Dynamic ? int(ei_traits<MatrixType>::MaxRowsAtCompileTime) : BlockRows),
+    MaxColsAtCompileTime = ColsAtCompileTime == 1 ? 1
+      : (BlockCols==Dynamic ? int(ei_traits<MatrixType>::MaxColsAtCompileTime) : BlockCols),
+    RowMajor = int(ei_traits<MatrixType>::Flags)&RowMajorBit,
+    InnerSize = RowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+    InnerMaxSize = RowMajor ? int(MaxColsAtCompileTime) : int(MaxRowsAtCompileTime),
+    MaskPacketAccessBit = (InnerMaxSize == Dynamic || (InnerSize >= ei_packet_traits<Scalar>::size))
+                        ? PacketAccessBit : 0,
+    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+    Flags = (ei_traits<MatrixType>::Flags & (HereditaryBits | MaskPacketAccessBit | DirectAccessBit)) | FlagsLinearAccessBit,
+    CoeffReadCost = ei_traits<MatrixType>::CoeffReadCost,
+    PacketAccess = _PacketAccess
+  };
+  typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
+                 Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectAccessStatus>&,
+                 Block<MatrixType, BlockRows, BlockCols, ForceAligned, _DirectAccessStatus> >::ret AlignedDerivedType;
+};
+
+template<typename MatrixType, int BlockRows, int BlockCols, int PacketAccess, int _DirectAccessStatus> class Block
+  : public MatrixBase<Block<MatrixType, BlockRows, BlockCols, PacketAccess, _DirectAccessStatus> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
+
+    class InnerIterator;
+
+    /** Column or Row constructor
+      */
+    inline Block(const MatrixType& matrix, int i)
+      : m_matrix(matrix),
+        // It is a row if and only if BlockRows==1 and BlockCols==MatrixType::ColsAtCompileTime,
+        // and it is a column if and only if BlockRows==MatrixType::RowsAtCompileTime and BlockCols==1,
+        // all other cases are invalid.
+        // The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
+        m_startRow( (BlockRows==1) && (BlockCols==MatrixType::ColsAtCompileTime) ? i : 0),
+        m_startCol( (BlockRows==MatrixType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+        m_blockRows(matrix.rows()), // if it is a row, then m_blockRows has a fixed-size of 1, so no pb to try to overwrite it
+        m_blockCols(matrix.cols())  // same for m_blockCols
+    {
+      ei_assert( (i>=0) && (
+          ((BlockRows==1) && (BlockCols==MatrixType::ColsAtCompileTime) && i<matrix.rows())
+        ||((BlockRows==MatrixType::RowsAtCompileTime) && (BlockCols==1) && i<matrix.cols())));
+    }
+
+    /** Fixed-size constructor
+      */
+    inline Block(const MatrixType& matrix, int startRow, int startCol)
+      : m_matrix(matrix), m_startRow(startRow), m_startCol(startCol),
+        m_blockRows(matrix.rows()), m_blockCols(matrix.cols())
+    {
+      EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+      ei_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= matrix.rows()
+          && startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= matrix.cols());
+    }
+
+    /** Dynamic-size constructor
+      */
+    inline Block(const MatrixType& matrix,
+          int startRow, int startCol,
+          int blockRows, int blockCols)
+      : m_matrix(matrix), m_startRow(startRow), m_startCol(startCol),
+                          m_blockRows(blockRows), m_blockCols(blockCols)
+    {
+      ei_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+          && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+      ei_assert(startRow >= 0 && blockRows >= 1 && startRow + blockRows <= matrix.rows()
+          && startCol >= 0 && blockCols >= 1 && startCol + blockCols <= matrix.cols());
+    }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+    inline int rows() const { return m_blockRows.value(); }
+    inline int cols() const { return m_blockCols.value(); }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived()
+               .coeffRef(row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    inline const CoeffReturnType coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_matrix.const_cast_derived()
+             .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                       m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    inline const CoeffReturnType coeff(int index) const
+    {
+      return m_matrix
+             .coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                    m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(int row, int col) const
+    {
+      return m_matrix.template packet<Unaligned>
+              (row + m_startRow.value(), col + m_startCol.value());
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<Unaligned>
+              (row + m_startRow.value(), col + m_startCol.value(), x);
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(int index) const
+    {
+      return m_matrix.template packet<Unaligned>
+              (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+               m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<Unaligned>
+         (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+          m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), x);
+    }
+
+  protected:
+
+    const typename MatrixType::Nested m_matrix;
+    const ei_int_if_dynamic<MatrixType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+    const ei_int_if_dynamic<MatrixType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+    const ei_int_if_dynamic<RowsAtCompileTime> m_blockRows;
+    const ei_int_if_dynamic<ColsAtCompileTime> m_blockCols;
+};
+
+/** \internal */
+template<typename MatrixType, int BlockRows, int BlockCols, int PacketAccess>
+class Block<MatrixType,BlockRows,BlockCols,PacketAccess,HasDirectAccess>
+  : public MapBase<Block<MatrixType, BlockRows, BlockCols,PacketAccess,HasDirectAccess> >
+{
+  public:
+
+    _EIGEN_GENERIC_PUBLIC_INTERFACE(Block, MapBase<Block>)
+
+    class InnerIterator;
+    typedef typename ei_traits<Block>::AlignedDerivedType AlignedDerivedType;
+    friend class Block<MatrixType,BlockRows,BlockCols,PacketAccess==AsRequested?ForceAligned:AsRequested,HasDirectAccess>;
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+    AlignedDerivedType _convertToForceAligned()
+    {
+      return Block<MatrixType,BlockRows,BlockCols,ForceAligned,HasDirectAccess>
+                    (m_matrix, Base::m_data, Base::m_rows.value(), Base::m_cols.value());
+    }
+
+    /** Column or Row constructor
+      */
+    inline Block(const MatrixType& matrix, int i)
+      : Base(&matrix.const_cast_derived().coeffRef(
+              (BlockRows==1) && (BlockCols==MatrixType::ColsAtCompileTime) ? i : 0,
+              (BlockRows==MatrixType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+             BlockRows==1 ? 1 : matrix.rows(),
+             BlockCols==1 ? 1 : matrix.cols()),
+        m_matrix(matrix)
+    {
+      ei_assert( (i>=0) && (
+          ((BlockRows==1) && (BlockCols==MatrixType::ColsAtCompileTime) && i<matrix.rows())
+        ||((BlockRows==MatrixType::RowsAtCompileTime) && (BlockCols==1) && i<matrix.cols())));
+    }
+
+    /** Fixed-size constructor
+      */
+    inline Block(const MatrixType& matrix, int startRow, int startCol)
+      : Base(&matrix.const_cast_derived().coeffRef(startRow,startCol)), m_matrix(matrix)
+    {
+      ei_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= matrix.rows()
+             && startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= matrix.cols());
+    }
+
+    /** Dynamic-size constructor
+      */
+    inline Block(const MatrixType& matrix,
+          int startRow, int startCol,
+          int blockRows, int blockCols)
+      : Base(&matrix.const_cast_derived().coeffRef(startRow,startCol), blockRows, blockCols),
+        m_matrix(matrix)
+    {
+      ei_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+             && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+      ei_assert(startRow >= 0 && blockRows >= 1 && startRow + blockRows <= matrix.rows()
+             && startCol >= 0 && blockCols >= 1 && startCol + blockCols <= matrix.cols());
+    }
+
+    inline int stride(void) const { return m_matrix.stride(); }
+
+  protected:
+
+    /** \internal used by allowAligned() */
+    inline Block(const MatrixType& matrix, const Scalar* data, int blockRows, int blockCols)
+      : Base(data, blockRows, blockCols), m_matrix(matrix)
+    {}
+
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \returns a dynamic-size expression of a block in *this.
+  *
+  * \param startRow the first row in the block
+  * \param startCol the first column in the block
+  * \param blockRows the number of rows in the block
+  * \param blockCols the number of columns in the block
+  *
+  * \addexample BlockIntIntIntInt \label How to reference a sub-matrix (dynamic-size)
+  *
+  * Example: \include MatrixBase_block_int_int_int_int.cpp
+  * Output: \verbinclude MatrixBase_block_int_int_int_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(int,int)
+  */
+template<typename Derived>
+inline typename BlockReturnType<Derived>::Type MatrixBase<Derived>
+  ::block(int startRow, int startCol, int blockRows, int blockCols)
+{
+  return typename BlockReturnType<Derived>::Type(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/** This is the const version of block(int,int,int,int). */
+template<typename Derived>
+inline const typename BlockReturnType<Derived>::Type MatrixBase<Derived>
+  ::block(int startRow, int startCol, int blockRows, int blockCols) const
+{
+  return typename BlockReturnType<Derived>::Type(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/** \returns a dynamic-size expression of a segment (i.e. a vector block) in *this.
+  *
+  * \only_for_vectors
+  *
+  * \addexample SegmentIntInt \label How to reference a sub-vector (dynamic size)
+  *
+  * \param start the first coefficient in the segment
+  * \param size the number of coefficients in the segment
+  *
+  * Example: \include MatrixBase_segment_int_int.cpp
+  * Output: \verbinclude MatrixBase_segment_int_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, segment(int)
+  */
+template<typename Derived>
+inline typename BlockReturnType<Derived>::SubVectorType MatrixBase<Derived>
+  ::segment(int start, int size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename BlockReturnType<Derived>::SubVectorType(derived(), RowsAtCompileTime == 1 ? 0 : start,
+                                   ColsAtCompileTime == 1 ? 0 : start,
+                                   RowsAtCompileTime == 1 ? 1 : size,
+                                   ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** This is the const version of segment(int,int).*/
+template<typename Derived>
+inline const typename BlockReturnType<Derived>::SubVectorType
+MatrixBase<Derived>::segment(int start, int size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return typename BlockReturnType<Derived>::SubVectorType(derived(), RowsAtCompileTime == 1 ? 0 : start,
+                                   ColsAtCompileTime == 1 ? 0 : start,
+                                   RowsAtCompileTime == 1 ? 1 : size,
+                                   ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** \returns a dynamic-size expression of the first coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * \param size the number of coefficients in the block
+  *
+  * \addexample BlockInt \label How to reference a sub-vector (fixed-size)
+  *
+  * Example: \include MatrixBase_start_int.cpp
+  * Output: \verbinclude MatrixBase_start_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(int,int)
+  */
+template<typename Derived>
+inline typename BlockReturnType<Derived,Dynamic>::SubVectorType
+MatrixBase<Derived>::start(int size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,
+               RowsAtCompileTime == 1 ? 1 : Dynamic,
+               ColsAtCompileTime == 1 ? 1 : Dynamic>
+              (derived(), 0, 0,
+               RowsAtCompileTime == 1 ? 1 : size,
+               ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** This is the const version of start(int).*/
+template<typename Derived>
+inline const typename BlockReturnType<Derived,Dynamic>::SubVectorType
+MatrixBase<Derived>::start(int size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,
+               RowsAtCompileTime == 1 ? 1 : Dynamic,
+               ColsAtCompileTime == 1 ? 1 : Dynamic>
+              (derived(), 0, 0,
+               RowsAtCompileTime == 1 ? 1 : size,
+               ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** \returns a dynamic-size expression of the last coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * \param size the number of coefficients in the block
+  *
+  * \addexample BlockEnd \label How to reference the end of a vector (fixed-size)
+  *
+  * Example: \include MatrixBase_end_int.cpp
+  * Output: \verbinclude MatrixBase_end_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(int,int)
+  */
+template<typename Derived>
+inline typename BlockReturnType<Derived,Dynamic>::SubVectorType
+MatrixBase<Derived>::end(int size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,
+               RowsAtCompileTime == 1 ? 1 : Dynamic,
+               ColsAtCompileTime == 1 ? 1 : Dynamic>
+              (derived(),
+               RowsAtCompileTime == 1 ? 0 : rows() - size,
+               ColsAtCompileTime == 1 ? 0 : cols() - size,
+               RowsAtCompileTime == 1 ? 1 : size,
+               ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** This is the const version of end(int).*/
+template<typename Derived>
+inline const typename BlockReturnType<Derived,Dynamic>::SubVectorType
+MatrixBase<Derived>::end(int size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,
+               RowsAtCompileTime == 1 ? 1 : Dynamic,
+               ColsAtCompileTime == 1 ? 1 : Dynamic>
+              (derived(),
+               RowsAtCompileTime == 1 ? 0 : rows() - size,
+               ColsAtCompileTime == 1 ? 0 : cols() - size,
+               RowsAtCompileTime == 1 ? 1 : size,
+               ColsAtCompileTime == 1 ? 1 : size);
+}
+
+/** \returns a fixed-size expression of a segment (i.e. a vector block) in \c *this
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * \param start the index of the first element of the sub-vector
+  *
+  * Example: \include MatrixBase_template_int_segment.cpp
+  * Output: \verbinclude MatrixBase_template_int_segment.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::segment(int start)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,  (RowsAtCompileTime == 1 ? 1 : Size),
+                         (ColsAtCompileTime == 1 ? 1 : Size)>
+              (derived(), RowsAtCompileTime == 1 ? 0 : start,
+                          ColsAtCompileTime == 1 ? 0 : start);
+}
+
+/** This is the const version of segment<int>(int).*/
+template<typename Derived>
+template<int Size>
+inline const typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::segment(int start) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived,  (RowsAtCompileTime == 1 ? 1 : Size),
+                         (ColsAtCompileTime == 1 ? 1 : Size)>
+              (derived(), RowsAtCompileTime == 1 ? 0 : start,
+                          ColsAtCompileTime == 1 ? 0 : start);
+}
+
+/** \returns a fixed-size expression of the first coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * \addexample BlockStart \label How to reference the start of a vector (fixed-size)
+  *
+  * Example: \include MatrixBase_template_int_start.cpp
+  * Output: \verbinclude MatrixBase_template_int_start.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::start()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived, (RowsAtCompileTime == 1 ? 1 : Size),
+                        (ColsAtCompileTime == 1 ? 1 : Size)>(derived(), 0, 0);
+}
+
+/** This is the const version of start<int>().*/
+template<typename Derived>
+template<int Size>
+inline const typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::start() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived, (RowsAtCompileTime == 1 ? 1 : Size),
+                        (ColsAtCompileTime == 1 ? 1 : Size)>(derived(), 0, 0);
+}
+
+/** \returns a fixed-size expression of the last coefficients of *this.
+  *
+  * \only_for_vectors
+  *
+  * The template parameter \a Size is the number of coefficients in the block
+  *
+  * Example: \include MatrixBase_template_int_end.cpp
+  * Output: \verbinclude MatrixBase_template_int_end.out
+  *
+  * \sa class Block
+  */
+template<typename Derived>
+template<int Size>
+inline typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::end()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived, RowsAtCompileTime == 1 ? 1 : Size,
+                        ColsAtCompileTime == 1 ? 1 : Size>
+           (derived(),
+            RowsAtCompileTime == 1 ? 0 : rows() - Size,
+            ColsAtCompileTime == 1 ? 0 : cols() - Size);
+}
+
+/** This is the const version of end<int>.*/
+template<typename Derived>
+template<int Size>
+inline const typename BlockReturnType<Derived,Size>::SubVectorType
+MatrixBase<Derived>::end() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return Block<Derived, RowsAtCompileTime == 1 ? 1 : Size,
+                        ColsAtCompileTime == 1 ? 1 : Size>
+           (derived(),
+            RowsAtCompileTime == 1 ? 0 : rows() - Size,
+            ColsAtCompileTime == 1 ? 0 : cols() - Size);
+}
+
+/** \returns a dynamic-size expression of a corner of *this.
+  *
+  * \param type the type of corner. Can be \a Eigen::TopLeft, \a Eigen::TopRight,
+  * \a Eigen::BottomLeft, \a Eigen::BottomRight.
+  * \param cRows the number of rows in the corner
+  * \param cCols the number of columns in the corner
+  *
+  * \addexample BlockCornerDynamicSize \label How to reference a sub-corner of a matrix
+  *
+  * Example: \include MatrixBase_corner_enum_int_int.cpp
+  * Output: \verbinclude MatrixBase_corner_enum_int_int.out
+  *
+  * \note Even though the returned expression has dynamic size, in the case
+  * when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
+  * which means that evaluating it does not cause a dynamic memory allocation.
+  *
+  * \sa class Block, block(int,int,int,int)
+  */
+template<typename Derived>
+inline typename BlockReturnType<Derived>::Type MatrixBase<Derived>
+  ::corner(CornerType type, int cRows, int cCols)
+{
+  switch(type)
+  {
+    default:
+      ei_assert(false && "Bad corner type.");
+    case TopLeft:
+      return typename BlockReturnType<Derived>::Type(derived(), 0, 0, cRows, cCols);
+    case TopRight:
+      return typename BlockReturnType<Derived>::Type(derived(), 0, cols() - cCols, cRows, cCols);
+    case BottomLeft:
+      return typename BlockReturnType<Derived>::Type(derived(), rows() - cRows, 0, cRows, cCols);
+    case BottomRight:
+      return typename BlockReturnType<Derived>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+  }
+}
+
+/** This is the const version of corner(CornerType, int, int).*/
+template<typename Derived>
+inline const typename BlockReturnType<Derived>::Type
+MatrixBase<Derived>::corner(CornerType type, int cRows, int cCols) const
+{
+  switch(type)
+  {
+    default:
+      ei_assert(false && "Bad corner type.");
+    case TopLeft:
+      return typename BlockReturnType<Derived>::Type(derived(), 0, 0, cRows, cCols);
+    case TopRight:
+      return typename BlockReturnType<Derived>::Type(derived(), 0, cols() - cCols, cRows, cCols);
+    case BottomLeft:
+      return typename BlockReturnType<Derived>::Type(derived(), rows() - cRows, 0, cRows, cCols);
+    case BottomRight:
+      return typename BlockReturnType<Derived>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+  }
+}
+
+/** \returns a fixed-size expression of a corner of *this.
+  *
+  * \param type the type of corner. Can be \a Eigen::TopLeft, \a Eigen::TopRight,
+  * \a Eigen::BottomLeft, \a Eigen::BottomRight.
+  *
+  * The template parameters CRows and CCols arethe number of rows and columns in the corner.
+  *
+  * Example: \include MatrixBase_template_int_int_corner_enum.cpp
+  * Output: \verbinclude MatrixBase_template_int_int_corner_enum.out
+  *
+  * \sa class Block, block(int,int,int,int)
+  */
+template<typename Derived>
+template<int CRows, int CCols>
+inline typename BlockReturnType<Derived, CRows, CCols>::Type
+MatrixBase<Derived>::corner(CornerType type)
+{
+  switch(type)
+  {
+    default:
+      ei_assert(false && "Bad corner type.");
+    case TopLeft:
+      return Block<Derived, CRows, CCols>(derived(), 0, 0);
+    case TopRight:
+      return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+    case BottomLeft:
+      return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+    case BottomRight:
+      return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+  }
+}
+
+/** This is the const version of corner<int, int>(CornerType).*/
+template<typename Derived>
+template<int CRows, int CCols>
+inline const typename BlockReturnType<Derived, CRows, CCols>::Type
+MatrixBase<Derived>::corner(CornerType type) const
+{
+  switch(type)
+  {
+    default:
+      ei_assert(false && "Bad corner type.");
+    case TopLeft:
+      return Block<Derived, CRows, CCols>(derived(), 0, 0);
+    case TopRight:
+      return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
+    case BottomLeft:
+      return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
+    case BottomRight:
+      return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
+  }
+}
+
+/** \returns a fixed-size expression of a block in *this.
+  *
+  * The template parameters \a BlockRows and \a BlockCols are the number of
+  * rows and columns in the block.
+  *
+  * \param startRow the first row in the block
+  * \param startCol the first column in the block
+  *
+  * \addexample BlockSubMatrixFixedSize \label How to reference a sub-matrix (fixed-size)
+  *
+  * Example: \include MatrixBase_block_int_int.cpp
+  * Output: \verbinclude MatrixBase_block_int_int.out
+  *
+  * \note since block is a templated member, the keyword template has to be used
+  * if the matrix type is also a template parameter: \code m.template block<3,3>(1,1); \endcode
+  *
+  * \sa class Block, block(int,int,int,int)
+  */
+template<typename Derived>
+template<int BlockRows, int BlockCols>
+inline typename BlockReturnType<Derived, BlockRows, BlockCols>::Type
+MatrixBase<Derived>::block(int startRow, int startCol)
+{
+  return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
+}
+
+/** This is the const version of block<>(int, int). */
+template<typename Derived>
+template<int BlockRows, int BlockCols>
+inline const typename BlockReturnType<Derived, BlockRows, BlockCols>::Type
+MatrixBase<Derived>::block(int startRow, int startCol) const
+{
+  return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
+}
+
+/** \returns an expression of the \a i-th column of *this. Note that the numbering starts at 0.
+  *
+  * \addexample BlockColumn \label How to reference a single column of a matrix
+  *
+  * Example: \include MatrixBase_col.cpp
+  * Output: \verbinclude MatrixBase_col.out
+  *
+  * \sa row(), class Block */
+template<typename Derived>
+inline typename MatrixBase<Derived>::ColXpr
+MatrixBase<Derived>::col(int i)
+{
+  return ColXpr(derived(), i);
+}
+
+/** This is the const version of col(). */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::ColXpr
+MatrixBase<Derived>::col(int i) const
+{
+  return ColXpr(derived(), i);
+}
+
+/** \returns an expression of the \a i-th row of *this. Note that the numbering starts at 0.
+  *
+  * \addexample BlockRow \label How to reference a single row of a matrix
+  *
+  * Example: \include MatrixBase_row.cpp
+  * Output: \verbinclude MatrixBase_row.out
+  *
+  * \sa col(), class Block */
+template<typename Derived>
+inline typename MatrixBase<Derived>::RowXpr
+MatrixBase<Derived>::row(int i)
+{
+  return RowXpr(derived(), i);
+}
+
+/** This is the const version of row(). */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::RowXpr
+MatrixBase<Derived>::row(int i) const
+{
+  return RowXpr(derived(), i);
+}
+
+#endif // EIGEN_BLOCK_H

Eigen/src/Core/CMakeLists.txt

@@ -0,0 +1,17 @@
+FILE(GLOB Eigen_Core_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core COMPONENT Devel
+  )
+
+FILE(GLOB Eigen_Core_Product_SRCS "products/*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_Product_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/products COMPONENT Devel
+  )
+
+
+ADD_SUBDIRECTORY(util)
+ADD_SUBDIRECTORY(arch)

Eigen/src/Core/Coeffs.h

@@ -0,0 +1,384 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COEFFS_H
+#define EIGEN_COEFFS_H
+
+/** Short version: don't use this function, use
+  * \link operator()(int,int) const \endlink instead.
+  *
+  * Long version: this function is similar to
+  * \link operator()(int,int) const \endlink, but without the assertion.
+  * Use this for limiting the performance cost of debugging code when doing
+  * repeated coefficient access. Only use this when it is guaranteed that the
+  * parameters \a row and \a col are in range.
+  *
+  * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+  * function equivalent to \link operator()(int,int) const \endlink.
+  *
+  * \sa operator()(int,int) const, coeffRef(int,int), coeff(int) const
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::coeff(int row, int col) const
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  return derived().coeff(row, col);
+}
+
+/** \returns the coefficient at given the given row and column.
+  *
+  * \sa operator()(int,int), operator[](int) const
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::operator()(int row, int col) const
+{
+  ei_assert(row >= 0 && row < rows()
+      && col >= 0 && col < cols());
+  return derived().coeff(row, col);
+}
+
+/** Short version: don't use this function, use
+  * \link operator()(int,int) \endlink instead.
+  *
+  * Long version: this function is similar to
+  * \link operator()(int,int) \endlink, but without the assertion.
+  * Use this for limiting the performance cost of debugging code when doing
+  * repeated coefficient access. Only use this when it is guaranteed that the
+  * parameters \a row and \a col are in range.
+  *
+  * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+  * function equivalent to \link operator()(int,int) \endlink.
+  *
+  * \sa operator()(int,int), coeff(int, int) const, coeffRef(int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::coeffRef(int row, int col)
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  return derived().coeffRef(row, col);
+}
+
+/** \returns a reference to the coefficient at given the given row and column.
+  *
+  * \sa operator()(int,int) const, operator[](int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::operator()(int row, int col)
+{
+  ei_assert(row >= 0 && row < rows()
+      && col >= 0 && col < cols());
+  return derived().coeffRef(row, col);
+}
+
+/** Short version: don't use this function, use
+  * \link operator[](int) const \endlink instead.
+  *
+  * Long version: this function is similar to
+  * \link operator[](int) const \endlink, but without the assertion.
+  * Use this for limiting the performance cost of debugging code when doing
+  * repeated coefficient access. Only use this when it is guaranteed that the
+  * parameter \a index is in range.
+  *
+  * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+  * function equivalent to \link operator[](int) const \endlink.
+  *
+  * \sa operator[](int) const, coeffRef(int), coeff(int,int) const
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::coeff(int index) const
+{
+  ei_internal_assert(index >= 0 && index < size());
+  return derived().coeff(index);
+}
+
+/** \returns the coefficient at given index.
+  *
+  * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+  *
+  * \sa operator[](int), operator()(int,int) const, x() const, y() const,
+  * z() const, w() const
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::operator[](int index) const
+{
+  ei_assert(index >= 0 && index < size());
+  return derived().coeff(index);
+}
+
+/** \returns the coefficient at given index.
+  *
+  * This is synonymous to operator[](int) const.
+  *
+  * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+  *
+  * \sa operator[](int), operator()(int,int) const, x() const, y() const,
+  * z() const, w() const
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::operator()(int index) const
+{
+  ei_assert(index >= 0 && index < size());
+  return derived().coeff(index);
+}
+
+/** Short version: don't use this function, use
+  * \link operator[](int) \endlink instead.
+  *
+  * Long version: this function is similar to
+  * \link operator[](int) \endlink, but without the assertion.
+  * Use this for limiting the performance cost of debugging code when doing
+  * repeated coefficient access. Only use this when it is guaranteed that the
+  * parameters \a row and \a col are in range.
+  *
+  * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+  * function equivalent to \link operator[](int) \endlink.
+  *
+  * \sa operator[](int), coeff(int) const, coeffRef(int,int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::coeffRef(int index)
+{
+  ei_internal_assert(index >= 0 && index < size());
+  return derived().coeffRef(index);
+}
+
+/** \returns a reference to the coefficient at given index.
+  *
+  * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+  *
+  * \sa operator[](int) const, operator()(int,int), x(), y(), z(), w()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::operator[](int index)
+{
+  ei_assert(index >= 0 && index < size());
+  return derived().coeffRef(index);
+}
+
+/** \returns a reference to the coefficient at given index.
+  *
+  * This is synonymous to operator[](int).
+  *
+  * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+  *
+  * \sa operator[](int) const, operator()(int,int), x(), y(), z(), w()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::operator()(int index)
+{
+  ei_assert(index >= 0 && index < size());
+  return derived().coeffRef(index);
+}
+
+/** equivalent to operator[](0).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::x() const { return (*this)[0]; }
+
+/** equivalent to operator[](1).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::y() const { return (*this)[1]; }
+
+/** equivalent to operator[](2).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::z() const { return (*this)[2]; }
+
+/** equivalent to operator[](3).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::CoeffReturnType MatrixBase<Derived>
+  ::w() const { return (*this)[3]; }
+
+/** equivalent to operator[](0).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::x() { return (*this)[0]; }
+
+/** equivalent to operator[](1).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::y() { return (*this)[1]; }
+
+/** equivalent to operator[](2).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::z() { return (*this)[2]; }
+
+/** equivalent to operator[](3).  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar& MatrixBase<Derived>
+  ::w() { return (*this)[3]; }
+
+/** \returns the packet of coefficients starting at the given row and column. It is your responsibility
+  * to ensure that a packet really starts there. This method is only available on expressions having the
+  * PacketAccessBit.
+  *
+  * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+  * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+  * starting at an address which is a multiple of the packet size.
+  */
+template<typename Derived>
+template<int LoadMode>
+EIGEN_STRONG_INLINE typename ei_packet_traits<typename ei_traits<Derived>::Scalar>::type
+MatrixBase<Derived>::packet(int row, int col) const
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  return derived().template packet<LoadMode>(row,col);
+}
+
+/** Stores the given packet of coefficients, at the given row and column of this expression. It is your responsibility
+  * to ensure that a packet really starts there. This method is only available on expressions having the
+  * PacketAccessBit.
+  *
+  * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+  * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+  * starting at an address which is a multiple of the packet size.
+  */
+template<typename Derived>
+template<int StoreMode>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::writePacket
+(int row, int col, const typename ei_packet_traits<typename ei_traits<Derived>::Scalar>::type& x)
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  derived().template writePacket<StoreMode>(row,col,x);
+}
+
+/** \returns the packet of coefficients starting at the given index. It is your responsibility
+  * to ensure that a packet really starts there. This method is only available on expressions having the
+  * PacketAccessBit and the LinearAccessBit.
+  *
+  * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+  * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+  * starting at an address which is a multiple of the packet size.
+  */
+template<typename Derived>
+template<int LoadMode>
+EIGEN_STRONG_INLINE typename ei_packet_traits<typename ei_traits<Derived>::Scalar>::type
+MatrixBase<Derived>::packet(int index) const
+{
+  ei_internal_assert(index >= 0 && index < size());
+  return derived().template packet<LoadMode>(index);
+}
+
+/** Stores the given packet of coefficients, at the given index in this expression. It is your responsibility
+  * to ensure that a packet really starts there. This method is only available on expressions having the
+  * PacketAccessBit and the LinearAccessBit.
+  *
+  * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
+  * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+  * starting at an address which is a multiple of the packet size.
+  */
+template<typename Derived>
+template<int StoreMode>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::writePacket
+(int index, const typename ei_packet_traits<typename ei_traits<Derived>::Scalar>::type& x)
+{
+  ei_internal_assert(index >= 0 && index < size());
+  derived().template writePacket<StoreMode>(index,x);
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+/** \internal Copies the coefficient at position (row,col) of other into *this.
+  *
+  * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+  * with usual assignments.
+  *
+  * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::copyCoeff(int row, int col, const MatrixBase<OtherDerived>& other)
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  derived().coeffRef(row, col) = other.derived().coeff(row, col);
+}
+
+/** \internal Copies the coefficient at the given index of other into *this.
+  *
+  * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+  * with usual assignments.
+  *
+  * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::copyCoeff(int index, const MatrixBase<OtherDerived>& other)
+{
+  ei_internal_assert(index >= 0 && index < size());
+  derived().coeffRef(index) = other.derived().coeff(index);
+}
+
+/** \internal Copies the packet at position (row,col) of other into *this.
+  *
+  * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+  * with usual assignments.
+  *
+  * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+  */
+template<typename Derived>
+template<typename OtherDerived, int StoreMode, int LoadMode>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::copyPacket(int row, int col, const MatrixBase<OtherDerived>& other)
+{
+  ei_internal_assert(row >= 0 && row < rows()
+                     && col >= 0 && col < cols());
+  derived().template writePacket<StoreMode>(row, col,
+    other.derived().template packet<LoadMode>(row, col));
+}
+
+/** \internal Copies the packet at the given index of other into *this.
+  *
+  * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
+  * with usual assignments.
+  *
+  * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
+  */
+template<typename Derived>
+template<typename OtherDerived, int StoreMode, int LoadMode>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::copyPacket(int index, const MatrixBase<OtherDerived>& other)
+{
+  ei_internal_assert(index >= 0 && index < size());
+  derived().template writePacket<StoreMode>(index,
+    other.derived().template packet<LoadMode>(index));
+}
+
+#endif
+
+#endif // EIGEN_COEFFS_H

Eigen/src/Core/CommaInitializer.h

@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COMMAINITIALIZER_H
+#define EIGEN_COMMAINITIALIZER_H
+
+/** \class CommaInitializer
+  *
+  * \brief Helper class used by the comma initializer operator
+  *
+  * This class is internally used to implement the comma initializer feature. It is
+  * the return type of MatrixBase::operator<<, and most of the time this is the only
+  * way it is used.
+  *
+  * \sa \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
+  */
+template<typename MatrixType>
+struct CommaInitializer
+{
+  typedef typename ei_traits<MatrixType>::Scalar Scalar;
+  inline CommaInitializer(MatrixType& mat, const Scalar& s)
+    : m_matrix(mat), m_row(0), m_col(1), m_currentBlockRows(1)
+  {
+    m_matrix.coeffRef(0,0) = s;
+  }
+
+  template<typename OtherDerived>
+  inline CommaInitializer(MatrixType& mat, const MatrixBase<OtherDerived>& other)
+    : m_matrix(mat), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
+  {
+    m_matrix.block(0, 0, other.rows(), other.cols()) = other;
+  }
+
+  /* inserts a scalar value in the target matrix */
+  CommaInitializer& operator,(const Scalar& s)
+  {
+    if (m_col==m_matrix.cols())
+    {
+      m_row+=m_currentBlockRows;
+      m_col = 0;
+      m_currentBlockRows = 1;
+      ei_assert(m_row<m_matrix.rows()
+        && "Too many rows passed to comma initializer (operator<<)");
+    }
+    ei_assert(m_col<m_matrix.cols()
+      && "Too many coefficients passed to comma initializer (operator<<)");
+    ei_assert(m_currentBlockRows==1);
+    m_matrix.coeffRef(m_row, m_col++) = s;
+    return *this;
+  }
+
+  /* inserts a matrix expression in the target matrix */
+  template<typename OtherDerived>
+  CommaInitializer& operator,(const MatrixBase<OtherDerived>& other)
+  {
+    if (m_col==m_matrix.cols())
+    {
+      m_row+=m_currentBlockRows;
+      m_col = 0;
+      m_currentBlockRows = other.rows();
+      ei_assert(m_row+m_currentBlockRows<=m_matrix.rows()
+        && "Too many rows passed to comma initializer (operator<<)");
+    }
+    ei_assert(m_col<m_matrix.cols()
+      && "Too many coefficients passed to comma initializer (operator<<)");
+    ei_assert(m_currentBlockRows==other.rows());
+    if (OtherDerived::SizeAtCompileTime != Dynamic)
+      m_matrix.template block<OtherDerived::RowsAtCompileTime != Dynamic ? OtherDerived::RowsAtCompileTime : 1,
+                              OtherDerived::ColsAtCompileTime != Dynamic ? OtherDerived::ColsAtCompileTime : 1>
+                    (m_row, m_col) = other;
+    else
+      m_matrix.block(m_row, m_col, other.rows(), other.cols()) = other;
+    m_col += other.cols();
+    return *this;
+  }
+
+  inline ~CommaInitializer()
+  {
+    ei_assert((m_row+m_currentBlockRows) == m_matrix.rows()
+         && m_col == m_matrix.cols()
+         && "Too few coefficients passed to comma initializer (operator<<)");
+  }
+
+  /** \returns the built matrix once all its coefficients have been set.
+    * Calling finished is 100% optional. Its purpose is to write expressions
+    * like this:
+    * \code
+    * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
+    * \endcode
+    */
+  inline MatrixType& finished() { return m_matrix; }
+
+  MatrixType& m_matrix;   // target matrix
+  int m_row;              // current row id
+  int m_col;              // current col id
+  int m_currentBlockRows; // current block height
+};
+
+/** \anchor MatrixBaseCommaInitRef
+  * Convenient operator to set the coefficients of a matrix.
+  *
+  * The coefficients must be provided in a row major order and exactly match
+  * the size of the matrix. Otherwise an assertion is raised.
+  *
+  * \addexample CommaInit \label How to easily set all the coefficients of a matrix
+  *
+  * Example: \include MatrixBase_set.cpp
+  * Output: \verbinclude MatrixBase_set.out
+  *
+  * \sa CommaInitializer::finished(), class CommaInitializer
+  */
+template<typename Derived>
+inline CommaInitializer<Derived> MatrixBase<Derived>::operator<< (const Scalar& s)
+{
+  return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
+}
+
+/** \sa operator<<(const Scalar&) */
+template<typename Derived>
+template<typename OtherDerived>
+inline CommaInitializer<Derived>
+MatrixBase<Derived>::operator<<(const MatrixBase<OtherDerived>& other)
+{
+  return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
+}
+
+#endif // EIGEN_COMMAINITIALIZER_H

Eigen/src/Core/CoreInstantiations.cpp

@@ -0,0 +1,47 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifdef EIGEN_EXTERN_INSTANTIATIONS
+#undef EIGEN_EXTERN_INSTANTIATIONS
+#endif
+
+#include "../../Core"
+
+namespace Eigen
+{
+
+#define EIGEN_INSTANTIATE_PRODUCT(TYPE) \
+template static void ei_cache_friendly_product<TYPE>( \
+  int _rows, int _cols, int depth, \
+  bool _lhsRowMajor, const TYPE* _lhs, int _lhsStride, \
+  bool _rhsRowMajor, const TYPE* _rhs, int _rhsStride, \
+  bool resRowMajor, TYPE* res, int resStride)
+
+EIGEN_INSTANTIATE_PRODUCT(float);
+EIGEN_INSTANTIATE_PRODUCT(double);
+EIGEN_INSTANTIATE_PRODUCT(int);
+EIGEN_INSTANTIATE_PRODUCT(std::complex<float>);
+EIGEN_INSTANTIATE_PRODUCT(std::complex<double>);
+
+}

Eigen/src/Core/Cwise.h

@@ -0,0 +1,211 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_H
+#define EIGEN_CWISE_H
+
+/** \internal
+  * convenient macro to defined the return type of a cwise binary operation */
+#define EIGEN_CWISE_BINOP_RETURN_TYPE(OP) \
+    CwiseBinaryOp<OP<typename ei_traits<ExpressionType>::Scalar>, ExpressionType, OtherDerived>
+
+#define EIGEN_CWISE_PRODUCT_RETURN_TYPE \
+    CwiseBinaryOp< \
+      ei_scalar_product_op< \
+        typename ei_scalar_product_traits< \
+          typename ei_traits<ExpressionType>::Scalar, \
+          typename ei_traits<OtherDerived>::Scalar \
+        >::ReturnType \
+      >, \
+      ExpressionType, \
+      OtherDerived \
+    >
+
+/** \internal
+  * convenient macro to defined the return type of a cwise unary operation */
+#define EIGEN_CWISE_UNOP_RETURN_TYPE(OP) \
+    CwiseUnaryOp<OP<typename ei_traits<ExpressionType>::Scalar>, ExpressionType>
+
+/** \internal
+  * convenient macro to defined the return type of a cwise comparison to a scalar */
+#define EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(OP) \
+    CwiseBinaryOp<OP<typename ei_traits<ExpressionType>::Scalar>, ExpressionType, \
+        NestByValue<typename ExpressionType::ConstantReturnType> >
+
+/** \class Cwise
+  *
+  * \brief Pseudo expression providing additional coefficient-wise operations
+  *
+  * \param ExpressionType the type of the object on which to do coefficient-wise operations
+  *
+  * This class represents an expression with additional coefficient-wise features.
+  * It is the return type of MatrixBase::cwise()
+  * and most of the time this is the only way it is used.
+  *
+  * Note that some methods are defined in the \ref Array_Module array module.
+  *
+  * Example: \include MatrixBase_cwise_const.cpp
+  * Output: \verbinclude MatrixBase_cwise_const.out
+  *
+  * \sa MatrixBase::cwise() const, MatrixBase::cwise()
+  */
+template<typename ExpressionType> class Cwise
+{
+  public:
+
+    typedef typename ei_traits<ExpressionType>::Scalar Scalar;
+    typedef typename ei_meta_if<ei_must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, const ExpressionType&>::ret ExpressionTypeNested;
+    typedef CwiseUnaryOp<ei_scalar_add_op<Scalar>, ExpressionType> ScalarAddReturnType;
+
+    inline Cwise(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+    /** \internal */
+    inline const ExpressionType& _expression() const { return m_matrix; }
+
+    template<typename OtherDerived>
+    const EIGEN_CWISE_PRODUCT_RETURN_TYPE
+    operator*(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_quotient_op)
+    operator/(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_min_op)
+    min(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_max_op)
+    max(const MatrixBase<OtherDerived> &other) const;
+
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_abs_op)      abs() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_abs2_op)     abs2() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_square_op)   square() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_cube_op)     cube() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_inverse_op)  inverse() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_sqrt_op)     sqrt() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_exp_op)      exp() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_log_op)      log() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_cos_op)      cos() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_sin_op)      sin() const;
+    const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_pow_op)      pow(const Scalar& exponent) const;
+
+    const ScalarAddReturnType
+    operator+(const Scalar& scalar) const;
+
+    /** \relates Cwise */
+    friend const ScalarAddReturnType
+    operator+(const Scalar& scalar, const Cwise& mat)
+    { return mat + scalar; }
+
+    ExpressionType& operator+=(const Scalar& scalar);
+
+    const ScalarAddReturnType
+    operator-(const Scalar& scalar) const;
+
+    ExpressionType& operator-=(const Scalar& scalar);
+
+    template<typename OtherDerived>
+    inline ExpressionType& operator*=(const MatrixBase<OtherDerived> &other);
+
+    template<typename OtherDerived>
+    inline ExpressionType& operator/=(const MatrixBase<OtherDerived> &other);
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less)
+    operator<(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::less_equal)
+    operator<=(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater)
+    operator>(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::greater_equal)
+    operator>=(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::equal_to)
+    operator==(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived> const EIGEN_CWISE_BINOP_RETURN_TYPE(std::not_equal_to)
+    operator!=(const MatrixBase<OtherDerived>& other) const;
+
+    // comparisons to a scalar value
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less)
+    operator<(Scalar s) const;
+
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::less_equal)
+    operator<=(Scalar s) const;
+
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater)
+    operator>(Scalar s) const;
+
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::greater_equal)
+    operator>=(Scalar s) const;
+
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::equal_to)
+    operator==(Scalar s) const;
+
+    const EIGEN_CWISE_COMP_TO_SCALAR_RETURN_TYPE(std::not_equal_to)
+    operator!=(Scalar s) const;
+
+    // allow to extend Cwise outside Eigen
+    #ifdef EIGEN_CWISE_PLUGIN
+    #include EIGEN_CWISE_PLUGIN
+    #endif
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \returns a Cwise wrapper of *this providing additional coefficient-wise operations
+  *
+  * Example: \include MatrixBase_cwise_const.cpp
+  * Output: \verbinclude MatrixBase_cwise_const.out
+  *
+  * \sa class Cwise, cwise()
+  */
+template<typename Derived>
+inline const Cwise<Derived>
+MatrixBase<Derived>::cwise() const
+{
+  return derived();
+}
+
+/** \returns a Cwise wrapper of *this providing additional coefficient-wise operations
+  *
+  * Example: \include MatrixBase_cwise.cpp
+  * Output: \verbinclude MatrixBase_cwise.out
+  *
+  * \sa class Cwise, cwise() const
+  */
+template<typename Derived>
+inline Cwise<Derived>
+MatrixBase<Derived>::cwise()
+{
+  return derived();
+}
+
+#endif // EIGEN_CWISE_H

Eigen/src/Core/CwiseBinaryOp.h

@@ -0,0 +1,304 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_BINARY_OP_H
+#define EIGEN_CWISE_BINARY_OP_H
+
+/** \class CwiseBinaryOp
+  *
+  * \brief Generic expression of a coefficient-wise operator between two matrices or vectors
+  *
+  * \param BinaryOp template functor implementing the operator
+  * \param Lhs the type of the left-hand side
+  * \param Rhs the type of the right-hand side
+  *
+  * This class represents an expression of a generic binary operator of two matrices or vectors.
+  * It is the return type of the operator+, operator-, and the Cwise methods, and most
+  * of the time this is the only way it is used.
+  *
+  * However, if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
+  */
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct ei_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 ei_result_of<
+                     BinaryOp(
+                       typename Lhs::Scalar,
+                       typename Rhs::Scalar
+                     )
+                   >::type Scalar;
+  typedef typename Lhs::Nested LhsNested;
+  typedef typename Rhs::Nested RhsNested;
+  typedef typename ei_unref<LhsNested>::type _LhsNested;
+  typedef typename ei_unref<RhsNested>::type _RhsNested;
+  enum {
+    LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+    RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+    RowsAtCompileTime = Lhs::RowsAtCompileTime,
+    ColsAtCompileTime = Lhs::ColsAtCompileTime,
+    MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = Lhs::MaxColsAtCompileTime,
+    Flags = (int(LhsFlags) | int(RhsFlags)) & (
+        HereditaryBits
+      | (int(LhsFlags) & int(RhsFlags) & (LinearAccessBit | AlignedBit))
+      | (ei_functor_traits<BinaryOp>::PacketAccess && ((int(LhsFlags) & RowMajorBit)==(int(RhsFlags) & RowMajorBit))
+        ? (int(LhsFlags) & int(RhsFlags) & PacketAccessBit) : 0)),
+    CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + ei_functor_traits<BinaryOp>::Cost
+  };
+};
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOp : ei_no_assignment_operator,
+  public MatrixBase<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
+    typedef typename ei_traits<CwiseBinaryOp>::LhsNested LhsNested;
+    typedef typename ei_traits<CwiseBinaryOp>::RhsNested RhsNested;
+
+    EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& lhs, const Rhs& rhs, const BinaryOp& func = BinaryOp())
+      : m_lhs(lhs), m_rhs(rhs), m_functor(func)
+    {
+      // we require Lhs and Rhs to have the same scalar type. Currently there is no example of a binary functor
+      // that would take two operands of different types. If there were such an example, then this check should be
+      // moved to the BinaryOp functors, on a per-case basis. This would however require a change in the BinaryOp functors, as
+      // currently they take only one typename Scalar template parameter.
+      // It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
+      // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
+      // add together a float matrix and a double matrix.
+      EIGEN_STATIC_ASSERT((ei_functor_allows_mixing_real_and_complex<BinaryOp>::ret
+                           ? int(ei_is_same_type<typename Lhs::RealScalar, typename Rhs::RealScalar>::ret)
+                           : int(ei_is_same_type<typename Lhs::Scalar, typename Rhs::Scalar>::ret)),
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+      // require the sizes to match
+      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
+      ei_assert(lhs.rows() == rhs.rows() && lhs.cols() == rhs.cols());
+    }
+
+    EIGEN_STRONG_INLINE int rows() const { return m_lhs.rows(); }
+    EIGEN_STRONG_INLINE int cols() const { return m_lhs.cols(); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int row, int col) const
+    {
+      return m_functor(m_lhs.coeff(row, col), m_rhs.coeff(row, col));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int row, int col) const
+    {
+      return m_functor.packetOp(m_lhs.template packet<LoadMode>(row, col), m_rhs.template packet<LoadMode>(row, col));
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int index) const
+    {
+      return m_functor(m_lhs.coeff(index), m_rhs.coeff(index));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int index) const
+    {
+      return m_functor.packetOp(m_lhs.template packet<LoadMode>(index), m_rhs.template packet<LoadMode>(index));
+    }
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+    const BinaryOp m_functor;
+};
+
+/**\returns an expression of the difference of \c *this and \a other
+  *
+  * \note If you want to substract a given scalar from all coefficients, see Cwise::operator-().
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator-=(), Cwise::operator-()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<ei_scalar_difference_op<typename ei_traits<Derived>::Scalar>,
+                                 Derived, OtherDerived>
+MatrixBase<Derived>::operator-(const MatrixBase<OtherDerived> &other) const
+{
+  return CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
+                       Derived, OtherDerived>(derived(), other.derived());
+}
+
+/** replaces \c *this by \c *this - \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
+{
+  return *this = *this - other;
+}
+
+/** \relates MatrixBase
+  *
+  * \returns an expression of the sum of \c *this and \a other
+  *
+  * \note If you want to add a given scalar to all coefficients, see Cwise::operator+().
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator+=(), Cwise::operator+()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<ei_scalar_sum_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
+MatrixBase<Derived>::operator+(const MatrixBase<OtherDerived> &other) const
+{
+  return CwiseBinaryOp<ei_scalar_sum_op<Scalar>, Derived, OtherDerived>(derived(), other.derived());
+}
+
+/** replaces \c *this by \c *this + \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
+{
+  return *this = *this + other;
+}
+
+/** \returns an expression of the Schur product (coefficient wise product) of *this and \a other
+  *
+  * Example: \include Cwise_product.cpp
+  * Output: \verbinclude Cwise_product.out
+  *
+  * \sa class CwiseBinaryOp, operator/(), square()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE
+Cwise<ExpressionType>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_PRODUCT_RETURN_TYPE(_expression(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise quotient of *this and \a other
+  *
+  * Example: \include Cwise_quotient.cpp
+  * Output: \verbinclude Cwise_quotient.out
+  *
+  * \sa class CwiseBinaryOp, operator*(), inverse()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_quotient_op)
+Cwise<ExpressionType>::operator/(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_quotient_op)(_expression(), other.derived());
+}
+
+/** Replaces this expression by its coefficient-wise product with \a other.
+  *
+  * Example: \include Cwise_times_equal.cpp
+  * Output: \verbinclude Cwise_times_equal.out
+  *
+  * \sa operator*(), operator/=()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline ExpressionType& Cwise<ExpressionType>::operator*=(const MatrixBase<OtherDerived> &other)
+{
+  return m_matrix.const_cast_derived() = *this * other;
+}
+
+/** Replaces this expression by its coefficient-wise quotient by \a other.
+  *
+  * Example: \include Cwise_slash_equal.cpp
+  * Output: \verbinclude Cwise_slash_equal.out
+  *
+  * \sa operator/(), operator*=()
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+inline ExpressionType& Cwise<ExpressionType>::operator/=(const MatrixBase<OtherDerived> &other)
+{
+  return m_matrix.const_cast_derived() = *this / other;
+}
+
+/** \returns an expression of the coefficient-wise min of *this and \a other
+  *
+  * Example: \include Cwise_min.cpp
+  * Output: \verbinclude Cwise_min.out
+  *
+  * \sa class CwiseBinaryOp
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_min_op)
+Cwise<ExpressionType>::min(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_min_op)(_expression(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise max of *this and \a other
+  *
+  * Example: \include Cwise_max.cpp
+  * Output: \verbinclude Cwise_max.out
+  *
+  * \sa class CwiseBinaryOp
+  */
+template<typename ExpressionType>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_max_op)
+Cwise<ExpressionType>::max(const MatrixBase<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINOP_RETURN_TYPE(ei_scalar_max_op)(_expression(), other.derived());
+}
+
+/** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
+  *
+  * The template parameter \a CustomBinaryOp is the type of the functor
+  * of the custom operator (see class CwiseBinaryOp for an example)
+  *
+  * \addexample CustomCwiseBinaryFunctors \label How to use custom coeff wise binary functors
+  *
+  * Here is an example illustrating the use of custom functors:
+  * \include class_CwiseBinaryOp.cpp
+  * Output: \verbinclude class_CwiseBinaryOp.out
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator+, MatrixBase::operator-, Cwise::operator*, Cwise::operator/
+  */
+template<typename Derived>
+template<typename CustomBinaryOp, typename OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>
+MatrixBase<Derived>::binaryExpr(const MatrixBase<OtherDerived> &other, const CustomBinaryOp& func) const
+{
+  return CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>(derived(), other.derived(), func);
+}
+
+#endif // EIGEN_CWISE_BINARY_OP_H

Eigen/src/Core/CwiseNullaryOp.h

@@ -0,0 +1,763 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_NULLARY_OP_H
+#define EIGEN_CWISE_NULLARY_OP_H
+
+/** \class CwiseNullaryOp
+  *
+  * \brief Generic expression of a matrix where all coefficients are defined by a functor
+  *
+  * \param NullaryOp template functor implementing the operator
+  *
+  * This class represents an expression of a generic nullary operator.
+  * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() functions,
+  * and most of the time this is the only way it is used.
+  *
+  * However, if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * \sa class CwiseUnaryOp, class CwiseBinaryOp, MatrixBase::NullaryExpr()
+  */
+template<typename NullaryOp, typename MatrixType>
+struct ei_traits<CwiseNullaryOp<NullaryOp, MatrixType> > : ei_traits<MatrixType>
+{
+  enum {
+    Flags = (ei_traits<MatrixType>::Flags
+      & (  HereditaryBits
+         | (ei_functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
+         | (ei_functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
+      | (ei_functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
+    CoeffReadCost = ei_functor_traits<NullaryOp>::Cost
+  };
+};
+
+template<typename NullaryOp, typename MatrixType>
+class CwiseNullaryOp : ei_no_assignment_operator,
+  public MatrixBase<CwiseNullaryOp<NullaryOp, MatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseNullaryOp)
+
+    CwiseNullaryOp(int rows, int cols, const NullaryOp& func = NullaryOp())
+      : m_rows(rows), m_cols(cols), m_functor(func)
+    {
+      ei_assert(rows > 0
+          && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+          && cols > 0
+          && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+    }
+
+    EIGEN_STRONG_INLINE int rows() const { return m_rows.value(); }
+    EIGEN_STRONG_INLINE int cols() const { return m_cols.value(); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int rows, int cols) const
+    {
+      return m_functor(rows, cols);
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int, int) const
+    {
+      return m_functor.packetOp();
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int index) const
+    {
+      if(RowsAtCompileTime == 1)
+        return m_functor(0, index);
+      else
+        return m_functor(index, 0);
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int) const
+    {
+      return m_functor.packetOp();
+    }
+
+  protected:
+    const ei_int_if_dynamic<RowsAtCompileTime> m_rows;
+    const ei_int_if_dynamic<ColsAtCompileTime> m_cols;
+    const NullaryOp m_functor;
+};
+
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::NullaryExpr(int rows, int cols, const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(rows, cols, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::NullaryExpr(int size, const CustomNullaryOp& func)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  ei_assert(IsVectorAtCompileTime);
+  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, Derived>(1, size, func);
+  else return CwiseNullaryOp<CustomNullaryOp, Derived>(size, 1, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(RowsAtCompileTime, ColsAtCompileTime, func);
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Constant(int rows, int cols, const Scalar& value)
+{
+  return NullaryExpr(rows, cols, ei_scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Constant(int size, const Scalar& value)
+{
+  return NullaryExpr(size, ei_scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor.
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Constant(const Scalar& value)
+{
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_constant_op<Scalar>(value));
+}
+
+/** \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+bool MatrixBase<Derived>::isApproxToConstant
+(const Scalar& value, RealScalar prec) const
+{
+  for(int j = 0; j < cols(); ++j)
+    for(int i = 0; i < rows(); ++i)
+      if(!ei_isApprox(coeff(i, j), value, prec))
+        return false;
+  return true;
+}
+
+/** This is just an alias for isApproxToConstant().
+  *
+  * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+bool MatrixBase<Derived>::isConstant
+(const Scalar& value, RealScalar prec) const
+{
+  return isApproxToConstant(value, prec);
+}
+
+/** Alias for setConstant(): sets all coefficients in this expression to \a value.
+  *
+  * \sa setConstant(), Constant(), class CwiseNullaryOp
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE void MatrixBase<Derived>::fill(const Scalar& value)
+{
+  setConstant(value);
+}
+
+/** Sets all coefficients in this expression to \a value.
+  *
+  * \sa fill(), setConstant(int,const Scalar&), setConstant(int,int,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setConstant(const Scalar& value)
+{
+  return derived() = Constant(rows(), cols(), value);
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to the given \a value.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_set_int.cpp
+  * Output: \verbinclude Matrix_setConstant_int.out
+  *
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(int,int,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setConstant(int size, const Scalar& value)
+{
+  resize(size);
+  return setConstant(value);
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to the given \a value.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setConstant_int_int.cpp
+  * Output: \verbinclude Matrix_setConstant_int_int.out
+  *
+  * \sa MatrixBase::setConstant(const Scalar&), setConstant(int,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setConstant(int rows, int cols, const Scalar& value)
+{
+  resize(rows, cols);
+  return setConstant(value);
+}
+
+
+// zero:
+
+/** \returns an expression of a zero matrix.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+  * instead.
+  *
+  * \addexample Zero \label How to take get a zero matrix
+  *
+  * Example: \include MatrixBase_zero_int_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int_int.out
+  *
+  * \sa Zero(), Zero(int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Zero(int rows, int cols)
+{
+  return Constant(rows, cols, Scalar(0));
+}
+
+/** \returns an expression of a zero vector.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Zero() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_zero_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int.out
+  *
+  * \sa Zero(), Zero(int,int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Zero(int size)
+{
+  return Constant(size, Scalar(0));
+}
+
+/** \returns an expression of a fixed-size zero matrix or vector.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_zero.cpp
+  * Output: \verbinclude MatrixBase_zero.out
+  *
+  * \sa Zero(int), Zero(int,int)
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Zero()
+{
+  return Constant(Scalar(0));
+}
+
+/** \returns true if *this is approximately equal to the zero matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isZero.cpp
+  * Output: \verbinclude MatrixBase_isZero.out
+  *
+  * \sa class CwiseNullaryOp, Zero()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isZero(RealScalar prec) const
+{
+  for(int j = 0; j < cols(); ++j)
+    for(int i = 0; i < rows(); ++i)
+      if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
+        return false;
+  return true;
+}
+
+/** Sets all coefficients in this expression to zero.
+  *
+  * Example: \include MatrixBase_setZero.cpp
+  * Output: \verbinclude MatrixBase_setZero.out
+  *
+  * \sa class CwiseNullaryOp, Zero()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setZero()
+{
+  return setConstant(Scalar(0));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setZero_int.cpp
+  * Output: \verbinclude Matrix_setZero_int.out
+  *
+  * \sa MatrixBase::setZero(), setZero(int,int), class CwiseNullaryOp, MatrixBase::Zero()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setZero(int size)
+{
+  resize(size);
+  return setConstant(Scalar(0));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to zero.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setZero_int_int.cpp
+  * Output: \verbinclude Matrix_setZero_int_int.out
+  *
+  * \sa MatrixBase::setZero(), setZero(int), class CwiseNullaryOp, MatrixBase::Zero()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setZero(int rows, int cols)
+{
+  resize(rows, cols);
+  return setConstant(Scalar(0));
+}
+
+// ones:
+
+/** \returns an expression of a matrix where all coefficients equal one.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
+  * instead.
+  *
+  * \addexample One \label How to get a matrix with all coefficients equal one
+  *
+  * Example: \include MatrixBase_ones_int_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int_int.out
+  *
+  * \sa Ones(), Ones(int), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Ones(int rows, int cols)
+{
+  return Constant(rows, cols, Scalar(1));
+}
+
+/** \returns an expression of a vector where all coefficients equal one.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so Ones() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_ones_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int.out
+  *
+  * \sa Ones(), Ones(int,int), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Ones(int size)
+{
+  return Constant(size, Scalar(1));
+}
+
+/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_ones.cpp
+  * Output: \verbinclude MatrixBase_ones.out
+  *
+  * \sa Ones(int), Ones(int,int), isOnes(), class Ones
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ConstantReturnType
+MatrixBase<Derived>::Ones()
+{
+  return Constant(Scalar(1));
+}
+
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+  *          are equal to 1, within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOnes.cpp
+  * Output: \verbinclude MatrixBase_isOnes.out
+  *
+  * \sa class CwiseNullaryOp, Ones()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isOnes
+(RealScalar prec) const
+{
+  return isApproxToConstant(Scalar(1), prec);
+}
+
+/** Sets all coefficients in this expression to one.
+  *
+  * Example: \include MatrixBase_setOnes.cpp
+  * Output: \verbinclude MatrixBase_setOnes.out
+  *
+  * \sa class CwiseNullaryOp, Ones()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setOnes()
+{
+  return setConstant(Scalar(1));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to one.
+  *
+  * \only_for_vectors
+  *
+  * Example: \include Matrix_setOnes_int.cpp
+  * Output: \verbinclude Matrix_setOnes_int.out
+  *
+  * \sa MatrixBase::setOnes(), setOnes(int,int), class CwiseNullaryOp, MatrixBase::Ones()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setOnes(int size)
+{
+  resize(size);
+  return setConstant(Scalar(1));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to one.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setOnes_int_int.cpp
+  * Output: \verbinclude Matrix_setOnes_int_int.out
+  *
+  * \sa MatrixBase::setOnes(), setOnes(int), class CwiseNullaryOp, MatrixBase::Ones()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setOnes(int rows, int cols)
+{
+  resize(rows, cols);
+  return setConstant(Scalar(1));
+}
+
+// Identity:
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
+  * instead.
+  *
+  * \addexample Identity \label How to get an identity matrix
+  *
+  * Example: \include MatrixBase_identity_int_int.cpp
+  * Output: \verbinclude MatrixBase_identity_int_int.out
+  *
+  * \sa Identity(), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity(int rows, int cols)
+{
+  return NullaryExpr(rows, cols, ei_scalar_identity_op<Scalar>());
+}
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variant taking size arguments.
+  *
+  * Example: \include MatrixBase_identity.cpp
+  * Output: \verbinclude MatrixBase_identity.out
+  *
+  * \sa Identity(int,int), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity()
+{
+  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_identity_op<Scalar>());
+}
+
+/** \returns true if *this is approximately equal to the identity matrix
+  *          (not necessarily square),
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isIdentity.cpp
+  * Output: \verbinclude MatrixBase_isIdentity.out
+  *
+  * \sa class CwiseNullaryOp, Identity(), Identity(int,int), setIdentity()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isIdentity
+(RealScalar prec) const
+{
+  for(int j = 0; j < cols(); ++j)
+  {
+    for(int i = 0; i < rows(); ++i)
+    {
+      if(i == j)
+      {
+        if(!ei_isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
+          return false;
+      }
+      else
+      {
+        if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<RealScalar>(1), prec))
+          return false;
+      }
+    }
+  }
+  return true;
+}
+
+template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
+struct ei_setIdentity_impl
+{
+  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+  {
+    return m = Derived::Identity(m.rows(), m.cols());
+  }
+};
+
+template<typename Derived>
+struct ei_setIdentity_impl<Derived, true>
+{
+  static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+  {
+    m.setZero();
+    const int size = std::min(m.rows(), m.cols());
+    for(int i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
+    return m;
+  }
+};
+
+/** Writes the identity expression (not necessarily square) into *this.
+  *
+  * Example: \include MatrixBase_setIdentity.cpp
+  * Output: \verbinclude MatrixBase_setIdentity.out
+  *
+  * \sa class CwiseNullaryOp, Identity(), Identity(int,int), isIdentity()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
+{
+  return ei_setIdentity_impl<Derived>::run(derived());
+}
+
+/** Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
+  *
+  * \param rows the new number of rows
+  * \param cols the new number of columns
+  *
+  * Example: \include Matrix_setIdentity_int_int.cpp
+  * Output: \verbinclude Matrix_setIdentity_int_int.out
+  *
+  * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+EIGEN_STRONG_INLINE Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::setIdentity(int rows, int cols)
+{
+  resize(rows, cols);
+  return setIdentity();
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(int size, int i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return BasisReturnType(SquareMatrixType::Identity(size,size), i);
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * This variant is for fixed-size vector only.
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(int i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return BasisReturnType(SquareMatrixType::Identity(),i);
+}
+
+/** \returns an expression of the X axis unit vector (1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
+{ return Derived::Unit(0); }
+
+/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
+{ return Derived::Unit(1); }
+
+/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
+{ return Derived::Unit(2); }
+
+/** \returns an expression of the W axis unit vector (0,0,0,1)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
+{ return Derived::Unit(3); }
+
+#endif // EIGEN_CWISE_NULLARY_OP_H

Eigen/src/Core/CwiseUnaryOp.h

@@ -0,0 +1,233 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_UNARY_OP_H
+#define EIGEN_CWISE_UNARY_OP_H
+
+/** \class CwiseUnaryOp
+  *
+  * \brief Generic expression of a coefficient-wise unary operator of a matrix or a vector
+  *
+  * \param UnaryOp template functor implementing the operator
+  * \param MatrixType the type of the matrix we are applying the unary operator
+  *
+  * This class represents an expression of a generic unary operator of a matrix or a vector.
+  * It is the return type of the unary operator-, of a matrix or a vector, and most
+  * of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
+  */
+template<typename UnaryOp, typename MatrixType>
+struct ei_traits<CwiseUnaryOp<UnaryOp, MatrixType> >
+ : ei_traits<MatrixType>
+{
+  typedef typename ei_result_of<
+                     UnaryOp(typename MatrixType::Scalar)
+                   >::type Scalar;
+  typedef typename MatrixType::Nested MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    Flags = (_MatrixTypeNested::Flags & (
+      HereditaryBits | LinearAccessBit | AlignedBit
+      | (ei_functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0))),
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost + ei_functor_traits<UnaryOp>::Cost
+  };
+};
+
+template<typename UnaryOp, typename MatrixType>
+class CwiseUnaryOp : ei_no_assignment_operator,
+  public MatrixBase<CwiseUnaryOp<UnaryOp, MatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
+
+    inline CwiseUnaryOp(const MatrixType& mat, const UnaryOp& func = UnaryOp())
+      : m_matrix(mat), m_functor(func) {}
+
+    EIGEN_STRONG_INLINE int rows() const { return m_matrix.rows(); }
+    EIGEN_STRONG_INLINE int cols() const { return m_matrix.cols(); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int row, int col) const
+    {
+      return m_functor(m_matrix.coeff(row, col));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int row, int col) const
+    {
+      return m_functor.packetOp(m_matrix.template packet<LoadMode>(row, col));
+    }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int index) const
+    {
+      return m_functor(m_matrix.coeff(index));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int index) const
+    {
+      return m_functor.packetOp(m_matrix.template packet<LoadMode>(index));
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+    const UnaryOp m_functor;
+};
+
+/** \returns an expression of a custom coefficient-wise unary operator \a func of *this
+  *
+  * The template parameter \a CustomUnaryOp is the type of the functor
+  * of the custom unary operator.
+  *
+  * \addexample CustomCwiseUnaryFunctors \label How to use custom coeff wise unary functors
+  *
+  * Example:
+  * \include class_CwiseUnaryOp.cpp
+  * Output: \verbinclude class_CwiseUnaryOp.out
+  *
+  * \sa class CwiseUnaryOp, class CwiseBinarOp, MatrixBase::operator-, Cwise::abs
+  */
+template<typename Derived>
+template<typename CustomUnaryOp>
+EIGEN_STRONG_INLINE const CwiseUnaryOp<CustomUnaryOp, Derived>
+MatrixBase<Derived>::unaryExpr(const CustomUnaryOp& func) const
+{
+  return CwiseUnaryOp<CustomUnaryOp, Derived>(derived(), func);
+}
+
+/** \returns an expression of the opposite of \c *this
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE const CwiseUnaryOp<ei_scalar_opposite_op<typename ei_traits<Derived>::Scalar>,Derived>
+MatrixBase<Derived>::operator-() const
+{
+  return derived();
+}
+
+/** \returns an expression of the coefficient-wise absolute value of \c *this
+  *
+  * Example: \include Cwise_abs.cpp
+  * Output: \verbinclude Cwise_abs.out
+  *
+  * \sa abs2()
+  */
+template<typename ExpressionType>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_abs_op)
+Cwise<ExpressionType>::abs() const
+{
+  return _expression();
+}
+
+/** \returns an expression of the coefficient-wise squared absolute value of \c *this
+  *
+  * Example: \include Cwise_abs2.cpp
+  * Output: \verbinclude Cwise_abs2.out
+  *
+  * \sa abs(), square()
+  */
+template<typename ExpressionType>
+EIGEN_STRONG_INLINE const EIGEN_CWISE_UNOP_RETURN_TYPE(ei_scalar_abs2_op)
+Cwise<ExpressionType>::abs2() const
+{
+  return _expression();
+}
+
+/** \returns an expression of the complex conjugate of \c *this.
+  *
+  * \sa adjoint() */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename MatrixBase<Derived>::ConjugateReturnType
+MatrixBase<Derived>::conjugate() const
+{
+  return ConjugateReturnType(derived());
+}
+
+/** \returns an expression of the real part of \c *this.
+  *
+  * \sa imag() */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::RealReturnType
+MatrixBase<Derived>::real() const { return derived(); }
+
+/** \returns an expression of the imaginary part of \c *this.
+  *
+  * \sa real() */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ImagReturnType
+MatrixBase<Derived>::imag() const { return derived(); }
+
+/** \returns an expression of *this with the \a Scalar type casted to
+  * \a NewScalar.
+  *
+  * The template parameter \a NewScalar is the type we are casting the scalars to.
+  *
+  * \sa class CwiseUnaryOp
+  */
+template<typename Derived>
+template<typename NewType>
+EIGEN_STRONG_INLINE
+typename ei_cast_return_type<
+            Derived,
+            const CwiseUnaryOp<ei_scalar_cast_op<typename ei_traits<Derived>::Scalar, NewType>, Derived>
+          >::type
+MatrixBase<Derived>::cast() const
+{
+  return derived();
+}
+
+/** \relates MatrixBase */
+template<typename Derived>
+EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::ScalarMultipleReturnType
+MatrixBase<Derived>::operator*(const Scalar& scalar) const
+{
+  return CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, Derived>
+    (derived(), ei_scalar_multiple_op<Scalar>(scalar));
+}
+
+/** \relates MatrixBase */
+template<typename Derived>
+EIGEN_STRONG_INLINE const CwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::operator/(const Scalar& scalar) const
+{
+  return CwiseUnaryOp<ei_scalar_quotient1_op<Scalar>, Derived>
+    (derived(), ei_scalar_quotient1_op<Scalar>(scalar));
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+MatrixBase<Derived>::operator*=(const Scalar& other)
+{
+  return *this = *this * other;
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+MatrixBase<Derived>::operator/=(const Scalar& other)
+{
+  return *this = *this / other;
+}
+
+#endif // EIGEN_CWISE_UNARY_OP_H

Eigen/src/Core/Diagonal.h

@@ -0,0 +1,187 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONAL_H
+#define EIGEN_DIAGONAL_H
+
+/** \class Diagonal
+  *
+  * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
+  *
+  * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
+  * \param Index the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
+  *              A positive value means a superdiagonal, a negative value means a subdiagonal.
+  *              You can also use Dynamic so the index can be set at runtime.
+  *
+  * The matrix is not required to be square.
+  *
+  * This class represents an expression of the main diagonal, or any sub/super diagonal
+  * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(int) and most of the
+  * time this is the only way it is used.
+  *
+  * \sa MatrixBase::diagonal(), MatrixBase::diagonal(int)
+  */
+template<typename MatrixType, int Index>
+struct ei_traits<Diagonal<MatrixType,Index> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    AbsIndex = Index<0 ? -Index : Index, // only used if Index != Dynamic
+    RowsAtCompileTime = (int(Index) == Dynamic || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
+                      : (EIGEN_ENUM_MIN(MatrixType::RowsAtCompileTime,
+                                        MatrixType::ColsAtCompileTime) - AbsIndex),
+    ColsAtCompileTime = 1,
+    MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
+                         : (EIGEN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime,
+                                          MatrixType::MaxColsAtCompileTime) - AbsIndex),
+    MaxColsAtCompileTime = 1,
+    Flags = (unsigned int)_MatrixTypeNested::Flags & (HereditaryBits | LinearAccessBit),
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType, int Index> class Diagonal
+   : public MatrixBase<Diagonal<MatrixType, Index> >
+{
+    // some compilers may fail to optimize std::max etc in case of compile-time constants...
+    EIGEN_STRONG_INLINE int absIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
+    EIGEN_STRONG_INLINE int rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
+    EIGEN_STRONG_INLINE int colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
+    
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Diagonal)
+
+    inline Diagonal(const MatrixType& matrix, int index = Index) : m_matrix(matrix), m_index(index) {}
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
+
+    inline int rows() const{ return m_matrix.diagonalSize() - absIndex(); }
+    inline int cols() const { return 1; }
+
+    inline Scalar& coeffRef(int row, int)
+    {
+      return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+    }
+
+    inline const Scalar coeff(int row, int) const
+    {
+      return m_matrix.coeff(row+rowOffset(), row+colOffset());
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(index+rowOffset(), index+colOffset());
+    }
+
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(index+rowOffset(), index+colOffset());
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+    const ei_int_if_dynamic<Index> m_index;
+};
+
+/** \returns an expression of the main diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * Example: \include MatrixBase_diagonal.cpp
+  * Output: \verbinclude MatrixBase_diagonal.out
+  *
+  * \sa class Diagonal */
+template<typename Derived>
+inline Diagonal<Derived, 0>
+MatrixBase<Derived>::diagonal()
+{
+  return Diagonal<Derived, 0>(derived());
+}
+
+/** This is the const version of diagonal(). */
+template<typename Derived>
+inline const Diagonal<Derived, 0>
+MatrixBase<Derived>::diagonal() const
+{
+  return Diagonal<Derived, 0>(derived());
+}
+
+/** \returns an expression of the \a Index-th sub or super diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * The template parameter \a Index represent a super diagonal if \a Index > 0
+  * and a sub diagonal otherwise. \a Index == 0 is equivalent to the main diagonal.
+  *
+  * Example: \include MatrixBase_diagonal_int.cpp
+  * Output: \verbinclude MatrixBase_diagonal_int.out
+  *
+  * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+inline Diagonal<Derived, Dynamic>
+MatrixBase<Derived>::diagonal(int index)
+{
+  return Diagonal<Derived, Dynamic>(derived(), index);
+}
+
+/** This is the const version of diagonal(int). */
+template<typename Derived>
+inline const Diagonal<Derived, Dynamic>
+MatrixBase<Derived>::diagonal(int index) const
+{
+  return Diagonal<Derived, Dynamic>(derived(), index);
+}
+
+/** \returns an expression of the \a Index-th sub or super diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * The template parameter \a Index represent a super diagonal if \a Index > 0
+  * and a sub diagonal otherwise. \a Index == 0 is equivalent to the main diagonal.
+  *
+  * Example: \include MatrixBase_diagonal_template_int.cpp
+  * Output: \verbinclude MatrixBase_diagonal_template_int.out
+  *
+  * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+template<int Index>
+inline Diagonal<Derived,Index>
+MatrixBase<Derived>::diagonal()
+{
+  return Diagonal<Derived,Index>(derived());
+}
+
+/** This is the const version of diagonal<int>(). */
+template<typename Derived>
+template<int Index>
+inline const Diagonal<Derived,Index>
+MatrixBase<Derived>::diagonal() const
+{
+  return Diagonal<Derived,Index>(derived());
+}
+
+#endif // EIGEN_DIAGONAL_H

Eigen/src/Core/DiagonalMatrix.h

@@ -0,0 +1,319 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONALMATRIX_H
+#define EIGEN_DIAGONALMATRIX_H
+
+
+template<typename CoeffsVectorType, typename Derived>
+class DiagonalMatrixBase : ei_no_assignment_operator,
+   public MatrixBase<Derived>
+{
+  public:
+    typedef MatrixBase<Derived> Base;
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+    typedef typename Base::PacketScalar PacketScalar;
+    using Base::derived;
+    typedef typename ei_cleantype<CoeffsVectorType>::type _CoeffsVectorType;
+
+  protected:
+
+    // MSVC gets crazy if we define default parameters
+    template<typename OtherDerived, bool IsVector, bool IsDiagonal> struct construct_from_expression;
+
+    // = vector
+    template<typename OtherDerived>
+    struct construct_from_expression<OtherDerived,true,false>
+    {
+      static void run(Derived& dst, const OtherDerived& src)
+      { dst.diagonal() = src; }
+    };
+
+    // = diagonal expression
+    template<typename OtherDerived, bool IsVector>
+    struct construct_from_expression<OtherDerived,IsVector,true>
+    {
+      static void run(Derived& dst, const OtherDerived& src)
+      { dst.diagonal() = src.diagonal(); }
+    };
+
+    /** Default constructor without initialization */
+    inline DiagonalMatrixBase() {}
+    /** Constructs a diagonal matrix with given dimension */
+    inline DiagonalMatrixBase(int dim) : m_coeffs(dim) {}
+    /** Generic constructor from an expression */
+    template<typename OtherDerived>
+    inline DiagonalMatrixBase(const MatrixBase<OtherDerived>& other)
+    {
+      construct_from_expression<OtherDerived,OtherDerived::IsVectorAtCompileTime,ei_is_diagonal<OtherDerived>::ret>
+        ::run(derived(),other.derived());
+    }
+    
+    template<typename NewType,int dummy=0>
+    struct cast_selector {
+      typedef const DiagonalMatrixWrapper<NestByValue<CwiseUnaryOp<ei_scalar_cast_op<Scalar, NewType>, _CoeffsVectorType> > > return_type;
+      inline static return_type run(const DiagonalMatrixBase& d) {
+        return d.m_coeffs.template cast<NewType>().nestByValue().asDiagonal();
+      }
+    };
+    
+    template<int dummy>
+    struct cast_selector<Scalar,dummy> {
+      typedef const Derived& return_type;
+      inline static return_type run(const DiagonalMatrixBase& d) {
+        return d.derived();
+      }
+    };
+
+  public:
+
+    inline DiagonalMatrixBase(const _CoeffsVectorType& coeffs) : m_coeffs(coeffs)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(_CoeffsVectorType);
+      ei_assert(coeffs.size() > 0);
+    }
+
+    template<typename NewType>
+    inline typename cast_selector<NewType,0>::return_type
+    cast() const
+    {
+      return cast_selector<NewType,0>::run(*this);
+    }
+
+    /** Assignment operator.
+      * The right-hand-side \a other must be either a vector representing the diagonal
+      * coefficients or a diagonal matrix expression.
+      */
+    template<typename OtherDerived>
+    inline Derived& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      construct_from_expression<OtherDerived,OtherDerived::IsVectorAtCompileTime,ei_is_diagonal<OtherDerived>::ret>
+        ::run(derived(),other);
+      return derived();
+    }
+
+    inline int rows() const { return m_coeffs.size(); }
+    inline int cols() const { return m_coeffs.size(); }
+
+    inline const Scalar coeff(int row, int col) const
+    {
+      return row == col ? m_coeffs.coeff(row) : static_cast<Scalar>(0);
+    }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      ei_assert(row==col);
+      return m_coeffs.coeffRef(row);
+    }
+
+    inline _CoeffsVectorType& diagonal() { return m_coeffs; }
+    inline const _CoeffsVectorType& diagonal() const { return m_coeffs; }
+
+  protected:
+    CoeffsVectorType m_coeffs;
+};
+
+/** \class DiagonalMatrix
+  * \nonstableyet
+  *
+  * \brief Represent a diagonal matrix with its storage
+  *
+  * \param _Scalar the type of coefficients
+  * \param _Size the dimension of the matrix
+  *
+  * \sa class Matrix
+  */
+template<typename _Scalar,int _Size>
+struct ei_traits<DiagonalMatrix<_Scalar,_Size> > : ei_traits<Matrix<_Scalar,_Size,_Size> >
+{
+  enum {
+    Flags = (ei_traits<Matrix<_Scalar,_Size,_Size> >::Flags & HereditaryBits) | DiagonalBits
+  };
+};
+
+template<typename _Scalar, int _Size>
+class DiagonalMatrix
+  : public DiagonalMatrixBase<Matrix<_Scalar,_Size,1>, DiagonalMatrix<_Scalar,_Size> >
+{
+  public:
+    EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalMatrix)
+    typedef DiagonalMatrixBase<Matrix<_Scalar,_Size,1>, DiagonalMatrix<_Scalar,_Size> > DiagonalBase;
+
+  protected:
+    typedef Matrix<_Scalar,_Size,1> CoeffVectorType;
+    using DiagonalBase::m_coeffs;
+
+  public:
+
+    /** Default constructor without initialization */
+    inline DiagonalMatrix() : DiagonalBase()
+    {}
+
+    /** Constructs a diagonal matrix with given dimension  */
+    inline DiagonalMatrix(int dim) : DiagonalBase(dim)
+    {}
+
+    /** 2D only */
+    inline DiagonalMatrix(const Scalar& sx, const Scalar& sy)
+    {
+      EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(DiagonalMatrix,2,2);
+      m_coeffs.x() = sx;
+      m_coeffs.y() = sy;
+    }
+    /** 3D only */
+    inline DiagonalMatrix(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+    {
+      EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(DiagonalMatrix,3,3);
+      m_coeffs.x() = sx;
+      m_coeffs.y() = sy;
+      m_coeffs.z() = sz;
+    }
+
+    /** copy constructor */
+    inline DiagonalMatrix(const DiagonalMatrix& other) : DiagonalBase(other.m_coeffs)
+    {}
+
+    /** generic constructor from expression */
+    template<typename OtherDerived>
+    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : DiagonalBase(other)
+    {}
+
+    DiagonalMatrix& operator=(const DiagonalMatrix& other)
+    {
+      m_coeffs = other.m_coeffs;
+      return *this;
+    }
+
+    template<typename OtherDerived>
+    DiagonalMatrix& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      EIGEN_STATIC_ASSERT(ei_is_diagonal<OtherDerived>::ret, THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX);
+      m_coeffs = other.diagonal();
+      return *this;
+    }
+    
+    inline void resize(int size)
+    {
+      m_coeffs.resize(size);
+    }
+    
+    inline void resize(int rows, int cols)
+    {
+      ei_assert(rows==cols && "a diagonal matrix must be square");
+      m_coeffs.resize(rows);
+    }
+    
+    inline void setZero() { m_coeffs.setZero(); }
+};
+
+/** \class DiagonalMatrixWrapper
+  * \nonstableyet
+  *
+  * \brief Expression of a diagonal matrix
+  *
+  * \param CoeffsVectorType the type of the vector of diagonal coefficients
+  *
+  * This class is an expression of a diagonal matrix with given vector of diagonal
+  * coefficients. It is the return type of MatrixBase::diagonal(const OtherDerived&)
+  * and most of the time this is the only way it is used.
+  *
+  * \sa class DiagonalMatrixBase, class DiagonalMatrix, MatrixBase::asDiagonal()
+  */
+template<typename CoeffsVectorType>
+struct ei_traits<DiagonalMatrixWrapper<CoeffsVectorType> >
+{
+  typedef typename CoeffsVectorType::Scalar Scalar;
+  typedef typename ei_nested<CoeffsVectorType>::type CoeffsVectorTypeNested;
+  typedef typename ei_unref<CoeffsVectorTypeNested>::type _CoeffsVectorTypeNested;
+  enum {
+    RowsAtCompileTime = CoeffsVectorType::SizeAtCompileTime,
+    ColsAtCompileTime = CoeffsVectorType::SizeAtCompileTime,
+    MaxRowsAtCompileTime = CoeffsVectorType::MaxSizeAtCompileTime,
+    MaxColsAtCompileTime = CoeffsVectorType::MaxSizeAtCompileTime,
+    Flags = (_CoeffsVectorTypeNested::Flags & HereditaryBits) | DiagonalBits,
+    CoeffReadCost = _CoeffsVectorTypeNested::CoeffReadCost
+  };
+};
+template<typename CoeffsVectorType>
+class DiagonalMatrixWrapper
+  : public DiagonalMatrixBase<typename CoeffsVectorType::Nested, DiagonalMatrixWrapper<CoeffsVectorType> >
+{
+    typedef typename CoeffsVectorType::Nested CoeffsVectorTypeNested;
+    typedef DiagonalMatrixBase<CoeffsVectorTypeNested, DiagonalMatrixWrapper<CoeffsVectorType> > DiagonalBase;
+  public:
+    EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalMatrixWrapper)
+    inline DiagonalMatrixWrapper(const CoeffsVectorType& coeffs) : DiagonalBase(coeffs)
+    {}
+};
+
+/** \nonstableyet
+  * \returns an expression of a diagonal matrix with *this as vector of diagonal coefficients
+  *
+  * \only_for_vectors
+  *
+  * \addexample AsDiagonalExample \label How to build a diagonal matrix from a vector
+  *
+  * Example: \include MatrixBase_asDiagonal.cpp
+  * Output: \verbinclude MatrixBase_asDiagonal.out
+  *
+  * \sa class DiagonalMatrix, isDiagonal()
+  **/
+template<typename Derived>
+inline const DiagonalMatrixWrapper<Derived>
+MatrixBase<Derived>::asDiagonal() const
+{
+  return derived();
+}
+
+/** \nonstableyet
+  * \returns true if *this is approximately equal to a diagonal matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isDiagonal.cpp
+  * Output: \verbinclude MatrixBase_isDiagonal.out
+  *
+  * \sa asDiagonal()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isDiagonal
+(RealScalar prec) const
+{
+  if(cols() != rows()) return false;
+  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
+  for(int j = 0; j < cols(); ++j)
+  {
+    RealScalar absOnDiagonal = ei_abs(coeff(j,j));
+    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
+  }
+  for(int j = 0; j < cols(); ++j)
+    for(int i = 0; i < j; ++i)
+    {
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+      if(!ei_isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+    }
+  return true;
+}
+
+#endif // EIGEN_DIAGONALMATRIX_H

Eigen/src/Core/DiagonalProduct.h

@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DIAGONALPRODUCT_H
+#define EIGEN_DIAGONALPRODUCT_H
+
+/** \internal Specialization of ei_nested for DiagonalMatrix.
+ *  Unlike ei_nested, if the argument is a DiagonalMatrix and if it must be evaluated,
+ *  then it evaluated to a DiagonalMatrix having its own argument evaluated.
+ */
+template<typename T, int N, bool IsDiagonal = ei_is_diagonal<T>::ret> struct ei_nested_diagonal : ei_nested<T,N> {};
+template<typename T, int N> struct ei_nested_diagonal<T,N,true>
+ : ei_nested<T, N, DiagonalMatrix<typename T::Scalar, EIGEN_ENUM_MIN(T::RowsAtCompileTime,T::ColsAtCompileTime)> >
+{};
+
+// specialization of ProductReturnType
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,DiagonalProduct>
+{
+  typedef typename ei_nested_diagonal<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+  typedef typename ei_nested_diagonal<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+
+  typedef Product<LhsNested, RhsNested, DiagonalProduct> Type;
+};
+
+template<typename LhsNested, typename RhsNested>
+struct ei_traits<Product<LhsNested, RhsNested, DiagonalProduct> >
+{
+  // clean the nested types:
+  typedef typename ei_cleantype<LhsNested>::type _LhsNested;
+  typedef typename ei_cleantype<RhsNested>::type _RhsNested;
+  typedef typename _LhsNested::Scalar Scalar;
+
+  enum {
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+    RowsAtCompileTime = _LhsNested::RowsAtCompileTime,
+    ColsAtCompileTime = _RhsNested::ColsAtCompileTime,
+    MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,
+
+    LhsIsDiagonal = ei_is_diagonal<_LhsNested>::ret,
+    RhsIsDiagonal = ei_is_diagonal<_RhsNested>::ret,
+
+    CanVectorizeRhs =  (!RhsIsDiagonal) && (RhsFlags & RowMajorBit) && (RhsFlags & PacketAccessBit)
+                     && (ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+
+    CanVectorizeLhs =  (!LhsIsDiagonal) && (!(LhsFlags & RowMajorBit)) && (LhsFlags & PacketAccessBit)
+                     && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+
+    RemovedBits = ~((RhsFlags & RowMajorBit) && (!CanVectorizeLhs) ? 0 : RowMajorBit),
+
+    Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
+          | (((CanVectorizeLhs&&RhsIsDiagonal) || (CanVectorizeRhs&&LhsIsDiagonal)) ? PacketAccessBit : 0),
+
+    CoeffReadCost = NumTraits<Scalar>::MulCost + _LhsNested::CoeffReadCost + _RhsNested::CoeffReadCost
+  };
+};
+
+template<typename LhsNested, typename RhsNested> class Product<LhsNested, RhsNested, DiagonalProduct> : ei_no_assignment_operator,
+  public MatrixBase<Product<LhsNested, RhsNested, DiagonalProduct> >
+{
+    typedef typename ei_traits<Product>::_LhsNested _LhsNested;
+    typedef typename ei_traits<Product>::_RhsNested _RhsNested;
+
+    enum {
+      RhsIsDiagonal = ei_is_diagonal<_RhsNested>::ret
+    };
+
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+
+    template<typename Lhs, typename Rhs>
+    inline Product(const Lhs& lhs, const Rhs& rhs)
+      : m_lhs(lhs), m_rhs(rhs)
+    {
+      ei_assert(lhs.cols() == rhs.rows());
+    }
+
+    inline int rows() const { return m_lhs.rows(); }
+    inline int cols() const { return m_rhs.cols(); }
+
+    const Scalar coeff(int row, int col) const
+    {
+      const int unique = RhsIsDiagonal ? col : row;
+      return m_lhs.coeff(row, unique) * m_rhs.coeff(unique, col);
+    }
+
+    template<int LoadMode>
+    const PacketScalar packet(int row, int col) const
+    {
+      if (RhsIsDiagonal)
+      {
+        return ei_pmul(m_lhs.template packet<LoadMode>(row, col), ei_pset1(m_rhs.coeff(col, col)));
+      }
+      else
+      {
+        return ei_pmul(ei_pset1(m_lhs.coeff(row, row)), m_rhs.template packet<LoadMode>(row, col));
+      }
+    }
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+};
+
+#endif // EIGEN_DIAGONALPRODUCT_H

Eigen/src/Core/Dot.h

@@ -0,0 +1,376 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_DOT_H
+#define EIGEN_DOT_H
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Derived1, typename Derived2>
+struct ei_dot_traits
+{
+public:
+  enum {
+    Vectorization = (int(Derived1::Flags)&int(Derived2::Flags)&ActualPacketAccessBit)
+                 && (int(Derived1::Flags)&int(Derived2::Flags)&LinearAccessBit)
+                  ? LinearVectorization
+                  : NoVectorization
+  };
+
+private:
+  typedef typename Derived1::Scalar Scalar;
+  enum {
+    PacketSize = ei_packet_traits<Scalar>::size,
+    Cost = Derived1::SizeAtCompileTime * (Derived1::CoeffReadCost + Derived2::CoeffReadCost + NumTraits<Scalar>::MulCost)
+           + (Derived1::SizeAtCompileTime-1) * NumTraits<Scalar>::AddCost,
+    UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Vectorization) == int(NoVectorization) ? 1 : int(PacketSize))
+  };
+
+public:
+  enum {
+    Unrolling = Cost <= UnrollingLimit
+              ? CompleteUnrolling
+              : NoUnrolling
+  };
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Derived1, typename Derived2, int Start, int Length>
+struct ei_dot_novec_unroller
+{
+  enum {
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived1::Scalar Scalar;
+
+  inline static Scalar run(const Derived1& v1, const Derived2& v2)
+  {
+    return ei_dot_novec_unroller<Derived1, Derived2, Start, HalfLength>::run(v1, v2)
+         + ei_dot_novec_unroller<Derived1, Derived2, Start+HalfLength, Length-HalfLength>::run(v1, v2);
+  }
+};
+
+template<typename Derived1, typename Derived2, int Start>
+struct ei_dot_novec_unroller<Derived1, Derived2, Start, 1>
+{
+  typedef typename Derived1::Scalar Scalar;
+
+  inline static Scalar run(const Derived1& v1, const Derived2& v2)
+  {
+    return v1.coeff(Start) * ei_conj(v2.coeff(Start));
+  }
+};
+
+/*** vectorization ***/
+
+template<typename Derived1, typename Derived2, int Index, int Stop,
+         bool LastPacket = (Stop-Index == ei_packet_traits<typename Derived1::Scalar>::size)>
+struct ei_dot_vec_unroller
+{
+  typedef typename Derived1::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  enum {
+    row1 = Derived1::RowsAtCompileTime == 1 ? 0 : Index,
+    col1 = Derived1::RowsAtCompileTime == 1 ? Index : 0,
+    row2 = Derived2::RowsAtCompileTime == 1 ? 0 : Index,
+    col2 = Derived2::RowsAtCompileTime == 1 ? Index : 0
+  };
+
+  inline static PacketScalar run(const Derived1& v1, const Derived2& v2)
+  {
+    return ei_pmadd(
+      v1.template packet<Aligned>(row1, col1),
+      v2.template packet<Aligned>(row2, col2),
+      ei_dot_vec_unroller<Derived1, Derived2, Index+ei_packet_traits<Scalar>::size, Stop>::run(v1, v2)
+    );
+  }
+};
+
+template<typename Derived1, typename Derived2, int Index, int Stop>
+struct ei_dot_vec_unroller<Derived1, Derived2, Index, Stop, true>
+{
+  enum {
+    row1 = Derived1::RowsAtCompileTime == 1 ? 0 : Index,
+    col1 = Derived1::RowsAtCompileTime == 1 ? Index : 0,
+    row2 = Derived2::RowsAtCompileTime == 1 ? 0 : Index,
+    col2 = Derived2::RowsAtCompileTime == 1 ? Index : 0,
+    alignment1 = (Derived1::Flags & AlignedBit) ? Aligned : Unaligned,
+    alignment2 = (Derived2::Flags & AlignedBit) ? Aligned : Unaligned
+  };
+
+  typedef typename Derived1::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  inline static PacketScalar run(const Derived1& v1, const Derived2& v2)
+  {
+    return ei_pmul(v1.template packet<alignment1>(row1, col1), v2.template packet<alignment2>(row2, col2));
+  }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Derived1, typename Derived2,
+         int Vectorization = ei_dot_traits<Derived1, Derived2>::Vectorization,
+         int Unrolling = ei_dot_traits<Derived1, Derived2>::Unrolling
+>
+struct ei_dot_impl;
+
+template<typename Derived1, typename Derived2>
+struct ei_dot_impl<Derived1, Derived2, NoVectorization, NoUnrolling>
+{
+  typedef typename Derived1::Scalar Scalar;
+  static Scalar run(const Derived1& v1, const Derived2& v2)
+  {
+    ei_assert(v1.size()>0 && "you are using a non initialized vector");
+    Scalar res;
+    res = v1.coeff(0) * ei_conj(v2.coeff(0));
+    for(int i = 1; i < v1.size(); ++i)
+      res += v1.coeff(i) * ei_conj(v2.coeff(i));
+    return res;
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_dot_impl<Derived1, Derived2, NoVectorization, CompleteUnrolling>
+  : public ei_dot_novec_unroller<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
+{};
+
+template<typename Derived1, typename Derived2>
+struct ei_dot_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>
+{
+  typedef typename Derived1::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  static Scalar run(const Derived1& v1, const Derived2& v2)
+  {
+    const int size = v1.size();
+    const int packetSize = ei_packet_traits<Scalar>::size;
+    const int alignedSize = (size/packetSize)*packetSize;
+    enum {
+      alignment1 = (Derived1::Flags & AlignedBit) ? Aligned : Unaligned,
+      alignment2 = (Derived2::Flags & AlignedBit) ? Aligned : Unaligned
+    };
+    Scalar res;
+
+    // do the vectorizable part of the sum
+    if(size >= packetSize)
+    {
+      PacketScalar packet_res = ei_pmul(
+                                  v1.template packet<alignment1>(0),
+                                  v2.template packet<alignment2>(0)
+                                );
+      for(int index = packetSize; index<alignedSize; index += packetSize)
+      {
+        packet_res = ei_pmadd(
+                       v1.template packet<alignment1>(index),
+                       v2.template packet<alignment2>(index),
+                       packet_res
+                     );
+      }
+      res = ei_predux(packet_res);
+
+      // now we must do the rest without vectorization.
+      if(alignedSize == size) return res;
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = Scalar(0);
+    }
+
+    // do the remainder of the vector
+    for(int index = alignedSize; index < size; ++index)
+    {
+      res += v1.coeff(index) * v2.coeff(index);
+    }
+
+    return res;
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_dot_impl<Derived1, Derived2, LinearVectorization, CompleteUnrolling>
+{
+  typedef typename Derived1::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  enum {
+    PacketSize = ei_packet_traits<Scalar>::size,
+    Size = Derived1::SizeAtCompileTime,
+    VectorizationSize = (Size / PacketSize) * PacketSize
+  };
+  static Scalar run(const Derived1& v1, const Derived2& v2)
+  {
+    Scalar res = ei_predux(ei_dot_vec_unroller<Derived1, Derived2, 0, VectorizationSize>::run(v1, v2));
+    if (VectorizationSize != Size)
+      res += ei_dot_novec_unroller<Derived1, Derived2, VectorizationSize, Size-VectorizationSize>::run(v1, v2);
+    return res;
+  }
+};
+
+/***************************************************************************
+* Part 4 : implementation of MatrixBase methods
+***************************************************************************/
+
+/** \returns the dot product of *this with other.
+  *
+  * \only_for_vectors
+  *
+  * \note If the scalar type is complex numbers, then this function returns the hermitian
+  * (sesquilinear) dot product, linear in the first variable and conjugate-linear in the
+  * second variable.
+  *
+  * \sa squaredNorm(), norm()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+  EIGEN_STATIC_ASSERT((ei_is_same_type<Scalar, typename OtherDerived::Scalar>::ret),
+    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+  ei_assert(size() == other.size());
+
+  // dot() must honor EvalBeforeNestingBit (eg: v.dot(M*v) )
+  typedef typename ei_cleantype<typename Derived::Nested>::type ThisNested;
+  typedef typename ei_cleantype<typename OtherDerived::Nested>::type OtherNested;
+  return ei_dot_impl<ThisNested, OtherNested>::run(derived(), other.derived());
+}
+
+/** \returns the squared \em l2 norm of *this, i.e., for vectors, the dot product of *this with itself.
+  *
+  * \sa dot(), norm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename ei_traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
+{
+  return ei_real((*this).cwise().abs2().sum());
+}
+
+/** \returns the \em l2 norm of *this, i.e., for vectors, the square root of the dot product of *this with itself.
+  *
+  * \sa dot(), squaredNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename ei_traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
+{
+  return ei_sqrt(squaredNorm());
+}
+
+/** \returns the \em l2 norm of \c *this using a numerically more stable
+  * algorithm.
+  *
+  * \sa norm(), dot(), squaredNorm()
+  */
+template<typename Derived>
+inline typename NumTraits<typename ei_traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::stableNorm() const
+{
+  return this->cwise().abs().redux(ei_scalar_hypot_op<RealScalar>());
+}
+
+/** \returns an expression of the quotient of *this by its own norm.
+  *
+  * \only_for_vectors
+  *
+  * \sa norm(), normalize()
+  */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::PlainMatrixType
+MatrixBase<Derived>::normalized() const
+{
+  typedef typename ei_nested<Derived>::type Nested;
+  typedef typename ei_unref<Nested>::type _Nested;
+  _Nested n(derived());
+  return n / n.norm();
+}
+
+/** Normalizes the vector, i.e. divides it by its own norm.
+  *
+  * \only_for_vectors
+  *
+  * \sa norm(), normalized()
+  */
+template<typename Derived>
+inline void MatrixBase<Derived>::normalize()
+{
+  *this /= norm();
+}
+
+/** \returns true if *this is approximately orthogonal to \a other,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOrthogonal.cpp
+  * Output: \verbinclude MatrixBase_isOrthogonal.out
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isOrthogonal
+(const MatrixBase<OtherDerived>& other, RealScalar prec) const
+{
+  typename ei_nested<Derived,2>::type nested(derived());
+  typename ei_nested<OtherDerived,2>::type otherNested(other.derived());
+  return ei_abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
+}
+
+/** \returns true if *this is approximately an unitary matrix,
+  *          within the precision given by \a prec. In the case where the \a Scalar
+  *          type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
+  *
+  * \note This can be used to check whether a family of vectors forms an orthonormal basis.
+  *       Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
+  *       orthonormal basis.
+  *
+  * Example: \include MatrixBase_isUnitary.cpp
+  * Output: \verbinclude MatrixBase_isUnitary.out
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isUnitary(RealScalar prec) const
+{
+  typename Derived::Nested nested(derived());
+  for(int i = 0; i < cols(); ++i)
+  {
+    if(!ei_isApprox(nested.col(i).squaredNorm(), static_cast<Scalar>(1), prec))
+      return false;
+    for(int j = 0; j < i; ++j)
+      if(!ei_isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
+        return false;
+  }
+  return true;
+}
+#endif // EIGEN_DOT_H

Eigen/src/Core/Flagged.h

@@ -0,0 +1,146 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FLAGGED_H
+#define EIGEN_FLAGGED_H
+
+/** \class Flagged
+  *
+  * \brief Expression with modified flags
+  *
+  * \param ExpressionType the type of the object of which we are modifying the flags
+  * \param Added the flags added to the expression
+  * \param Removed the flags removed from the expression (has priority over Added).
+  *
+  * This class represents an expression whose flags have been modified.
+  * It is the return type of MatrixBase::flagged()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::flagged()
+  */
+template<typename ExpressionType, unsigned int Added, unsigned int Removed>
+struct ei_traits<Flagged<ExpressionType, Added, Removed> > : ei_traits<ExpressionType>
+{
+  enum { Flags = (ExpressionType::Flags | Added) & ~Removed };
+};
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged
+  : public MatrixBase<Flagged<ExpressionType, Added, Removed> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Flagged)
+    typedef typename ei_meta_if<ei_must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, const ExpressionType&>::ret ExpressionTypeNested;
+    typedef typename ExpressionType::InnerIterator InnerIterator;
+
+    inline Flagged(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+    inline int rows() const { return m_matrix.rows(); }
+    inline int cols() const { return m_matrix.cols(); }
+    inline int stride() const { return m_matrix.stride(); }
+
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const Scalar coeff(int index) const
+    {
+      return m_matrix.coeff(index);
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int row, int col) const
+    {
+      return m_matrix.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int index) const
+    {
+      return m_matrix.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+    const ExpressionType& _expression() const { return m_matrix; }
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \returns an expression of *this with added flags
+  *
+  * \addexample MarkExample \label How to mark a triangular matrix as triangular
+  *
+  * Example: \include MatrixBase_marked.cpp
+  * Output: \verbinclude MatrixBase_marked.out
+  *
+  * \sa class Flagged, extract(), part()
+  */
+template<typename Derived>
+template<unsigned int Added>
+inline const Flagged<Derived, Added, 0>
+MatrixBase<Derived>::marked() const
+{
+  return derived();
+}
+
+/** \returns an expression of *this with the following flags removed:
+  * EvalBeforeNestingBit and EvalBeforeAssigningBit.
+  *
+  * Example: \include MatrixBase_lazy.cpp
+  * Output: \verbinclude MatrixBase_lazy.out
+  *
+  * \sa class Flagged, marked()
+  */
+template<typename Derived>
+inline const Flagged<Derived, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>
+MatrixBase<Derived>::lazy() const
+{
+  return derived();
+}
+
+#endif // EIGEN_FLAGGED_H

Eigen/src/Core/Functors.h

@@ -0,0 +1,427 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FUNCTORS_H
+#define EIGEN_FUNCTORS_H
+
+// associative functors:
+
+/** \internal
+  * \brief Template functor to compute the sum of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator+, class PartialRedux, MatrixBase::sum()
+  */
+template<typename Scalar> struct ei_scalar_sum_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_padd(a,b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const Scalar predux(const PacketScalar& a) const
+  { return ei_predux(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_sum_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the product of two scalars
+  *
+  * \sa class CwiseBinaryOp, Cwise::operator*(), class PartialRedux, MatrixBase::redux()
+  */
+template<typename Scalar> struct ei_scalar_product_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a * b; }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_pmul(a,b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const Scalar predux(const PacketScalar& a) const
+  { return ei_predux_mul(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_product_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::MulCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the min of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class PartialRedux, MatrixBase::minCoeff()
+  */
+template<typename Scalar> struct ei_scalar_min_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return std::min(a, b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_pmin(a,b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const Scalar predux(const PacketScalar& a) const
+  { return ei_predux_min(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_min_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the max of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class PartialRedux, MatrixBase::maxCoeff()
+  */
+template<typename Scalar> struct ei_scalar_max_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return std::max(a, b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_pmax(a,b); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const Scalar predux(const PacketScalar& a) const
+  { return ei_predux_max(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_max_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the hypot of two scalars
+  *
+  * \sa MatrixBase::stableNorm(), class Redux
+  */
+template<typename Scalar> struct ei_scalar_hypot_op EIGEN_EMPTY_STRUCT {
+//   typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
+  {
+//     typedef typename NumTraits<T>::Real RealScalar;
+//     RealScalar _x = ei_abs(x);
+//     RealScalar _y = ei_abs(y);
+    Scalar p = std::max(_x, _y);
+    Scalar q = std::min(_x, _y);
+    Scalar qp = q/p;
+    return p * ei_sqrt(Scalar(1) + qp*qp);
+  }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_hypot_op<Scalar> > {
+  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
+};
+
+// other binary functors:
+
+/** \internal
+  * \brief Template functor to compute the difference of two scalars
+  *
+  * \sa class CwiseBinaryOp, MatrixBase::operator-
+  */
+template<typename Scalar> struct ei_scalar_difference_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_psub(a,b); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_difference_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the quotient of two scalars
+  *
+  * \sa class CwiseBinaryOp, Cwise::operator/()
+  */
+template<typename Scalar> struct ei_scalar_quotient_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a / b; }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+  { return ei_pdiv(a,b); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_quotient_op<Scalar> > {
+  enum {
+    Cost = 2 * NumTraits<Scalar>::MulCost,
+    PacketAccess = ei_packet_traits<Scalar>::size>1
+                  #if (defined EIGEN_VECTORIZE_SSE)
+                  && NumTraits<Scalar>::HasFloatingPoint
+                  #endif
+  };
+};
+
+// unary functors:
+
+/** \internal
+  * \brief Template functor to compute the opposite of a scalar
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator-
+  */
+template<typename Scalar> struct ei_scalar_opposite_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pnegate(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_opposite_op<Scalar> >
+{ enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = int(ei_packet_traits<Scalar>::size)>1 };
+};
+
+/** \internal
+  * \brief Template functor to compute the absolute value of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::abs
+  */
+template<typename Scalar> struct ei_scalar_abs_op EIGEN_EMPTY_STRUCT {
+  typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return ei_abs(a); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pabs(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_abs_op<Scalar> >
+{
+  enum {
+    Cost = NumTraits<Scalar>::AddCost,
+    PacketAccess = int(ei_packet_traits<Scalar>::size)>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the squared absolute value of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::abs2
+  */
+template<typename Scalar> struct ei_scalar_abs2_op EIGEN_EMPTY_STRUCT {
+  typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return ei_abs2(a); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pmul(a,a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_abs2_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = int(ei_packet_traits<Scalar>::size)>1 }; };
+
+/** \internal
+  * \brief Template functor to compute the conjugate of a complex value
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::conjugate()
+  */
+template<typename Scalar> struct ei_scalar_conjugate_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return ei_conj(a); }
+  template<typename PacketScalar>
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const { return a; }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_conjugate_op<Scalar> >
+{
+  enum {
+    Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
+    PacketAccess = int(ei_packet_traits<Scalar>::size)>1
+  };
+};
+
+/** \internal
+  * \brief Template functor to cast a scalar to another type
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::cast()
+  */
+template<typename Scalar, typename NewType>
+struct ei_scalar_cast_op EIGEN_EMPTY_STRUCT {
+  typedef NewType result_type;
+  EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return static_cast<NewType>(a); }
+};
+template<typename Scalar, typename NewType>
+struct ei_functor_traits<ei_scalar_cast_op<Scalar,NewType> >
+{ enum { Cost = ei_is_same_type<Scalar, NewType>::ret ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the real part of a complex
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::real()
+  */
+template<typename Scalar>
+struct ei_scalar_real_op EIGEN_EMPTY_STRUCT {
+  typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return ei_real(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_real_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to extract the imaginary part of a complex
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::imag()
+  */
+template<typename Scalar>
+struct ei_scalar_imag_op EIGEN_EMPTY_STRUCT {
+  typedef typename NumTraits<Scalar>::Real result_type;
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return ei_imag(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_imag_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to multiply a scalar by a fixed other one
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator*, MatrixBase::operator/
+  */
+/* NOTE why doing the ei_pset1() in packetOp *is* an optimization ?
+ * indeed it seems better to declare m_other as a PacketScalar and do the ei_pset1() once
+ * in the constructor. However, in practice:
+ *  - GCC does not like m_other as a PacketScalar and generate a load every time it needs it
+ *  - on the other hand GCC is able to moves the ei_pset1() away the loop :)
+ *  - simpler code ;)
+ * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
+ */
+template<typename Scalar>
+struct ei_scalar_multiple_op {
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE ei_scalar_multiple_op(const ei_scalar_multiple_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE ei_scalar_multiple_op(const Scalar& other) : m_other(other) { }
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pmul(a, ei_pset1(m_other)); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_multiple_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = ei_packet_traits<Scalar>::size>1 }; };
+
+template<typename Scalar1, typename Scalar2>
+struct ei_scalar_multiple2_op {
+  typedef typename ei_scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
+  EIGEN_STRONG_INLINE ei_scalar_multiple2_op(const ei_scalar_multiple2_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE ei_scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
+  const Scalar2 m_other;
+};
+template<typename Scalar1,typename Scalar2>
+struct ei_functor_traits<ei_scalar_multiple2_op<Scalar1,Scalar2> >
+{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
+
+template<typename Scalar, bool HasFloatingPoint>
+struct ei_scalar_quotient1_impl {
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const ei_scalar_quotient1_impl& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const Scalar& other) : m_other(static_cast<Scalar>(1) / other) {}
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
+  EIGEN_STRONG_INLINE const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_pmul(a, ei_pset1(m_other)); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,true> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = ei_packet_traits<Scalar>::size>1 }; };
+
+template<typename Scalar>
+struct ei_scalar_quotient1_impl<Scalar,false> {
+  // FIXME default copy constructors seems bugged with std::complex<>
+  EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const ei_scalar_quotient1_impl& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const Scalar& other) : m_other(other) {}
+  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,false> >
+{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
+
+/** \internal
+  * \brief Template functor to divide a scalar by a fixed other one
+  *
+  * This functor is used to implement the quotient of a matrix by
+  * a scalar where the scalar type is not necessarily a floating point type.
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::operator/
+  */
+template<typename Scalar>
+struct ei_scalar_quotient1_op : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint > {
+  EIGEN_STRONG_INLINE ei_scalar_quotient1_op(const Scalar& other)
+    : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint >(other) {}
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_quotient1_op<Scalar> > 
+: ei_functor_traits<ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint> >
+{};
+
+// nullary functors
+
+template<typename Scalar>
+struct ei_scalar_constant_op {
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  EIGEN_STRONG_INLINE ei_scalar_constant_op(const ei_scalar_constant_op& other) : m_other(other.m_other) { }
+  EIGEN_STRONG_INLINE ei_scalar_constant_op(const Scalar& other) : m_other(other) { }
+  EIGEN_STRONG_INLINE const Scalar operator() (int, int = 0) const { return m_other; }
+  EIGEN_STRONG_INLINE const PacketScalar packetOp() const { return ei_pset1(m_other); }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_constant_op<Scalar> >
+{ enum { Cost = 1, PacketAccess = ei_packet_traits<Scalar>::size>1, IsRepeatable = true }; };
+
+template<typename Scalar> struct ei_scalar_identity_op EIGEN_EMPTY_STRUCT {
+  EIGEN_STRONG_INLINE ei_scalar_identity_op(void) {}
+  EIGEN_STRONG_INLINE const Scalar operator() (int row, int col) const { return row==col ? Scalar(1) : Scalar(0); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_identity_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
+
+// allow to add new functors and specializations of ei_functor_traits from outside Eigen.
+// this macro is really needed because ei_functor_traits must be specialized after it is declared but before it is used...
+#ifdef EIGEN_FUNCTORS_PLUGIN
+#include EIGEN_FUNCTORS_PLUGIN
+#endif
+
+// all functors allow linear access, except ei_scalar_identity_op. So we fix here a quick meta
+// to indicate whether a functor allows linear access, just always answering 'yes' except for
+// ei_scalar_identity_op.
+template<typename Functor> struct ei_functor_has_linear_access { enum { ret = 1 }; };
+template<typename Scalar> struct ei_functor_has_linear_access<ei_scalar_identity_op<Scalar> > { enum { ret = 0 }; };
+
+// in CwiseBinaryOp, we require the Lhs and Rhs to have the same scalar type, except for multiplication
+// where we only require them to have the same _real_ scalar type so one may multiply, say, float by complex<float>.
+template<typename Functor> struct ei_functor_allows_mixing_real_and_complex { enum { ret = 0 }; };
+template<typename Scalar> struct ei_functor_allows_mixing_real_and_complex<ei_scalar_product_op<Scalar> > { enum { ret = 1 }; };
+
+#endif // EIGEN_FUNCTORS_H

Eigen/src/Core/Fuzzy.h

@@ -0,0 +1,234 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FUZZY_H
+#define EIGEN_FUZZY_H
+
+#ifndef EIGEN_LEGACY_COMPARES
+
+/** \returns \c true if \c *this is approximately equal to \a other, within the precision
+  * determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
+  * are considered to be approximately equal within precision \f$ p \f$ if
+  * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
+  * L2 norm).
+  *
+  * \note Because of the multiplicativeness of this comparison, one can't use this function
+  * to check whether \c *this is approximately equal to the zero matrix or vector.
+  * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
+  * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
+  * RealScalar&, RealScalar) instead.
+  *
+  * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isApprox(
+  const MatrixBase<OtherDerived>& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  const typename ei_nested<Derived,2>::type nested(derived());
+  const typename ei_nested<OtherDerived,2>::type otherNested(other.derived());
+  return (nested - otherNested).cwise().abs2().sum() <= prec * prec * std::min(nested.cwise().abs2().sum(), otherNested.cwise().abs2().sum());
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
+  *
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
+  * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
+  * of a reference matrix of same dimensions.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const MatrixBase<OtherDerived>&, RealScalar) const
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isMuchSmallerThan(
+  const typename NumTraits<Scalar>::Real& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  return cwise().abs2().sum() <= prec * prec * other * other;
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
+  * For matrices, the comparison is done using the Hilbert-Schmidt norm.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isMuchSmallerThan(
+  const MatrixBase<OtherDerived>& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  return this->cwise().abs2().sum() <= prec * prec * other.cwise().abs2().sum();
+}
+
+#else
+
+template<typename Derived, typename OtherDerived=Derived, bool IsVector=Derived::IsVectorAtCompileTime>
+struct ei_fuzzy_selector;
+
+/** \returns \c true if \c *this is approximately equal to \a other, within the precision
+  * determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
+  * are considered to be approximately equal within precision \f$ p \f$ if
+  * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
+  * For matrices, the comparison is done on all columns.
+  *
+  * \note Because of the multiplicativeness of this comparison, one can't use this function
+  * to check whether \c *this is approximately equal to the zero matrix or vector.
+  * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
+  * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
+  * RealScalar&, RealScalar) instead.
+  *
+  * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isApprox(
+  const MatrixBase<OtherDerived>& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  return ei_fuzzy_selector<Derived,OtherDerived>::isApprox(derived(), other.derived(), prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
+  * For matrices, the comparison is done on all columns.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const MatrixBase<OtherDerived>&, RealScalar) const
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isMuchSmallerThan(
+  const typename NumTraits<Scalar>::Real& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  return ei_fuzzy_selector<Derived>::isMuchSmallerThan(derived(), other, prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
+  * within the precision determined by \a prec.
+  *
+  * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+  * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
+  * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
+  * For matrices, the comparison is done on all columns.
+  *
+  * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
+  */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isMuchSmallerThan(
+  const MatrixBase<OtherDerived>& other,
+  typename NumTraits<Scalar>::Real prec
+) const
+{
+  return ei_fuzzy_selector<Derived,OtherDerived>::isMuchSmallerThan(derived(), other.derived(), prec);
+}
+
+
+template<typename Derived, typename OtherDerived>
+struct ei_fuzzy_selector<Derived,OtherDerived,true>
+{
+  typedef typename Derived::RealScalar RealScalar;
+  static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
+  {
+    EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+    ei_assert(self.size() == other.size());
+    return((self - other).squaredNorm() <= std::min(self.squaredNorm(), other.squaredNorm()) * prec * prec);
+  }
+  static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
+  {
+    return(self.squaredNorm() <= ei_abs2(other * prec));
+  }
+  static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
+  {
+    EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+    ei_assert(self.size() == other.size());
+    return(self.squaredNorm() <= other.squaredNorm() * prec * prec);
+  }
+};
+
+template<typename Derived, typename OtherDerived>
+struct ei_fuzzy_selector<Derived,OtherDerived,false>
+{
+  typedef typename Derived::RealScalar RealScalar;
+  static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
+  {
+    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+    ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
+    typename Derived::Nested nested(self);
+    typename OtherDerived::Nested otherNested(other);
+    for(int i = 0; i < self.cols(); ++i)
+      if((nested.col(i) - otherNested.col(i)).squaredNorm()
+          > std::min(nested.col(i).squaredNorm(), otherNested.col(i).squaredNorm()) * prec * prec)
+        return false;
+    return true;
+  }
+  static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
+  {
+    typename Derived::Nested nested(self);
+    for(int i = 0; i < self.cols(); ++i)
+      if(nested.col(i).squaredNorm() > ei_abs2(other * prec))
+        return false;
+    return true;
+  }
+  static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
+  {
+    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+    ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
+    typename Derived::Nested nested(self);
+    typename OtherDerived::Nested otherNested(other);
+    for(int i = 0; i < self.cols(); ++i)
+      if(nested.col(i).squaredNorm() > otherNested.col(i).squaredNorm() * prec * prec)
+        return false;
+    return true;
+  }
+};
+
+#endif
+
+#endif // EIGEN_FUZZY_H

Eigen/src/Core/GenericPacketMath.h

@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_GENERIC_PACKET_MATH_H
+#define EIGEN_GENERIC_PACKET_MATH_H
+
+/** \internal
+  * \file GenericPacketMath.h
+  *
+  * Default implementation for types not supported by the vectorization.
+  * In practice these functions are provided to make easier the writing
+  * of generic vectorized code.
+  */
+
+struct ei_default_packet_traits
+{
+  enum {
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasNegate = 1,
+    HasAbs    = 1,
+    HasMin    = 1,
+    HasMax    = 1,
+    
+    HasDiv    = 0,
+    HasSqrt   = 0,
+    HasExp    = 0,
+    HasLog    = 0,
+    HasPow    = 0,
+    
+    HasSin    = 0,
+    HasCos    = 0,
+    HasTan    = 0,
+    HasASin   = 0,
+    HasACos   = 0,
+    HasATan   = 0
+  };
+};
+
+template<typename T> struct ei_packet_traits : ei_default_packet_traits
+{
+  typedef T type;
+  enum {size=1};
+  enum {
+    HasAdd    = 0,
+    HasSub    = 0,
+    HasMul    = 0,
+    HasNegate = 0,
+    HasAbs    = 0,
+    HasMin    = 0,
+    HasMax    = 0
+  };
+};
+
+/** \internal \returns a + b (coeff-wise) */
+template<typename Packet> inline Packet
+ei_padd(const Packet& a,
+        const Packet& b) { return a+b; }
+
+/** \internal \returns a - b (coeff-wise) */
+template<typename Packet> inline Packet
+ei_psub(const Packet& a,
+        const Packet& b) { return a-b; }
+
+/** \internal \returns -a (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pnegate(const Packet& a) { return -a; }
+
+/** \internal \returns a * b (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pmul(const Packet& a,
+        const Packet& b) { return a*b; }
+
+/** \internal \returns a / b (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pdiv(const Packet& a,
+        const Packet& b) { return a/b; }
+
+/** \internal \returns the min of \a a and \a b  (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pmin(const Packet& a,
+        const Packet& b) { return std::min(a, b); }
+
+/** \internal \returns the max of \a a and \a b  (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pmax(const Packet& a,
+        const Packet& b) { return std::max(a, b); }
+
+/** \internal \returns the absolute value of \a a */
+template<typename Packet> inline Packet
+ei_pabs(const Packet& a) { return ei_abs(a); }
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> inline Packet
+ei_pand(const Packet& a, const Packet& b) { return a & b; }
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> inline Packet
+ei_por(const Packet& a, const Packet& b) { return a | b; }
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> inline Packet
+ei_pxor(const Packet& a, const Packet& b) { return a ^ b; }
+
+/** \internal \returns the bitwise andnot of \a a and \a b */
+template<typename Packet> inline Packet
+ei_pandnot(const Packet& a, const Packet& b) { return a & (!b); }
+        
+/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
+template<typename Scalar> inline typename ei_packet_traits<Scalar>::type
+ei_pload(const Scalar* from) { return *from; }
+
+/** \internal \returns a packet version of \a *from, (un-aligned load) */
+template<typename Scalar> inline typename ei_packet_traits<Scalar>::type
+ei_ploadu(const Scalar* from) { return *from; }
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
+template<typename Scalar> inline typename ei_packet_traits<Scalar>::type
+ei_pset1(const Scalar& a) { return a; }
+
+/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet> inline void ei_pstore(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> inline void ei_pstoreu(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal \returns the first element of a packet */
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_pfirst(const Packet& a)
+{ return a; }
+
+/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
+template<typename Packet> inline Packet
+ei_preduxp(const Packet* vecs) { return vecs[0]; }
+
+/** \internal \returns the sum of the elements of \a a*/
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux(const Packet& a)
+{ return a; }
+
+/** \internal \returns the product of the elements of \a a*/
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux_mul(const Packet& a)
+{ return a; }
+
+/** \internal \returns the min of the elements of \a a*/
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux_min(const Packet& a)
+{ return a; }
+
+/** \internal \returns the max of the elements of \a a*/
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux_max(const Packet& a)
+{ return a; }
+
+/** \internal \returns the reversed elements of \a a*/
+template<typename Packet> inline Packet ei_preverse(const Packet& a)
+{ return a; }
+
+/**************************
+* Special math functions
+***************************/
+
+/** \internal \returns the sin of \a a (coeff-wise) */
+template<typename Packet> inline static Packet ei_psin(Packet a) { return ei_sin(a); }
+
+/** \internal \returns the cos of \a a (coeff-wise) */
+template<typename Packet> inline static Packet ei_pcos(Packet a) { return ei_cos(a); }
+
+/** \internal \returns the exp of \a a (coeff-wise) */
+template<typename Packet> inline static Packet ei_pexp(Packet a) { return ei_exp(a); }
+
+/** \internal \returns the log of \a a (coeff-wise) */
+template<typename Packet> inline static Packet ei_plog(Packet a) { return ei_log(a); }
+
+/** \internal \returns the square-root of \a a (coeff-wise) */
+template<typename Packet> inline static Packet ei_psqrt(Packet a) { return ei_sqrt(a); }
+
+/***************************************************************************
+* The following functions might not have to be overwritten for vectorized types
+***************************************************************************/
+
+/** \internal \returns a * b + c (coeff-wise) */
+template<typename Packet> inline Packet
+ei_pmadd(const Packet&  a,
+         const Packet&  b,
+         const Packet&  c)
+{ return ei_padd(ei_pmul(a, b),c); }
+
+/** \internal \returns a packet version of \a *from.
+  * \If LoadMode equals Aligned, \a from must be 16 bytes aligned */
+template<typename Scalar, int LoadMode>
+inline typename ei_packet_traits<Scalar>::type ei_ploadt(const Scalar* from)
+{
+  if(LoadMode == Aligned)
+    return ei_pload(from);
+  else
+    return ei_ploadu(from);
+}
+
+/** \internal copy the packet \a from to \a *to.
+  * If StoreMode equals Aligned, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet, int LoadMode>
+inline void ei_pstoret(Scalar* to, const Packet& from)
+{
+  if(LoadMode == Aligned)
+    ei_pstore(to, from);
+  else
+    ei_pstoreu(to, from);
+}
+
+/** \internal default implementation of ei_palign() allowing partial specialization */
+template<int Offset,typename PacketType>
+struct ei_palign_impl
+{
+  // by default data are aligned, so there is nothing to be done :)
+  inline static void run(PacketType&, const PacketType&) {}
+};
+
+/** \internal update \a first using the concatenation of the \a Offset last elements
+  * of \a first and packet_size minus \a Offset first elements of \a second */
+template<int Offset,typename PacketType>
+inline void ei_palign(PacketType& first, const PacketType& second)
+{
+  ei_palign_impl<Offset,PacketType>::run(first,second);
+}
+
+#endif // EIGEN_GENERIC_PACKET_MATH_H
+

Eigen/src/Core/IO.h

@@ -0,0 +1,184 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_IO_H
+#define EIGEN_IO_H
+
+enum { Raw, AlignCols };
+
+/** \class IOFormat
+  *
+  * \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
+  *  - \b flags can be either Raw (default) or AlignCols which aligns all the columns
+  *  - \b coeffSeparator string printed between two coefficients of the same row
+  *  - \b rowSeparator string printed between two rows
+  *  - \b rowPrefix string printed at the beginning of each row
+  *  - \b rowSuffix string printed at the end of each row
+  *  - \b matPrefix string printed at the beginning of the matrix
+  *  - \b matSuffix string printed at the end of the matrix
+  *
+  * Example: \include IOFormat.cpp
+  * Output: \verbinclude IOFormat.out
+  *
+  * \sa MatrixBase::format(), class WithFormat
+  */
+struct IOFormat
+{
+  /** Default contructor, see class IOFormat for the meaning of the parameters */
+  IOFormat(int _precision=4, int _flags=Raw,
+    const std::string& _coeffSeparator = " ",
+    const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
+    const std::string& _matPrefix="", const std::string& _matSuffix="")
+  : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
+    coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
+  {
+    rowSpacer = "";
+    int i = int(matSuffix.length())-1;
+    while (i>=0 && matSuffix[i]!='\n')
+    {
+      rowSpacer += ' ';
+      i--;
+    }
+  }
+  std::string matPrefix, matSuffix;
+  std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
+  std::string coeffSeparator;
+  int precision;
+  int flags;
+};
+
+/** \class WithFormat
+  *
+  * \brief Pseudo expression providing matrix output with given format
+  *
+  * \param ExpressionType the type of the object on which IO stream operations are performed
+  *
+  * This class represents an expression with stream operators controlled by a given IOFormat.
+  * It is the return type of MatrixBase::format()
+  * and most of the time this is the only way it is used.
+  *
+  * See class IOFormat for some examples.
+  *
+  * \sa MatrixBase::format(), class IOFormat
+  */
+template<typename ExpressionType>
+class WithFormat
+{
+  public:
+
+    WithFormat(const ExpressionType& matrix, const IOFormat& format)
+      : m_matrix(matrix), m_format(format)
+    {}
+
+    friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
+    {
+      return ei_print_matrix(s, wf.m_matrix.eval(), wf.m_format);
+    }
+
+  protected:
+    const typename ExpressionType::Nested m_matrix;
+    IOFormat m_format;
+};
+
+/** \returns a WithFormat proxy object allowing to print a matrix the with given
+  * format \a fmt.
+  *
+  * See class IOFormat for some examples.
+  *
+  * \sa class IOFormat, class WithFormat
+  */
+template<typename Derived>
+inline const WithFormat<Derived>
+MatrixBase<Derived>::format(const IOFormat& fmt) const
+{
+  return WithFormat<Derived>(derived(), fmt);
+}
+
+/** \internal
+  * print the matrix \a _m to the output stream \a s using the output format \a fmt */
+template<typename Derived>
+std::ostream & ei_print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
+{
+  const typename Derived::Nested m = _m;
+
+  int width = 0;
+  if (fmt.flags & AlignCols)
+  {
+    // compute the largest width
+    for(int j = 1; j < m.cols(); ++j)
+      for(int i = 0; i < m.rows(); ++i)
+      {
+        std::stringstream sstr;
+        sstr.precision(fmt.precision);
+        sstr << m.coeff(i,j);
+        width = std::max<int>(width, int(sstr.str().length()));
+      }
+  }
+  s.precision(fmt.precision);
+  s << fmt.matPrefix;
+  for(int i = 0; i < m.rows(); ++i)
+  {
+    if (i)
+      s << fmt.rowSpacer;
+    s << fmt.rowPrefix;
+    if(width) s.width(width);
+    s << m.coeff(i, 0);
+    for(int j = 1; j < m.cols(); ++j)
+    {
+      s << fmt.coeffSeparator;
+      if (width) s.width(width);
+      s << m.coeff(i, j);
+    }
+    s << fmt.rowSuffix;
+    if( i < m.rows() - 1)
+      s << fmt.rowSeparator;
+  }
+  s << fmt.matSuffix;
+  return s;
+}
+
+/** \relates MatrixBase
+  *
+  * Outputs the matrix, to the given stream.
+  *
+  * If you wish to print the matrix with a format different than the default, use MatrixBase::format().
+  *
+  * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
+  * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
+  *
+  * \sa MatrixBase::format()
+  */
+template<typename Derived>
+std::ostream & operator <<
+(std::ostream & s,
+ const MatrixBase<Derived> & m)
+{
+  return ei_print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
+}
+
+#endif // EIGEN_IO_H

Eigen/src/Core/Map.h

@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MAP_H
+#define EIGEN_MAP_H
+
+/** \class Map
+  *
+  * \brief A matrix or vector expression mapping an existing array of data.
+  *
+  * \param MatrixType the equivalent matrix type of the mapped data
+  * \param _PacketAccess allows to enforce aligned loads and stores if set to ForceAligned.
+  *                      The default is AsRequested. This parameter is internaly used by Eigen
+  *                      in expressions such as \code Map<...>(...) += other; \endcode and most
+  *                      of the time this is the only way it is used.
+  *
+  * This class represents a matrix or vector expression mapping an existing array of data.
+  * It can be used to let Eigen interface without any overhead with non-Eigen data structures,
+  * such as plain C arrays or structures from other libraries.
+  *
+  * \b Tips: to change the array of data mapped by a Map object, you can use the C++
+  * placement new syntax:
+  *
+  * Example: \include Map_placement_new.cpp
+  * Output: \verbinclude Map_placement_new.out
+  *
+  * This class is the return type of Matrix::Map() but can also be used directly.
+  *
+  * \sa Matrix::Map()
+  */
+template<typename MatrixType, int _PacketAccess>
+struct ei_traits<Map<MatrixType, _PacketAccess> > : public ei_traits<MatrixType>
+{
+  enum {
+    PacketAccess = _PacketAccess,
+    Flags = ei_traits<MatrixType>::Flags & ~AlignedBit
+  };
+  typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
+                              Map<MatrixType, _PacketAccess>&,
+                              Map<MatrixType, ForceAligned> >::ret AlignedDerivedType;
+};
+
+template<typename MatrixType, int PacketAccess> class Map
+  : public MapBase<Map<MatrixType, PacketAccess> >
+{
+  public:
+
+    _EIGEN_GENERIC_PUBLIC_INTERFACE(Map, MapBase<Map>)
+    typedef typename ei_traits<Map>::AlignedDerivedType AlignedDerivedType;
+
+    inline int stride() const { return this->innerSize(); }
+
+    AlignedDerivedType _convertToForceAligned()
+    {
+      return Map<MatrixType,ForceAligned>(Base::m_data, Base::m_rows.value(), Base::m_cols.value());
+    }
+
+    inline Map(const Scalar* data) : Base(data) {}
+
+    inline Map(const Scalar* data, int size) : Base(data, size) {}
+
+    inline Map(const Scalar* data, int rows, int cols) : Base(data, rows, cols) {}
+
+    inline void resize(int rows, int cols)
+    {
+      EIGEN_ONLY_USED_FOR_DEBUG(rows);
+      EIGEN_ONLY_USED_FOR_DEBUG(cols);
+      ei_assert(rows == this->rows());
+      ei_assert(cols == this->cols());
+    }
+
+    inline void resize(int size)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(MatrixType)
+      EIGEN_ONLY_USED_FOR_DEBUG(size);
+      ei_assert(size == this->size());
+    }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+};
+
+/** Constructor copying an existing array of data.
+  * Only for fixed-size matrices and vectors.
+  * \param data The array of data to copy
+  *
+  * \sa Matrix::Map(const Scalar *)
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _StorageOrder, int _MaxRows, int _MaxCols>
+inline Matrix<_Scalar, _Rows, _Cols, _StorageOrder, _MaxRows, _MaxCols>
+  ::Matrix(const Scalar *data)
+{
+  _set_noalias(Eigen::Map<Matrix>(data));
+}
+
+#endif // EIGEN_MAP_H

Eigen/src/Core/MapBase.h

@@ -0,0 +1,202 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MAPBASE_H
+#define EIGEN_MAPBASE_H
+
+/** \class MapBase
+  *
+  * \brief Base class for Map and Block expression with direct access
+  *
+  * Expression classes inheriting MapBase must define the constant \c PacketAccess,
+  * and type \c AlignedDerivedType in their respective ei_traits<> specialization structure.
+  * The value of \c PacketAccess can be either:
+  *  - \b ForceAligned which enforces both aligned loads and stores
+  *  - \b AsRequested which is the default behavior
+  * The type \c AlignedDerivedType should correspond to the equivalent expression type
+  * with \c PacketAccess being \c ForceAligned.
+  *
+  * \sa class Map, class Block
+  */
+template<typename Derived> class MapBase
+  : public MatrixBase<Derived>
+{
+  public:
+
+    typedef MatrixBase<Derived> Base;
+    enum {
+      IsRowMajor = (int(ei_traits<Derived>::Flags) & RowMajorBit) ? 1 : 0,
+      PacketAccess = ei_traits<Derived>::PacketAccess,
+      RowsAtCompileTime = ei_traits<Derived>::RowsAtCompileTime,
+      ColsAtCompileTime = ei_traits<Derived>::ColsAtCompileTime,
+      SizeAtCompileTime = Base::SizeAtCompileTime
+    };
+
+    typedef typename ei_traits<Derived>::AlignedDerivedType AlignedDerivedType;
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+    typedef typename Base::PacketScalar PacketScalar;
+    using Base::derived;
+
+    inline int rows() const { return m_rows.value(); }
+    inline int cols() const { return m_cols.value(); }
+
+    inline int stride() const { return derived().stride(); }
+    inline const Scalar* data() const { return m_data; }
+
+    template<bool IsForceAligned,typename Dummy> struct force_aligned_impl {
+      AlignedDerivedType static run(MapBase& a) { return a.derived(); }
+    };
+
+    template<typename Dummy> struct force_aligned_impl<false,Dummy> {
+      AlignedDerivedType static run(MapBase& a) { return a.derived()._convertToForceAligned(); }
+    };
+
+    /** \returns an expression equivalent to \c *this but having the \c PacketAccess constant
+      * set to \c ForceAligned. Must be reimplemented by the derived class. */
+    AlignedDerivedType forceAligned()
+    {
+      return force_aligned_impl<int(PacketAccess)==int(ForceAligned),Derived>::run(*this);
+    }
+
+    inline const Scalar& coeff(int row, int col) const
+    {
+      if(IsRowMajor)
+        return m_data[col + row * stride()];
+      else // column-major
+        return m_data[row + col * stride()];
+    }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      if(IsRowMajor)
+        return const_cast<Scalar*>(m_data)[col + row * stride()];
+      else // column-major
+        return const_cast<Scalar*>(m_data)[row + col * stride()];
+    }
+
+    inline const Scalar& coeff(int index) const
+    {
+      ei_assert(Derived::IsVectorAtCompileTime || (ei_traits<Derived>::Flags & LinearAccessBit));
+      if ( ((RowsAtCompileTime == 1) == IsRowMajor) )
+        return m_data[index];
+      else
+        return m_data[index*stride()];
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      ei_assert(Derived::IsVectorAtCompileTime || (ei_traits<Derived>::Flags & LinearAccessBit));
+      if ( ((RowsAtCompileTime == 1) == IsRowMajor) )
+        return const_cast<Scalar*>(m_data)[index];
+      else
+        return const_cast<Scalar*>(m_data)[index*stride()];
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(int row, int col) const
+    {
+      return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>
+               (m_data + (IsRowMajor ? col + row * stride()
+                                     : row + col * stride()));
+    }
+
+    template<int LoadMode>
+    inline PacketScalar packet(int index) const
+    {
+      return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>(m_data + index);
+    }
+
+    template<int StoreMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
+               (const_cast<Scalar*>(m_data) + (IsRowMajor ? col + row * stride()
+                                                          : row + col * stride()), x);
+    }
+
+    template<int StoreMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
+        (const_cast<Scalar*>(m_data) + index, x);
+    }
+
+    inline MapBase(const Scalar* data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+    {
+      EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+    }
+
+    inline MapBase(const Scalar* data, int size)
+            : m_data(data),
+              m_rows(RowsAtCompileTime == Dynamic ? size : RowsAtCompileTime),
+              m_cols(ColsAtCompileTime == Dynamic ? size : ColsAtCompileTime)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+      ei_assert(size > 0 || data == 0);
+      ei_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
+    }
+
+    inline MapBase(const Scalar* data, int rows, int cols)
+            : m_data(data), m_rows(rows), m_cols(cols)
+    {
+      ei_assert( (data == 0)
+              || (   rows > 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+                  && cols > 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
+    }
+
+    Derived& operator=(const MapBase& other)
+    {
+      return Base::operator=(other);
+    }
+
+    template<typename OtherDerived>
+    Derived& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      return Base::operator=(other);
+    }
+
+    using Base::operator*=;
+
+    template<typename OtherDerived>
+    Derived& operator+=(const MatrixBase<OtherDerived>& other)
+    { return derived() = forceAligned() + other; }
+
+    template<typename OtherDerived>
+    Derived& operator-=(const MatrixBase<OtherDerived>& other)
+    { return derived() = forceAligned() - other; }
+
+    Derived& operator*=(const Scalar& other)
+    { return derived() = forceAligned() * other; }
+
+    Derived& operator/=(const Scalar& other)
+    { return derived() = forceAligned() / other; }
+
+  protected:
+    const Scalar* EIGEN_RESTRICT m_data;
+    const ei_int_if_dynamic<RowsAtCompileTime> m_rows;
+    const ei_int_if_dynamic<ColsAtCompileTime> m_cols;
+};
+
+#endif // EIGEN_MAPBASE_H

Eigen/src/Core/MathFunctions.h

@@ -0,0 +1,303 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATHFUNCTIONS_H
+#define EIGEN_MATHFUNCTIONS_H
+
+template<typename T> inline typename NumTraits<T>::Real precision();
+template<typename T> inline typename NumTraits<T>::Real machine_epsilon();
+template<typename T> inline T ei_random(T a, T b);
+template<typename T> inline T ei_random();
+template<typename T> inline T ei_random_amplitude()
+{
+  if(NumTraits<T>::HasFloatingPoint) return static_cast<T>(1);
+  else return static_cast<T>(10);
+}
+
+template<typename T> inline typename NumTraits<T>::Real ei_hypot(T x, T y)
+{
+  typedef typename NumTraits<T>::Real RealScalar;
+  RealScalar _x = ei_abs(x);
+  RealScalar _y = ei_abs(y);
+  T p = std::max(_x, _y);
+  T q = std::min(_x, _y);
+  T qp = q/p;
+  return p * ei_sqrt(T(1) + qp*qp);
+}
+
+/**************
+***   int   ***
+**************/
+
+template<> inline int precision<int>() { return 0; }
+template<> inline int machine_epsilon<int>() { return 0; }
+inline int ei_real(int x)  { return x; }
+inline int ei_imag(int)    { return 0; }
+inline int ei_conj(int x)  { return x; }
+inline int ei_abs(int x)   { return abs(x); }
+inline int ei_abs2(int x)  { return x*x; }
+inline int ei_sqrt(int)  { ei_assert(false); return 0; }
+inline int ei_exp(int)  { ei_assert(false); return 0; }
+inline int ei_log(int)  { ei_assert(false); return 0; }
+inline int ei_sin(int)  { ei_assert(false); return 0; }
+inline int ei_cos(int)  { ei_assert(false); return 0; }
+inline int ei_pow(int x, int y)
+{
+  int res = 1;
+  if(y < 0) return 0;
+  if(y & 1) res *= x;
+  y >>= 1;
+  while(y)
+  {
+    x *= x;
+    if(y&1) res *= x;
+    y >>= 1;
+  }
+  return res;
+}
+
+template<> inline int ei_random(int a, int b)
+{
+  // We can't just do rand()%n as only the high-order bits are really random
+  return a + static_cast<int>((b-a+1) * (rand() / (RAND_MAX + 1.0)));
+}
+template<> inline int ei_random()
+{
+  return ei_random<int>(-ei_random_amplitude<int>(), ei_random_amplitude<int>());
+}
+inline bool ei_isMuchSmallerThan(int a, int, int = precision<int>())
+{
+  return a == 0;
+}
+inline bool ei_isApprox(int a, int b, int = precision<int>())
+{
+  return a == b;
+}
+inline bool ei_isApproxOrLessThan(int a, int b, int = precision<int>())
+{
+  return a <= b;
+}
+
+/**************
+*** float   ***
+**************/
+
+template<> inline float precision<float>() { return 1e-5f; }
+template<> inline float machine_epsilon<float>() { return 1.192e-07f; }
+inline float ei_real(float x)  { return x; }
+inline float ei_imag(float)    { return 0.f; }
+inline float ei_conj(float x)  { return x; }
+inline float ei_abs(float x)   { return std::abs(x); }
+inline float ei_abs2(float x)  { return x*x; }
+inline float ei_sqrt(float x)  { return std::sqrt(x); }
+inline float ei_exp(float x)   { return std::exp(x); }
+inline float ei_log(float x)   { return std::log(x); }
+inline float ei_sin(float x)   { return std::sin(x); }
+inline float ei_cos(float x)   { return std::cos(x); }
+inline float ei_pow(float x, float y)  { return std::pow(x, y); }
+
+template<> inline float ei_random(float a, float b)
+{
+#ifdef EIGEN_NICE_RANDOM
+  int i;
+  do { i = ei_random<int>(256*int(a),256*int(b));
+  } while(i==0);
+  return float(i)/256.f;
+#else
+  return a + (b-a) * float(std::rand()) / float(RAND_MAX);
+#endif
+}
+template<> inline float ei_random()
+{
+  return ei_random<float>(-ei_random_amplitude<float>(), ei_random_amplitude<float>());
+}
+inline bool ei_isMuchSmallerThan(float a, float b, float prec = precision<float>())
+{
+  return ei_abs(a) <= ei_abs(b) * prec;
+}
+inline bool ei_isApprox(float a, float b, float prec = precision<float>())
+{
+  return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
+}
+inline bool ei_isApproxOrLessThan(float a, float b, float prec = precision<float>())
+{
+  return a <= b || ei_isApprox(a, b, prec);
+}
+
+/**************
+*** double  ***
+**************/
+
+template<> inline double precision<double>() { return 1e-11; }
+template<> inline double machine_epsilon<double>() { return 2.220e-16; }
+
+inline double ei_real(double x)  { return x; }
+inline double ei_imag(double)    { return 0.; }
+inline double ei_conj(double x)  { return x; }
+inline double ei_abs(double x)   { return std::abs(x); }
+inline double ei_abs2(double x)  { return x*x; }
+inline double ei_sqrt(double x)  { return std::sqrt(x); }
+inline double ei_exp(double x)   { return std::exp(x); }
+inline double ei_log(double x)   { return std::log(x); }
+inline double ei_sin(double x)   { return std::sin(x); }
+inline double ei_cos(double x)   { return std::cos(x); }
+inline double ei_pow(double x, double y) { return std::pow(x, y); }
+
+template<> inline double ei_random(double a, double b)
+{
+#ifdef EIGEN_NICE_RANDOM
+  int i;
+  do { i= ei_random<int>(256*int(a),256*int(b));
+  } while(i==0);
+  return i/256.;
+#else
+  return a + (b-a) * std::rand() / RAND_MAX;
+#endif
+}
+template<> inline double ei_random()
+{
+  return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>());
+}
+inline bool ei_isMuchSmallerThan(double a, double b, double prec = precision<double>())
+{
+  return ei_abs(a) <= ei_abs(b) * prec;
+}
+inline bool ei_isApprox(double a, double b, double prec = precision<double>())
+{
+  return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
+}
+inline bool ei_isApproxOrLessThan(double a, double b, double prec = precision<double>())
+{
+  return a <= b || ei_isApprox(a, b, prec);
+}
+
+/*********************
+*** complex<float> ***
+*********************/
+
+template<> inline float precision<std::complex<float> >() { return precision<float>(); }
+template<> inline float machine_epsilon<std::complex<float> >() { return machine_epsilon<float>(); }
+inline float ei_real(const std::complex<float>& x) { return std::real(x); }
+inline float ei_imag(const std::complex<float>& x) { return std::imag(x); }
+inline std::complex<float> ei_conj(const std::complex<float>& x) { return std::conj(x); }
+inline float ei_abs(const std::complex<float>& x) { return std::abs(x); }
+inline float ei_abs2(const std::complex<float>& x) { return std::norm(x); }
+inline std::complex<float> ei_exp(std::complex<float> x)  { return std::exp(x); }
+inline std::complex<float> ei_sin(std::complex<float> x)  { return std::sin(x); }
+inline std::complex<float> ei_cos(std::complex<float> x)  { return std::cos(x); }
+
+template<> inline std::complex<float> ei_random()
+{
+  return std::complex<float>(ei_random<float>(), ei_random<float>());
+}
+inline bool ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
+{
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
+}
+inline bool ei_isMuchSmallerThan(const std::complex<float>& a, float b, float prec = precision<float>())
+{
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
+}
+inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
+{
+  return ei_isApprox(ei_real(a), ei_real(b), prec)
+      && ei_isApprox(ei_imag(a), ei_imag(b), prec);
+}
+// ei_isApproxOrLessThan wouldn't make sense for complex numbers
+
+/**********************
+*** complex<double> ***
+**********************/
+
+template<> inline double precision<std::complex<double> >() { return precision<double>(); }
+template<> inline double machine_epsilon<std::complex<double> >() { return machine_epsilon<double>(); }
+inline double ei_real(const std::complex<double>& x) { return std::real(x); }
+inline double ei_imag(const std::complex<double>& x) { return std::imag(x); }
+inline std::complex<double> ei_conj(const std::complex<double>& x) { return std::conj(x); }
+inline double ei_abs(const std::complex<double>& x) { return std::abs(x); }
+inline double ei_abs2(const std::complex<double>& x) { return std::norm(x); }
+inline std::complex<double> ei_exp(std::complex<double> x)  { return std::exp(x); }
+inline std::complex<double> ei_sin(std::complex<double> x)  { return std::sin(x); }
+inline std::complex<double> ei_cos(std::complex<double> x)  { return std::cos(x); }
+
+template<> inline std::complex<double> ei_random()
+{
+  return std::complex<double>(ei_random<double>(), ei_random<double>());
+}
+inline bool ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
+{
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
+}
+inline bool ei_isMuchSmallerThan(const std::complex<double>& a, double b, double prec = precision<double>())
+{
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
+}
+inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
+{
+  return ei_isApprox(ei_real(a), ei_real(b), prec)
+      && ei_isApprox(ei_imag(a), ei_imag(b), prec);
+}
+// ei_isApproxOrLessThan wouldn't make sense for complex numbers
+
+
+/******************
+*** long double ***
+******************/
+
+template<> inline long double precision<long double>() { return precision<double>(); }
+template<> inline long double machine_epsilon<long double>() { return 1.084e-19l; }
+inline long double ei_real(long double x)  { return x; }
+inline long double ei_imag(long double)    { return 0.; }
+inline long double ei_conj(long double x)  { return x; }
+inline long double ei_abs(long double x)   { return std::abs(x); }
+inline long double ei_abs2(long double x)  { return x*x; }
+inline long double ei_sqrt(long double x)  { return std::sqrt(x); }
+inline long double ei_exp(long double x)   { return std::exp(x); }
+inline long double ei_log(long double x)   { return std::log(x); }
+inline long double ei_sin(long double x)   { return std::sin(x); }
+inline long double ei_cos(long double x)   { return std::cos(x); }
+inline long double ei_pow(long double x, long double y)  { return std::pow(x, y); }
+
+template<> inline long double ei_random(long double a, long double b)
+{
+  return ei_random<double>(static_cast<double>(a),static_cast<double>(b));
+}
+template<> inline long double ei_random()
+{
+  return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>());
+}
+inline bool ei_isMuchSmallerThan(long double a, long double b, long double prec = precision<long double>())
+{
+  return ei_abs(a) <= ei_abs(b) * prec;
+}
+inline bool ei_isApprox(long double a, long double b, long double prec = precision<long double>())
+{
+  return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
+}
+inline bool ei_isApproxOrLessThan(long double a, long double b, long double prec = precision<long double>())
+{
+  return a <= b || ei_isApprox(a, b, prec);
+}
+
+#endif // EIGEN_MATHFUNCTIONS_H

Eigen/src/Core/Matrix.h

@@ -0,0 +1,620 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIX_H
+#define EIGEN_MATRIX_H
+
+
+/** \class Matrix
+  *
+  * \brief The matrix class, also used for vectors and row-vectors
+  *
+  * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
+  * Vectors are matrices with one column, and row-vectors are matrices with one row.
+  *
+  * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
+  *
+  * The first three template parameters are required:
+  * \param _Scalar Numeric type, i.e. float, double, int
+  * \param _Rows Number of rows, or \b Dynamic
+  * \param _Cols Number of columns, or \b Dynamic
+  *
+  * The remaining template parameters are optional -- in most cases you don't have to worry about them.
+  * \param _Options A combination of either \b RowMajor or \b ColMajor, and of either
+  *                 \b AutoAlign or \b DontAlign.
+  *                 The former controls storage order, and defaults to column-major. The latter controls alignment, which is required
+  *                 for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
+  * \param _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
+  * \param _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
+  *
+  * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
+  *
+  * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
+  * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
+  * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
+  *
+  * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
+  * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
+  *
+  * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
+  *
+  * You can access elements of vectors and matrices using normal subscripting:
+  *
+  * \code
+  * Eigen::VectorXd v(10);
+  * v[0] = 0.1;
+  * v[1] = 0.2;
+  * v(0) = 0.3;
+  * v(1) = 0.4;
+  *
+  * Eigen::MatrixXi m(10, 10);
+  * m(0, 1) = 1;
+  * m(0, 2) = 2;
+  * m(0, 3) = 3;
+  * \endcode
+  *
+  * <i><b>Some notes:</b></i>
+  *
+  * <dl>
+  * <dt><b>\anchor dense Dense versus sparse:</b></dt>
+  * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
+  *
+  * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
+  * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
+  *
+  * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
+  * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
+  * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
+  * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
+  *
+  * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
+  * variables, and the array of coefficients is allocated dynamically on the heap.
+  *
+  * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
+  * If you want this behavior, see the Sparse module.</dd>
+  *
+  * <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
+  * <dd>In most cases, one just leaves these parameters to the default values.
+  * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
+  * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
+  * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
+  * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
+  * </dl>
+  *
+  * \see MatrixBase for the majority of the API methods for matrices
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct ei_traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  typedef _Scalar Scalar;
+  enum {
+    RowsAtCompileTime = _Rows,
+    ColsAtCompileTime = _Cols,
+    MaxRowsAtCompileTime = _MaxRows,
+    MaxColsAtCompileTime = _MaxCols,
+    Flags = ei_compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
+    CoeffReadCost = NumTraits<Scalar>::ReadCost
+  };
+};
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+class Matrix
+  : public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  public:
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Matrix)
+    enum { Options = _Options };
+    friend class Eigen::Map<Matrix, Unaligned>;
+    typedef class Eigen::Map<Matrix, Unaligned> UnalignedMapType;
+    friend class Eigen::Map<Matrix, Aligned>;
+    typedef class Eigen::Map<Matrix, Aligned> AlignedMapType;
+
+  protected:
+    ei_matrix_storage<Scalar, MaxSizeAtCompileTime, RowsAtCompileTime, ColsAtCompileTime, Options> m_storage;
+
+  public:
+    enum { NeedsToAlign = (!(Options&DontAlign))
+                          && SizeAtCompileTime!=Dynamic && ((sizeof(Scalar)*SizeAtCompileTime)%16)==0 };
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+
+    EIGEN_STRONG_INLINE int rows() const { return m_storage.rows(); }
+    EIGEN_STRONG_INLINE int cols() const { return m_storage.cols(); }
+
+    EIGEN_STRONG_INLINE int stride(void) const
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.cols();
+      else
+        return m_storage.rows();
+    }
+
+    EIGEN_STRONG_INLINE const Scalar& coeff(int row, int col) const
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.data()[col + row * m_storage.cols()];
+      else // column-major
+        return m_storage.data()[row + col * m_storage.rows()];
+    }
+
+    EIGEN_STRONG_INLINE const Scalar& coeff(int index) const
+    {
+      return m_storage.data()[index];
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(int row, int col)
+    {
+      if(Flags & RowMajorBit)
+        return m_storage.data()[col + row * m_storage.cols()];
+      else // column-major
+        return m_storage.data()[row + col * m_storage.rows()];
+    }
+
+    EIGEN_STRONG_INLINE Scalar& coeffRef(int index)
+    {
+      return m_storage.data()[index];
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int row, int col) const
+    {
+      return ei_ploadt<Scalar, LoadMode>
+               (m_storage.data() + (Flags & RowMajorBit
+                                   ? col + row * m_storage.cols()
+                                   : row + col * m_storage.rows()));
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE PacketScalar packet(int index) const
+    {
+      return ei_ploadt<Scalar, LoadMode>(m_storage.data() + index);
+    }
+
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket(int row, int col, const PacketScalar& x)
+    {
+      ei_pstoret<Scalar, PacketScalar, StoreMode>
+              (m_storage.data() + (Flags & RowMajorBit
+                                   ? col + row * m_storage.cols()
+                                   : row + col * m_storage.rows()), x);
+    }
+
+    template<int StoreMode>
+    EIGEN_STRONG_INLINE void writePacket(int index, const PacketScalar& x)
+    {
+      ei_pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);
+    }
+
+    /** \returns a const pointer to the data array of this matrix */
+    EIGEN_STRONG_INLINE const Scalar *data() const
+    { return m_storage.data(); }
+
+    /** \returns a pointer to the data array of this matrix */
+    EIGEN_STRONG_INLINE Scalar *data()
+    { return m_storage.data(); }
+
+    /** Resizes \c *this to a \a rows x \a cols matrix.
+      *
+      * Makes sense for dynamic-size matrices only.
+      *
+      * If the current number of coefficients of \c *this exactly matches the
+      * product \a rows * \a cols, then no memory allocation is performed and
+      * the current values are left unchanged. In all other cases, including
+      * shrinking, the data is reallocated and all previous values are lost.
+      *
+      * \sa resize(int) for vectors.
+      */
+    inline void resize(int rows, int cols)
+    {
+      ei_assert((MaxRowsAtCompileTime == Dynamic || MaxRowsAtCompileTime >= rows)
+             && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+             && (MaxColsAtCompileTime == Dynamic || MaxColsAtCompileTime >= cols)
+             && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+      m_storage.resize(rows * cols, rows, cols);
+    }
+
+    /** Resizes \c *this to a vector of length \a size
+      *
+      * \sa resize(int,int) for the details.
+      */
+    inline void resize(int size)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
+      if(RowsAtCompileTime == 1)
+        m_storage.resize(size, 1, size);
+      else
+        m_storage.resize(size, size, 1);
+    }
+
+    /** Resizes *this to have the same dimensions as \a other.
+      * Takes care of doing all the checking that's needed.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void resizeLike(const MatrixBase<OtherDerived>& other)
+    {
+      if(RowsAtCompileTime == 1)
+      {
+        ei_assert(other.isVector());
+        resize(1, other.size());
+      }
+      else if(ColsAtCompileTime == 1)
+      {
+        ei_assert(other.isVector());
+        resize(other.size(), 1);
+      }
+      else resize(other.rows(), other.cols());
+    }
+
+    /** Copies the value of the expression \a other into \c *this with automatic resizing.
+      *
+      * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+      * it will be initialized.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      return _set(other);
+    }
+
+    /** This is a special case of the templated operator=. Its purpose is to
+      * prevent a default operator= from hiding the templated operator=.
+      */
+    EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
+    {
+      return  _set(other);
+    }
+
+    template<typename OtherDerived,typename OtherEvalType>
+    EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived,OtherEvalType>& func)
+    { return Base::operator=(func); }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Matrix, +=)
+    EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Matrix, -=)
+    EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Matrix, *=)
+    EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Matrix, /=)
+
+    /** Default constructor.
+      *
+      * For fixed-size matrices, does nothing.
+      *
+      * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+      * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+      * a matrix to 0 is not supported.
+      *
+      * \sa resize(int,int)
+      */
+    EIGEN_STRONG_INLINE explicit Matrix() : m_storage()
+    {
+      _check_template_params();
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal */
+    Matrix(ei_constructor_without_unaligned_array_assert)
+      : m_storage(ei_constructor_without_unaligned_array_assert())
+    {}
+#endif
+
+    /** Constructs a vector or row-vector with given dimension. \only_for_vectors
+      *
+      * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+      * it is redundant to pass the dimension here, so it makes more sense to use the default
+      * constructor Matrix() instead.
+      */
+    EIGEN_STRONG_INLINE explicit Matrix(int dim)
+      : m_storage(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
+    {
+      _check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
+      ei_assert(dim > 0);
+      ei_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
+    }
+
+    #ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
+    {
+      _check_template_params();
+      _init2<T0,T1>(x, y);
+    }
+    #else
+    /** constructs an uninitialized matrix with \a rows rows and \a cols columns.
+      *
+      * This is useful for dynamic-size matrices. For fixed-size matrices,
+      * it is redundant to pass these parameters, so one should use the default constructor
+      * Matrix() instead. */
+    Matrix(int rows, int cols);
+    /** constructs an initialized 2D vector with given coefficients */
+    Matrix(const Scalar& x, const Scalar& y);
+    #endif
+
+    /** constructs an initialized 3D vector with given coefficients */
+    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
+    {
+      _check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+    }
+    /** constructs an initialized 4D vector with given coefficients */
+    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
+    {
+      _check_template_params();
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+      m_storage.data()[2] = z;
+      m_storage.data()[3] = w;
+    }
+
+    explicit Matrix(const Scalar *data);
+
+    /** Constructor copying the value of the expression \a other */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
+             : m_storage(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      _check_template_params();
+      _set_noalias(other);
+    }
+    /** Copy constructor */
+    EIGEN_STRONG_INLINE Matrix(const Matrix& other)
+            : Base(), m_storage(other.rows() * other.cols(), other.rows(), other.cols())
+    {
+      _check_template_params();
+      _set_noalias(other);
+    }
+    /** Copy constructor with in-place evaluation */
+    template<typename OtherDerived,typename OtherEvalType>
+    EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived,OtherEvalType>& other)
+    { other.evalTo(*this); }
+    /** Destructor */
+    inline ~Matrix() {}
+
+    /** Override MatrixBase::swap() since for dynamic-sized matrices of same type it is enough to swap the
+      * data pointers.
+      */
+    inline void swap(Matrix& other)
+    {
+      if (Base::SizeAtCompileTime==Dynamic)
+        m_storage.swap(other.m_storage);
+      else
+        this->Base::swap(other);
+    }
+
+    /** \name Map
+      * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
+      * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
+      * \a data pointers.
+      *
+      * \see class Map
+      */
+    //@{
+    inline static const UnalignedMapType Map(const Scalar* data)
+    { return UnalignedMapType(data); }
+    inline static UnalignedMapType Map(Scalar* data)
+    { return UnalignedMapType(data); }
+    inline static const UnalignedMapType Map(const Scalar* data, int size)
+    { return UnalignedMapType(data, size); }
+    inline static UnalignedMapType Map(Scalar* data, int size)
+    { return UnalignedMapType(data, size); }
+    inline static const UnalignedMapType Map(const Scalar* data, int rows, int cols)
+    { return UnalignedMapType(data, rows, cols); }
+    inline static UnalignedMapType Map(Scalar* data, int rows, int cols)
+    { return UnalignedMapType(data, rows, cols); }
+
+    inline static const AlignedMapType MapAligned(const Scalar* data)
+    { return AlignedMapType(data); }
+    inline static AlignedMapType MapAligned(Scalar* data)
+    { return AlignedMapType(data); }
+    inline static const AlignedMapType MapAligned(const Scalar* data, int size)
+    { return AlignedMapType(data, size); }
+    inline static AlignedMapType MapAligned(Scalar* data, int size)
+    { return AlignedMapType(data, size); }
+    inline static const AlignedMapType MapAligned(const Scalar* data, int rows, int cols)
+    { return AlignedMapType(data, rows, cols); }
+    inline static AlignedMapType MapAligned(Scalar* data, int rows, int cols)
+    { return AlignedMapType(data, rows, cols); }
+    //@}
+
+    using Base::setConstant;
+    Matrix& setConstant(int size, const Scalar& value);
+    Matrix& setConstant(int rows, int cols, const Scalar& value);
+
+    using Base::setZero;
+    Matrix& setZero(int size);
+    Matrix& setZero(int rows, int cols);
+
+    using Base::setOnes;
+    Matrix& setOnes(int size);
+    Matrix& setOnes(int rows, int cols);
+
+    using Base::setRandom;
+    Matrix& setRandom(int size);
+    Matrix& setRandom(int rows, int cols);
+
+    using Base::setIdentity;
+    Matrix& setIdentity(int rows, int cols);
+
+/////////// Geometry module ///////////
+
+    template<typename OtherDerived>
+    explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    template<typename OtherDerived>
+    Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+
+    // allow to extend Matrix outside Eigen
+    #ifdef EIGEN_MATRIX_PLUGIN
+    #include EIGEN_MATRIX_PLUGIN
+    #endif
+
+  private:
+    /** \internal Resizes *this in preparation for assigning \a other to it.
+      * Takes care of doing all the checking that's needed.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE void _resize_to_match(const MatrixBase<OtherDerived>& other)
+    {
+      #ifdef EIGEN_NO_AUTOMATIC_RESIZING
+      ei_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())
+                 : (rows() == other.rows() && cols() == other.cols())))
+        && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
+      #endif
+      resizeLike(other);
+    }
+
+    /** \internal Copies the value of the expression \a other into \c *this with automatic resizing.
+      *
+      * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+      * it will be initialized.
+      *
+      * Note that copying a row-vector into a vector (and conversely) is allowed.
+      * The resizing, if any, is then done in the appropriate way so that row-vectors
+      * remain row-vectors and vectors remain vectors.
+      *
+      * \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& _set(const MatrixBase<OtherDerived>& other)
+    {
+      _resize_to_match(other);
+      return Base::operator=(other);
+    }
+
+    /** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
+      * is the case when creating a new matrix) so one can enforce lazy evaluation.
+      *
+      * \sa operator=(const MatrixBase<OtherDerived>&), _set()
+      */
+    template<typename OtherDerived>
+    EIGEN_STRONG_INLINE Matrix& _set_noalias(const MatrixBase<OtherDerived>& other)
+    {
+      _resize_to_match(other);
+      // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
+      // it wouldn't allow to copy a row-vector into a column-vector.
+      return ei_assign_selector<Matrix,OtherDerived,false>::run(*this, other.derived());
+    }
+
+    static EIGEN_STRONG_INLINE void _check_template_params()
+    {
+        EIGEN_STATIC_ASSERT(((_MaxRows >= _Rows || _Rows==Dynamic)
+                          && (_MaxCols >= _Cols || _Cols==Dynamic)
+                          && ((_MaxRows==Dynamic?1:_MaxRows)*(_MaxCols==Dynamic?1:_MaxCols)<Dynamic)
+                          && (_Options & (DontAlign|RowMajor)) == _Options),
+          INVALID_MATRIX_TEMPLATE_PARAMETERS)
+    }
+
+
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE void _init2(int rows, int cols, typename ei_enable_if<Base::SizeAtCompileTime!=2,T0>::type* = 0)
+    {
+      ei_assert(rows > 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+             && cols > 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+      m_storage.resize(rows*cols,rows,cols);
+    }
+    template<typename T0, typename T1>
+    EIGEN_STRONG_INLINE void _init2(const Scalar& x, const Scalar& y, typename ei_enable_if<Base::SizeAtCompileTime==2,T0>::type* = 0)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 2)
+      m_storage.data()[0] = x;
+      m_storage.data()[1] = y;
+    }
+};
+
+/** \defgroup matrixtypedefs Global matrix typedefs
+  *
+  * \ingroup Core_Module
+  *
+  * Eigen defines several typedef shortcuts for most common matrix and vector types.
+  *
+  * The general patterns are the following:
+  *
+  * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+  * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+  * for complex double.
+  *
+  * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
+  *
+  * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
+  * a fixed-size vector of 4 complex floats.
+  *
+  * \sa class Matrix
+  */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, 1>    Vector##SizeSuffix##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, 1, Size>    RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+
+#undef EIGEN_MAKE_TYPEDEFS_LARGE
+
+#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
+using Eigen::Matrix##SizeSuffix##TypeSuffix; \
+using Eigen::Vector##SizeSuffix##TypeSuffix; \
+using Eigen::RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(TypeSuffix) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
+
+#define EIGEN_USING_MATRIX_TYPEDEFS \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(i) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(f) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(d) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cf) \
+EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cd)
+
+#endif // EIGEN_MATRIX_H

Eigen/src/Core/MatrixBase.h

@@ -0,0 +1,686 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIXBASE_H
+#define EIGEN_MATRIXBASE_H
+
+/** \class MatrixBase
+  *
+  * \brief Base class for all matrices, vectors, and expressions
+  *
+  * This class is the base that is inherited by all matrix, vector, and expression
+  * types. Most of the Eigen API is contained in this class. Other important classes for
+  * the Eigen API are Matrix, Cwise, and PartialRedux.
+  *
+  * Note that some methods are defined in the \ref Array_Module array module.
+  *
+  * \param Derived is the derived type, e.g. a matrix type, or an expression, etc.
+  *
+  * When writing a function taking Eigen objects as argument, if you want your function
+  * to take as argument any matrix, vector, or expression, just let it take a
+  * MatrixBase argument. As an example, here is a function printFirstRow which, given
+  * a matrix, vector, or expression \a x, prints the first row of \a x.
+  *
+  * \code
+    template<typename Derived>
+    void printFirstRow(const Eigen::MatrixBase<Derived>& x)
+    {
+      cout << x.row(0) << endl;
+    }
+  * \endcode
+  *
+  */
+template<typename Derived> class MatrixBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  : public ei_special_scalar_op_base<Derived,typename ei_traits<Derived>::Scalar,
+                typename NumTraits<typename ei_traits<Derived>::Scalar>::Real>
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+{
+  public:
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    using ei_special_scalar_op_base<Derived,typename ei_traits<Derived>::Scalar,
+                typename NumTraits<typename ei_traits<Derived>::Scalar>::Real>::operator*;
+
+    class InnerIterator;
+
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+    typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    enum {
+
+      RowsAtCompileTime = ei_traits<Derived>::RowsAtCompileTime,
+        /**< The number of rows at compile-time. This is just a copy of the value provided
+          * by the \a Derived type. If a value is not known at compile-time,
+          * it is set to the \a Dynamic constant.
+          * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+      ColsAtCompileTime = ei_traits<Derived>::ColsAtCompileTime,
+        /**< The number of columns at compile-time. This is just a copy of the value provided
+          * by the \a Derived type. If a value is not known at compile-time,
+          * it is set to the \a Dynamic constant.
+          * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+      SizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::RowsAtCompileTime,
+                                                   ei_traits<Derived>::ColsAtCompileTime>::ret),
+        /**< This is equal to the number of coefficients, i.e. the number of
+          * rows times the number of columns, or to \a Dynamic if this is not
+          * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+      MaxRowsAtCompileTime = ei_traits<Derived>::MaxRowsAtCompileTime,
+        /**< This value is equal to the maximum possible number of rows that this expression
+          * might have. If this expression might have an arbitrarily high number of rows,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
+          */
+
+      MaxColsAtCompileTime = ei_traits<Derived>::MaxColsAtCompileTime,
+        /**< This value is equal to the maximum possible number of columns that this expression
+          * might have. If this expression might have an arbitrarily high number of columns,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
+          */
+
+      MaxSizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::MaxRowsAtCompileTime,
+                                                      ei_traits<Derived>::MaxColsAtCompileTime>::ret),
+        /**< This value is equal to the maximum possible number of coefficients that this expression
+          * might have. If this expression might have an arbitrarily high number of coefficients,
+          * this value is set to \a Dynamic.
+          *
+          * This value is useful to know when evaluating an expression, in order to determine
+          * whether it is possible to avoid doing a dynamic memory allocation.
+          *
+          * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
+          */
+
+      IsVectorAtCompileTime = ei_traits<Derived>::RowsAtCompileTime == 1
+                           || ei_traits<Derived>::ColsAtCompileTime == 1,
+        /**< This is set to true if either the number of rows or the number of
+          * columns is known at compile-time to be equal to 1. Indeed, in that case,
+          * we are dealing with a column-vector (if there is only one column) or with
+          * a row-vector (if there is only one row). */
+
+      Flags = ei_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".
+          */
+
+      CoeffReadCost = ei_traits<Derived>::CoeffReadCost
+        /**< This is a rough measure of how expensive it is to read one coefficient from
+          * this expression.
+          */
+    };
+
+    /** Default constructor. Just checks at compile-time for self-consistency of the flags. */
+    MatrixBase()
+    {
+      ei_assert(ei_are_flags_consistent<Flags>::ret);
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is the "real scalar" type; if the \a Scalar type is already real numbers
+      * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
+      * \a Scalar is \a std::complex<T> then RealScalar is \a T.
+      *
+      * \sa class NumTraits
+      */
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    /** type of the equivalent square matrix */
+    typedef Matrix<Scalar,EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime),
+                          EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+    inline int rows() const { return derived().rows(); }
+    /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+    inline int cols() const { return derived().cols(); }
+    /** \returns the number of coefficients, which is rows()*cols().
+      * \sa rows(), cols(), SizeAtCompileTime. */
+    inline int size() const { return rows() * cols(); }
+    /** \returns the size of the main diagonal, which is min(rows(),cols()).
+      * \sa rows(), cols(), SizeAtCompileTime. */
+    inline int diagonalSize() const { return std::min(rows(),cols()); }
+    /** \returns the number of nonzero coefficients which is in practice the number
+      * of stored coefficients. */
+    inline int nonZeros() const { return derived().nonZeros(); }
+    /** \returns true if either the number of rows or the number of columns is equal to 1.
+      * In other words, this function returns
+      * \code rows()==1 || cols()==1 \endcode
+      * \sa rows(), cols(), IsVectorAtCompileTime. */
+    inline bool isVector() const { return rows()==1 || cols()==1; }
+    /** \returns the size of the storage major dimension,
+      * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
+    int outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }
+    /** \returns the size of the inner dimension according to the storage order,
+      * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
+    int innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
+      * exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
+      * reference to a matrix, not a matrix! It guaranteed however, that the return type of eval() is either
+      * PlainMatrixType or const PlainMatrixType&.
+      */
+    typedef typename ei_plain_matrix_type<Derived>::type PlainMatrixType;
+    /** \internal the column-major plain matrix type corresponding to this expression. Note that is not necessarily
+      * exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
+      * reference to a matrix, not a matrix!
+      * The only difference from PlainMatrixType is that PlainMatrixType_ColMajor is guaranteed to be column-major.
+      */
+    typedef typename ei_plain_matrix_type<Derived>::type PlainMatrixType_ColMajor;
+
+    /** \internal the return type of coeff()
+      */
+    typedef typename ei_meta_if<bool(int(Flags)&DirectAccessBit), const Scalar&, Scalar>::ret CoeffReturnType;
+
+    /** \internal Represents a matrix with all coefficients equal to one another*/
+    typedef CwiseNullaryOp<ei_scalar_constant_op<Scalar>,Derived> ConstantReturnType;
+    /** \internal Represents a scalar multiple of a matrix */
+    typedef CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, Derived> ScalarMultipleReturnType;
+    /** \internal Represents a quotient of a matrix by a scalar*/
+    typedef CwiseUnaryOp<ei_scalar_quotient1_op<Scalar>, Derived> ScalarQuotient1ReturnType;
+    /** \internal the return type of MatrixBase::conjugate() */
+    typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
+                        const CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, Derived>,
+                        const Derived&
+                     >::ret ConjugateReturnType;
+    /** \internal the return type of MatrixBase::real() */
+    typedef CwiseUnaryOp<ei_scalar_real_op<Scalar>, Derived> RealReturnType;
+    /** \internal the return type of MatrixBase::imag() */
+    typedef CwiseUnaryOp<ei_scalar_imag_op<Scalar>, Derived> ImagReturnType;
+    /** \internal the return type of MatrixBase::adjoint() */
+    typedef Eigen::Transpose<NestByValue<typename ei_cleantype<ConjugateReturnType>::type> >
+            AdjointReturnType;
+    /** \internal the return type of MatrixBase::eigenvalues() */
+    typedef Matrix<typename NumTraits<typename ei_traits<Derived>::Scalar>::Real, ei_traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+    /** \internal expression tyepe of a column */
+    typedef Block<Derived, ei_traits<Derived>::RowsAtCompileTime, 1> ColXpr;
+    /** \internal expression tyepe of a column */
+    typedef Block<Derived, 1, ei_traits<Derived>::ColsAtCompileTime> RowXpr;
+    /** \internal the return type of identity */
+    typedef CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> IdentityReturnType;
+    /** \internal the return type of unit vectors */
+    typedef Block<CwiseNullaryOp<ei_scalar_identity_op<Scalar>, SquareMatrixType>,
+                  ei_traits<Derived>::RowsAtCompileTime,
+                  ei_traits<Derived>::ColsAtCompileTime> BasisReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+
+    /** Copies \a other into *this. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& operator=(const MatrixBase<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)
+      */
+    inline Derived& operator=(const MatrixBase& other)
+    {
+      return this->operator=<Derived>(other);
+    }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** Copies \a other into *this without evaluating other. \returns a reference to *this. */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const MatrixBase<OtherDerived>& other);
+
+    /** Overloaded for cache friendly product evaluation */
+    template<typename Lhs, typename Rhs>
+    Derived& lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product);
+
+    /** Overloaded for cache friendly product evaluation */
+    template<typename OtherDerived>
+    Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>& other)
+    { return lazyAssign(other._expression()); }
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    CommaInitializer<Derived> operator<< (const Scalar& s);
+
+    template<typename OtherDerived>
+    CommaInitializer<Derived> operator<< (const MatrixBase<OtherDerived>& other);
+
+    const CoeffReturnType coeff(int row, int col) const;
+    const CoeffReturnType operator()(int row, int col) const;
+
+    Scalar& coeffRef(int row, int col);
+    Scalar& operator()(int row, int col);
+
+    const CoeffReturnType coeff(int index) const;
+    const CoeffReturnType operator[](int index) const;
+    const CoeffReturnType operator()(int index) const;
+
+    Scalar& coeffRef(int index);
+    Scalar& operator[](int index);
+    Scalar& operator()(int index);
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    template<typename OtherDerived>
+    void copyCoeff(int row, int col, const MatrixBase<OtherDerived>& other);
+    template<typename OtherDerived>
+    void copyCoeff(int index, const MatrixBase<OtherDerived>& other);
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(int row, int col, const MatrixBase<OtherDerived>& other);
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(int index, const MatrixBase<OtherDerived>& other);
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    template<int LoadMode>
+    PacketScalar packet(int row, int col) const;
+    template<int StoreMode>
+    void writePacket(int row, int col, const PacketScalar& x);
+
+    template<int LoadMode>
+    PacketScalar packet(int index) const;
+    template<int StoreMode>
+    void writePacket(int index, const PacketScalar& x);
+
+    const CoeffReturnType x() const;
+    const CoeffReturnType y() const;
+    const CoeffReturnType z() const;
+    const CoeffReturnType w() const;
+    Scalar& x();
+    Scalar& y();
+    Scalar& z();
+    Scalar& w();
+
+
+    const CwiseUnaryOp<ei_scalar_opposite_op<typename ei_traits<Derived>::Scalar>,Derived> operator-() const;
+
+    template<typename OtherDerived>
+    const CwiseBinaryOp<ei_scalar_sum_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
+    operator+(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    const CwiseBinaryOp<ei_scalar_difference_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
+    operator-(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    Derived& operator+=(const MatrixBase<OtherDerived>& other);
+    template<typename OtherDerived>
+    Derived& operator-=(const MatrixBase<OtherDerived>& other);
+
+    template<typename Lhs,typename Rhs>
+    Derived& operator+=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProduct>, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>& other);
+
+    Derived& operator*=(const Scalar& other);
+    Derived& operator/=(const Scalar& other);
+
+    const ScalarMultipleReturnType operator*(const Scalar& scalar) const;
+    #ifdef EIGEN_PARSED_BY_DOXYGEN
+    const ScalarMultipleReturnType operator*(const RealScalar& scalar) const;
+    #endif
+    const CwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<Derived>::Scalar>, Derived>
+    operator/(const Scalar& scalar) const;
+
+    inline friend const CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<Derived>::Scalar>, Derived>
+    operator*(const Scalar& scalar, const MatrixBase& matrix)
+    { return matrix*scalar; }
+
+
+    template<typename OtherDerived>
+    const typename ProductReturnType<Derived,OtherDerived>::Type
+    operator*(const MatrixBase<OtherDerived> &other) const;
+
+    template<typename OtherDerived>
+    Derived& operator*=(const MatrixBase<OtherDerived>& other);
+
+    template<typename OtherDerived>
+    typename ei_plain_matrix_type_column_major<OtherDerived>::type
+		solveTriangular(const MatrixBase<OtherDerived>& other) const;
+
+    template<typename OtherDerived>
+    void solveTriangularInPlace(const MatrixBase<OtherDerived>& other) const;
+
+
+    template<typename OtherDerived>
+    Scalar dot(const MatrixBase<OtherDerived>& other) const;
+    RealScalar squaredNorm() const;
+    RealScalar norm()  const;
+    RealScalar stableNorm()  const;
+    const PlainMatrixType normalized() const;
+    void normalize();
+
+    Eigen::Transpose<Derived> transpose();
+    const Eigen::Transpose<Derived> transpose() const;
+    void transposeInPlace();
+    const AdjointReturnType adjoint() const;
+    void adjointInPlace();
+
+    RowXpr row(int i);
+    const RowXpr row(int i) const;
+
+    ColXpr col(int i);
+    const ColXpr col(int i) const;
+
+    Minor<Derived> minor(int row, int col);
+    const Minor<Derived> minor(int row, int col) const;
+
+    typename BlockReturnType<Derived>::Type block(int startRow, int startCol, int blockRows, int blockCols);
+    const typename BlockReturnType<Derived>::Type
+    block(int startRow, int startCol, int blockRows, int blockCols) const;
+
+    typename BlockReturnType<Derived>::SubVectorType segment(int start, int size);
+    const typename BlockReturnType<Derived>::SubVectorType segment(int start, int size) const;
+
+    typename BlockReturnType<Derived,Dynamic>::SubVectorType start(int size);
+    const typename BlockReturnType<Derived,Dynamic>::SubVectorType start(int size) const;
+
+    typename BlockReturnType<Derived,Dynamic>::SubVectorType end(int size);
+    const typename BlockReturnType<Derived,Dynamic>::SubVectorType end(int size) const;
+
+    typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols);
+    const typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols) const;
+
+    template<int BlockRows, int BlockCols>
+    typename BlockReturnType<Derived, BlockRows, BlockCols>::Type block(int startRow, int startCol);
+    template<int BlockRows, int BlockCols>
+    const typename BlockReturnType<Derived, BlockRows, BlockCols>::Type block(int startRow, int startCol) const;
+
+    template<int CRows, int CCols>
+    typename BlockReturnType<Derived, CRows, CCols>::Type corner(CornerType type);
+    template<int CRows, int CCols>
+    const typename BlockReturnType<Derived, CRows, CCols>::Type corner(CornerType type) const;
+
+    template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType start(void);
+    template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType start() const;
+
+    template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType end();
+    template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType end() const;
+
+    template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType segment(int start);
+    template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType segment(int start) const;
+
+    Diagonal<Derived,0> diagonal();
+    const Diagonal<Derived,0> diagonal() const;
+
+    template<int Index> Diagonal<Derived,Index> diagonal();
+    template<int Index> const Diagonal<Derived,Index> diagonal() const;
+    
+    Diagonal<Derived, Dynamic> diagonal(int index);
+    const Diagonal<Derived, Dynamic> diagonal(int index) const;
+    
+    template<unsigned int Mode> Part<Derived, Mode> part();
+    template<unsigned int Mode> const Part<Derived, Mode> part() const;
+
+
+    static const ConstantReturnType
+    Constant(int rows, int cols, const Scalar& value);
+    static const ConstantReturnType
+    Constant(int size, const Scalar& value);
+    static const ConstantReturnType
+    Constant(const Scalar& value);
+
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(int rows, int cols, const CustomNullaryOp& func);
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(int size, const CustomNullaryOp& func);
+    template<typename CustomNullaryOp>
+    static const CwiseNullaryOp<CustomNullaryOp, Derived>
+    NullaryExpr(const CustomNullaryOp& func);
+
+    static const ConstantReturnType Zero(int rows, int cols);
+    static const ConstantReturnType Zero(int size);
+    static const ConstantReturnType Zero();
+    static const ConstantReturnType Ones(int rows, int cols);
+    static const ConstantReturnType Ones(int size);
+    static const ConstantReturnType Ones();
+    static const IdentityReturnType Identity();
+    static const IdentityReturnType Identity(int rows, int cols);
+    static const BasisReturnType Unit(int size, int i);
+    static const BasisReturnType Unit(int i);
+    static const BasisReturnType UnitX();
+    static const BasisReturnType UnitY();
+    static const BasisReturnType UnitZ();
+    static const BasisReturnType UnitW();
+
+    const DiagonalMatrixWrapper<Derived> asDiagonal() const;
+
+    void fill(const Scalar& value);
+    Derived& setConstant(const Scalar& value);
+    Derived& setZero();
+    Derived& setOnes();
+    Derived& setRandom();
+    Derived& setIdentity();
+
+
+    template<typename OtherDerived>
+    bool isApprox(const MatrixBase<OtherDerived>& other,
+                  RealScalar prec = precision<Scalar>()) const;
+    bool isMuchSmallerThan(const RealScalar& other,
+                           RealScalar prec = precision<Scalar>()) const;
+    template<typename OtherDerived>
+    bool isMuchSmallerThan(const MatrixBase<OtherDerived>& other,
+                           RealScalar prec = precision<Scalar>()) const;
+
+    bool isApproxToConstant(const Scalar& value, RealScalar prec = precision<Scalar>()) const;
+    bool isConstant(const Scalar& value, RealScalar prec = precision<Scalar>()) const;
+    bool isZero(RealScalar prec = precision<Scalar>()) const;
+    bool isOnes(RealScalar prec = precision<Scalar>()) const;
+    bool isIdentity(RealScalar prec = precision<Scalar>()) const;
+    bool isDiagonal(RealScalar prec = precision<Scalar>()) const;
+
+    bool isUpperTriangular(RealScalar prec = precision<Scalar>()) const;
+    bool isLowerTriangular(RealScalar prec = precision<Scalar>()) const;
+
+    template<typename OtherDerived>
+    bool isOrthogonal(const MatrixBase<OtherDerived>& other,
+                      RealScalar prec = precision<Scalar>()) const;
+    bool isUnitary(RealScalar prec = precision<Scalar>()) const;
+
+    template<typename OtherDerived>
+    inline bool operator==(const MatrixBase<OtherDerived>& other) const
+    { return (cwise() == other).all(); }
+
+    template<typename OtherDerived>
+    inline bool operator!=(const MatrixBase<OtherDerived>& other) const
+    { return (cwise() != other).any(); }
+
+
+    template<typename NewType>
+    typename ei_cast_return_type<
+        Derived,
+        const CwiseUnaryOp<ei_scalar_cast_op<typename ei_traits<Derived>::Scalar, NewType>, Derived>
+      >::type
+    cast() const;
+           
+    /** \returns the matrix or vector obtained by evaluating this expression.
+      *
+      * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+      * a const reference, in order to avoid a useless copy.
+      */
+    EIGEN_STRONG_INLINE const typename ei_eval<Derived>::type eval() const
+    { return typename ei_eval<Derived>::type(derived()); }
+
+    template<typename OtherDerived>
+    void swap(const MatrixBase<OtherDerived>& other);
+
+    template<unsigned int Added>
+    const Flagged<Derived, Added, 0> marked() const;
+    const Flagged<Derived, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit> lazy() const;
+
+    /** \returns number of elements to skip to pass from one row (resp. column) to another
+      * for a row-major (resp. column-major) matrix.
+      * Combined with coeffRef() and the \ref flags flags, it allows a direct access to the data
+      * of the underlying matrix.
+      */
+    inline int stride(void) const { return derived().stride(); }
+
+    inline const NestByValue<Derived> nestByValue() const;
+
+
+    ConjugateReturnType conjugate() const;
+    const RealReturnType real() const;
+    const ImagReturnType imag() const;
+
+    template<typename CustomUnaryOp>
+    const CwiseUnaryOp<CustomUnaryOp, Derived> unaryExpr(const CustomUnaryOp& func = CustomUnaryOp()) const;
+
+    template<typename CustomBinaryOp, typename OtherDerived>
+    const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>
+    binaryExpr(const MatrixBase<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const;
+
+
+    Scalar sum() const;
+    Scalar trace() const;
+
+    Scalar prod() const;
+
+    typename ei_traits<Derived>::Scalar minCoeff() const;
+    typename ei_traits<Derived>::Scalar maxCoeff() const;
+
+    typename ei_traits<Derived>::Scalar minCoeff(int* row, int* col = 0) const;
+    typename ei_traits<Derived>::Scalar maxCoeff(int* row, int* col = 0) const;
+
+    template<typename BinaryOp>
+    typename ei_result_of<BinaryOp(typename ei_traits<Derived>::Scalar)>::type
+    redux(const BinaryOp& func) const;
+
+    template<typename Visitor>
+    void visit(Visitor& func) const;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+    inline Derived& derived() { return *static_cast<Derived*>(this); }
+    inline Derived& const_cast_derived() const
+    { return *static_cast<Derived*>(const_cast<MatrixBase*>(this)); }
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    const Cwise<Derived> cwise() const;
+    Cwise<Derived> cwise();
+
+    inline const WithFormat<Derived> format(const IOFormat& fmt) const;
+
+/////////// Array module ///////////
+
+    bool all(void) const;
+    bool any(void) const;
+    int count() const;
+
+    const PartialRedux<Derived,Horizontal> rowwise() const;
+    const PartialRedux<Derived,Vertical> colwise() const;
+
+    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random(int rows, int cols);
+    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random(int size);
+    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random();
+
+    template<typename ThenDerived,typename ElseDerived>
+    const Select<Derived,ThenDerived,ElseDerived>
+    select(const MatrixBase<ThenDerived>& thenMatrix,
+           const MatrixBase<ElseDerived>& elseMatrix) const;
+
+    template<typename ThenDerived>
+    inline const Select<Derived,ThenDerived, NestByValue<typename ThenDerived::ConstantReturnType> >
+    select(const MatrixBase<ThenDerived>& thenMatrix, typename ThenDerived::Scalar elseScalar) const;
+
+    template<typename ElseDerived>
+    inline const Select<Derived, NestByValue<typename ElseDerived::ConstantReturnType>, ElseDerived >
+    select(typename ElseDerived::Scalar thenScalar, const MatrixBase<ElseDerived>& elseMatrix) const;
+
+    template<int p> RealScalar lpNorm() const;
+
+    template<int RowFactor, int ColFactor>
+    const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+    const Replicate<Derived,Dynamic,Dynamic> replicate(int rowFacor,int colFactor) const;
+
+    Eigen::Reverse<Derived, BothDirections> reverse();
+    const Eigen::Reverse<Derived, BothDirections> reverse() const;
+    void reverseInPlace();
+
+/////////// LU module ///////////
+
+    const LU<PlainMatrixType> lu() const;
+    const PartialLU<PlainMatrixType> partialLu() const;    
+    const PlainMatrixType inverse() const;
+    void computeInverse(PlainMatrixType *result) const;
+    Scalar determinant() const;
+
+/////////// Cholesky module ///////////
+
+    const LLT<PlainMatrixType>  llt() const;
+    const LDLT<PlainMatrixType> ldlt() const;
+
+/////////// QR module ///////////
+
+    const QR<PlainMatrixType> qr() const;
+
+    EigenvaluesReturnType eigenvalues() const;
+    RealScalar operatorNorm() const;
+
+/////////// SVD module ///////////
+
+    SVD<PlainMatrixType> svd() const;
+
+/////////// Geometry module ///////////
+
+    template<typename OtherDerived>
+    PlainMatrixType cross(const MatrixBase<OtherDerived>& other) const;
+    template<typename OtherDerived>
+    PlainMatrixType cross3(const MatrixBase<OtherDerived>& other) const;
+    PlainMatrixType unitOrthogonal(void) const;
+    Matrix<Scalar,3,1> eulerAngles(int a0, int a1, int a2) const;
+    const ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
+    enum {
+      SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
+    };
+    typedef Block<Derived,
+                  ei_traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
+                  ei_traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> StartMinusOne;
+    typedef CwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<Derived>::Scalar>,
+                NestByValue<StartMinusOne> > HNormalizedReturnType;
+
+    const HNormalizedReturnType hnormalized() const;
+    typedef Homogeneous<Derived,MatrixBase<Derived>::ColsAtCompileTime==1?Vertical:Horizontal> HomogeneousReturnType;
+    const HomogeneousReturnType homogeneous() const;
+
+/////////// Sparse module ///////////
+
+    // dense = spasre * dense
+    template<typename Derived1, typename Derived2>
+    Derived& lazyAssign(const SparseProduct<Derived1,Derived2,SparseTimeDenseProduct>& product);
+    // dense = dense * spasre
+    template<typename Derived1, typename Derived2>
+    Derived& lazyAssign(const SparseProduct<Derived1,Derived2,DenseTimeSparseProduct>& product);
+
+    template<typename OtherDerived,typename OtherEvalType>
+    Derived& operator=(const ReturnByValue<OtherDerived,OtherEvalType>& func);
+
+    #ifdef EIGEN_MATRIXBASE_PLUGIN
+    #include EIGEN_MATRIXBASE_PLUGIN
+    #endif
+};
+
+#endif // EIGEN_MATRIXBASE_H

Eigen/src/Core/MatrixStorage.h

@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MATRIXSTORAGE_H
+#define EIGEN_MATRIXSTORAGE_H
+
+struct ei_constructor_without_unaligned_array_assert {};
+
+/** \internal
+  * Static array automatically aligned if the total byte size is a multiple of 16 and the matrix options require auto alignment
+  */
+template <typename T, int Size, int MatrixOptions,
+          bool Align = (!(MatrixOptions&DontAlign)) && (((Size*sizeof(T))&0xf)==0)
+> struct ei_matrix_array
+{
+  EIGEN_ALIGN_128 T array[Size];
+
+  ei_matrix_array()
+  {
+    #ifndef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+    ei_assert((reinterpret_cast<size_t>(array) & 0xf) == 0
+              && "this assertion is explained here: http://eigen.tuxfamily.org/dox/UnalignedArrayAssert.html  **** READ THIS WEB PAGE !!! ****");
+    #endif
+  }
+
+  ei_matrix_array(ei_constructor_without_unaligned_array_assert) {}
+};
+
+template <typename T, int Size, int MatrixOptions> struct ei_matrix_array<T,Size,MatrixOptions,false>
+{
+  T array[Size];
+  ei_matrix_array() {}
+  ei_matrix_array(ei_constructor_without_unaligned_array_assert) {}
+};
+
+/** \internal
+  *
+  * \class ei_matrix_storage
+  *
+  * \brief Stores the data of a matrix
+  *
+  * This class stores the data of fixed-size, dynamic-size or mixed matrices
+  * in a way as compact as possible.
+  *
+  * \sa Matrix
+  */
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class ei_matrix_storage;
+
+// purely fixed-size matrix
+template<typename T, int Size, int _Rows, int _Cols, int _Options> class ei_matrix_storage
+{
+    ei_matrix_array<T,Size,_Options> m_data;
+  public:
+    inline explicit ei_matrix_storage() {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert)
+      : m_data(ei_constructor_without_unaligned_array_assert()) {}
+    inline ei_matrix_storage(int,int,int) {}
+    inline void swap(ei_matrix_storage& other) { std::swap(m_data,other.m_data); }
+    inline static int rows(void) {return _Rows;}
+    inline static int cols(void) {return _Cols;}
+    inline void resize(int,int,int) {}
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// null matrix
+template<typename T, int _Rows, int _Cols, int _Options> class ei_matrix_storage<T, 0, _Rows, _Cols, _Options>
+{
+  public:
+    inline explicit ei_matrix_storage() {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert) {}
+    inline ei_matrix_storage(int,int,int) {}
+    inline void swap(ei_matrix_storage& other) {}
+    inline static int rows(void) {return _Rows;}
+    inline static int cols(void) {return _Cols;}
+    inline void resize(int,int,int) {}
+    inline const T *data() const { return 0; }
+    inline T *data() { return 0; }
+};
+
+// dynamic-size matrix with fixed-size storage
+template<typename T, int Size, int _Options> class ei_matrix_storage<T, Size, Dynamic, Dynamic, _Options>
+{
+    ei_matrix_array<T,Size,_Options> m_data;
+    int m_rows;
+    int m_cols;
+  public:
+    inline explicit ei_matrix_storage() : m_rows(0), m_cols(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert)
+      : m_data(ei_constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
+    inline ei_matrix_storage(int, int rows, int cols) : m_rows(rows), m_cols(cols) {}
+    inline ~ei_matrix_storage() {}
+    inline void swap(ei_matrix_storage& other)
+    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+    inline int rows(void) const {return m_rows;}
+    inline int cols(void) const {return m_cols;}
+    inline void resize(int, int rows, int cols)
+    {
+      m_rows = rows;
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed width
+template<typename T, int Size, int _Cols, int _Options> class ei_matrix_storage<T, Size, Dynamic, _Cols, _Options>
+{
+    ei_matrix_array<T,Size,_Options> m_data;
+    int m_rows;
+  public:
+    inline explicit ei_matrix_storage() : m_rows(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert)
+      : m_data(ei_constructor_without_unaligned_array_assert()), m_rows(0) {}
+    inline ei_matrix_storage(int, int rows, int) : m_rows(rows) {}
+    inline ~ei_matrix_storage() {}
+    inline void swap(ei_matrix_storage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    inline int rows(void) const {return m_rows;}
+    inline int cols(void) const {return _Cols;}
+    inline void resize(int /*size*/, int rows, int)
+    {
+      m_rows = rows;
+    }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed height
+template<typename T, int Size, int _Rows, int _Options> class ei_matrix_storage<T, Size, _Rows, Dynamic, _Options>
+{
+    ei_matrix_array<T,Size,_Options> m_data;
+    int m_cols;
+  public:
+    inline explicit ei_matrix_storage() : m_cols(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert)
+      : m_data(ei_constructor_without_unaligned_array_assert()), m_cols(0) {}
+    inline ei_matrix_storage(int, int, int cols) : m_cols(cols) {}
+    inline ~ei_matrix_storage() {}
+    inline void swap(ei_matrix_storage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    inline int rows(void) const {return _Rows;}
+    inline int cols(void) const {return m_cols;}
+    inline void resize(int, int, int cols)
+    {
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data.array; }
+    inline T *data() { return m_data.array; }
+};
+
+// purely dynamic matrix.
+template<typename T, int _Options> class ei_matrix_storage<T, Dynamic, Dynamic, Dynamic, _Options>
+{
+    T *m_data;
+    int m_rows;
+    int m_cols;
+  public:
+    inline explicit ei_matrix_storage() : m_data(0), m_rows(0), m_cols(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert)
+       : m_data(0), m_rows(0), m_cols(0) {}
+    inline ei_matrix_storage(int size, int rows, int cols)
+      : m_data(ei_aligned_new<T>(size)), m_rows(rows), m_cols(cols) {}
+    inline ~ei_matrix_storage() { ei_aligned_delete(m_data, m_rows*m_cols); }
+    inline void swap(ei_matrix_storage& other)
+    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
+    inline int rows(void) const {return m_rows;}
+    inline int cols(void) const {return m_cols;}
+    void resize(int size, int rows, int cols)
+    {
+      if(size != m_rows*m_cols)
+      {
+        ei_aligned_delete(m_data, m_rows*m_cols);
+        if (size)
+          m_data = ei_aligned_new<T>(size);
+        else
+          m_data = 0;
+      }
+      m_rows = rows;
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+// matrix with dynamic width and fixed height (so that matrix has dynamic size).
+template<typename T, int _Rows, int _Options> class ei_matrix_storage<T, Dynamic, _Rows, Dynamic, _Options>
+{
+    T *m_data;
+    int m_cols;
+  public:
+    inline explicit ei_matrix_storage() : m_data(0), m_cols(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
+    inline ei_matrix_storage(int size, int, int cols) : m_data(ei_aligned_new<T>(size)), m_cols(cols) {}
+    inline ~ei_matrix_storage() { ei_aligned_delete(m_data, _Rows*m_cols); }
+    inline void swap(ei_matrix_storage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
+    inline static int rows(void) {return _Rows;}
+    inline int cols(void) const {return m_cols;}
+    void resize(int size, int, int cols)
+    {
+      if(size != _Rows*m_cols)
+      {
+        ei_aligned_delete(m_data, _Rows*m_cols);
+        if (size)
+          m_data = ei_aligned_new<T>(size);
+        else
+          m_data = 0;
+      }
+      m_cols = cols;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+// matrix with dynamic height and fixed width (so that matrix has dynamic size).
+template<typename T, int _Cols, int _Options> class ei_matrix_storage<T, Dynamic, Dynamic, _Cols, _Options>
+{
+    T *m_data;
+    int m_rows;
+  public:
+    inline explicit ei_matrix_storage() : m_data(0), m_rows(0) {}
+    inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
+    inline ei_matrix_storage(int size, int rows, int) : m_data(ei_aligned_new<T>(size)), m_rows(rows) {}
+    inline ~ei_matrix_storage() { ei_aligned_delete(m_data, _Cols*m_rows); }
+    inline void swap(ei_matrix_storage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
+    inline int rows(void) const {return m_rows;}
+    inline static int cols(void) {return _Cols;}
+    void resize(int size, int rows, int)
+    {
+      if(size != m_rows*_Cols)
+      {
+        ei_aligned_delete(m_data, _Cols*m_rows);
+        if (size)
+          m_data = ei_aligned_new<T>(size);
+        else
+          m_data = 0;
+      }
+      m_rows = rows;
+    }
+    inline const T *data() const { return m_data; }
+    inline T *data() { return m_data; }
+};
+
+#endif // EIGEN_MATRIX_H

Eigen/src/Core/Minor.h

@@ -0,0 +1,122 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MINOR_H
+#define EIGEN_MINOR_H
+
+/** \nonstableyet 
+  * \class Minor
+  *
+  * \brief Expression of a minor
+  *
+  * \param MatrixType the type of the object in which we are taking a minor
+  *
+  * This class represents an expression of a minor. It is the return
+  * type of MatrixBase::minor() and most of the time this is the only way it
+  * is used.
+  *
+  * \sa MatrixBase::minor()
+  */
+template<typename MatrixType>
+struct ei_traits<Minor<MatrixType> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = (MatrixType::RowsAtCompileTime != Dynamic) ?
+                          int(MatrixType::RowsAtCompileTime) - 1 : Dynamic,
+    ColsAtCompileTime = (MatrixType::ColsAtCompileTime != Dynamic) ?
+                          int(MatrixType::ColsAtCompileTime) - 1 : Dynamic,
+    MaxRowsAtCompileTime = (MatrixType::MaxRowsAtCompileTime != Dynamic) ?
+                             int(MatrixType::MaxRowsAtCompileTime) - 1 : Dynamic,
+    MaxColsAtCompileTime = (MatrixType::MaxColsAtCompileTime != Dynamic) ?
+                             int(MatrixType::MaxColsAtCompileTime) - 1 : Dynamic,
+    Flags = _MatrixTypeNested::Flags & HereditaryBits,
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType> class Minor
+  : public MatrixBase<Minor<MatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Minor)
+
+    inline Minor(const MatrixType& matrix,
+                       int row, int col)
+      : m_matrix(matrix), m_row(row), m_col(col)
+    {
+      ei_assert(row >= 0 && row < matrix.rows()
+          && col >= 0 && col < matrix.cols());
+    }
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Minor)
+
+    inline int rows() const { return m_matrix.rows() - 1; }
+    inline int cols() const { return m_matrix.cols() - 1; }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(row + (row >= m_row), col + (col >= m_col));
+    }
+
+    inline const Scalar coeff(int row, int col) const
+    {
+      return m_matrix.coeff(row + (row >= m_row), col + (col >= m_col));
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+    const int m_row, m_col;
+};
+
+/** \nonstableyet 
+  * \return an expression of the (\a row, \a col)-minor of *this,
+  * i.e. an expression constructed from *this by removing the specified
+  * row and column.
+  *
+  * Example: \include MatrixBase_minor.cpp
+  * Output: \verbinclude MatrixBase_minor.out
+  *
+  * \sa class Minor
+  */
+template<typename Derived>
+inline Minor<Derived>
+MatrixBase<Derived>::minor(int row, int col)
+{
+  return Minor<Derived>(derived(), row, col);
+}
+
+/** \nonstableyet 
+  * This is the const version of minor(). */
+template<typename Derived>
+inline const Minor<Derived>
+MatrixBase<Derived>::minor(int row, int col) const
+{
+  return Minor<Derived>(derived(), row, col);
+}
+
+#endif // EIGEN_MINOR_H

Eigen/src/Core/NestByValue.h

@@ -0,0 +1,116 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_NESTBYVALUE_H
+#define EIGEN_NESTBYVALUE_H
+
+/** \class NestByValue
+  *
+  * \brief Expression which must be nested by value
+  *
+  * \param ExpressionType the type of the object of which we are requiring nesting-by-value
+  *
+  * This class is the return type of MatrixBase::nestByValue()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::nestByValue()
+  */
+template<typename ExpressionType>
+struct ei_traits<NestByValue<ExpressionType> > : public ei_traits<ExpressionType>
+{};
+
+template<typename ExpressionType> class NestByValue
+  : public MatrixBase<NestByValue<ExpressionType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(NestByValue)
+
+    inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
+
+    inline int rows() const { return m_expression.rows(); }
+    inline int cols() const { return m_expression.cols(); }
+    inline int stride() const { return m_expression.stride(); }
+
+    inline const CoeffReturnType coeff(int row, int col) const
+    {
+      return m_expression.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline const CoeffReturnType coeff(int index) const
+    {
+      return m_expression.coeff(index);
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int row, int col) const
+    {
+      return m_expression.template packet<LoadMode>(row, col);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int index) const
+    {
+      return m_expression.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+    
+    operator const ExpressionType&() const { return m_expression; }
+
+  protected:
+    const ExpressionType m_expression;
+};
+
+/** \returns an expression of the temporary version of *this.
+  */
+template<typename Derived>
+inline const NestByValue<Derived>
+MatrixBase<Derived>::nestByValue() const
+{
+  return NestByValue<Derived>(derived());
+}
+
+#endif // EIGEN_NESTBYVALUE_H

Eigen/src/Core/NumTraits.h

@@ -0,0 +1,142 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_NUMTRAITS_H
+#define EIGEN_NUMTRAITS_H
+
+/** \class NumTraits
+  *
+  * \brief Holds some data about the various numeric (i.e. scalar) types allowed by Eigen.
+  *
+  * \param T the numeric type about which this class provides data. Recall that Eigen allows
+  *          only the following types for \a T: \c int, \c float, \c double,
+  *          \c std::complex<float>, \c std::complex<double>, and \c long \c double (especially
+  *          useful to enforce x87 arithmetics when SSE is the default).
+  *
+  * The provided data consists of:
+  * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
+  *     then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
+  *     is a typedef to \a U.
+  * \li A typedef \a FloatingPoint, giving the "floating-point type" of \a T. If \a T is
+  *     \c int, then \a FloatingPoint is a typedef to \c double. Otherwise, \a FloatingPoint
+  *     is a typedef to \a T.
+  * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
+  *     type, and to 0 otherwise.
+  * \li An enum \a HasFloatingPoint. It is equal to \c 0 if \a T is \c int,
+  *     and to \c 1 otherwise.
+  */
+template<typename T> struct NumTraits;
+
+template<> struct NumTraits<int>
+{
+  typedef int Real;
+  typedef double FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 0,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+template<> struct NumTraits<float>
+{
+  typedef float Real;
+  typedef float FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 1,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+template<> struct NumTraits<double>
+{
+  typedef double Real;
+  typedef double FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 1,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+template<typename _Real> struct NumTraits<std::complex<_Real> >
+{
+  typedef _Real Real;
+  typedef std::complex<_Real> FloatingPoint;
+  enum {
+    IsComplex = 1,
+    HasFloatingPoint = NumTraits<Real>::HasFloatingPoint,
+    ReadCost = 2,
+    AddCost = 2 * NumTraits<Real>::AddCost,
+    MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
+  };
+};
+
+template<> struct NumTraits<long long int>
+{
+  typedef long long int Real;
+  typedef long double FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 0,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+template<> struct NumTraits<long double>
+{
+  typedef long double Real;
+  typedef long double FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 1,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+template<> struct NumTraits<bool>
+{
+  typedef bool Real;
+  typedef float FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 0,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+#endif // EIGEN_NUMTRAITS_H

Eigen/src/Core/Part.h

@@ -0,0 +1,375 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PART_H
+#define EIGEN_PART_H
+
+/** \nonstableyet
+  * \class Part
+  *
+  * \brief Expression of a triangular matrix extracted from a given matrix
+  *
+  * \param MatrixType the type of the object in which we are taking the triangular part
+  * \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular, StrictlyUpperTriangular,
+  *             UnitUpperTriangular, LowerTriangular, StrictlyLowerTriangular, UnitLowerTriangular. This is in fact a bit field; it must have either
+  *             UpperTriangularBit or LowerTriangularBit, and additionnaly it may have either ZeroDiagBit or
+  *             UnitDiagBit.
+  *
+  * This class represents an expression of the upper or lower triangular part of
+  * a square matrix, possibly with a further assumption on the diagonal. It is the return type
+  * of MatrixBase::part() and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::part()
+  */
+template<typename MatrixType, unsigned int Mode>
+struct ei_traits<Part<MatrixType, Mode> > : ei_traits<MatrixType>
+{
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    Flags = (_MatrixTypeNested::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode,
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType, unsigned int Mode> class Part
+  : public MatrixBase<Part<MatrixType, Mode> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Part)
+
+    inline Part(const MatrixType& matrix) : m_matrix(matrix)
+    { ei_assert(ei_are_flags_consistent<Mode>::ret); }
+
+    /** \sa MatrixBase::operator+=() */
+    template<typename Other> Part&  operator+=(const Other& other);
+    /** \sa MatrixBase::operator-=() */
+    template<typename Other> Part&  operator-=(const Other& other);
+    /** \sa MatrixBase::operator*=() */
+    Part&  operator*=(const typename ei_traits<MatrixType>::Scalar& other);
+    /** \sa MatrixBase::operator/=() */
+    Part&  operator/=(const typename ei_traits<MatrixType>::Scalar& other);
+
+    /** \sa operator=(), MatrixBase::lazyAssign() */
+    template<typename Other> void lazyAssign(const Other& other);
+    /** \sa MatrixBase::operator=() */
+    template<typename Other> Part& operator=(const Other& other);
+
+    inline int rows() const { return m_matrix.rows(); }
+    inline int cols() const { return m_matrix.cols(); }
+    inline int stride() const { return m_matrix.stride(); }
+
+    inline Scalar coeff(int row, int col) const
+    {
+      // SelfAdjointBit doesn't play any role here: just because a matrix is selfadjoint doesn't say anything about
+      // each individual coefficient, except for the not-very-useful-here fact that diagonal coefficients are real.
+      if( ((Flags & LowerTriangularBit) && (col>row)) || ((Flags & UpperTriangularBit) && (row>col)) )
+        return (Scalar)0;
+      if(Flags & UnitDiagBit)
+        return col==row ? (Scalar)1 : m_matrix.coeff(row, col);
+      else if(Flags & ZeroDiagBit)
+        return col==row ? (Scalar)0 : m_matrix.coeff(row, col);
+      else
+        return m_matrix.coeff(row, col);
+    }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      EIGEN_STATIC_ASSERT(!(Flags & UnitDiagBit), WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED)
+      EIGEN_STATIC_ASSERT(!(Flags & SelfAdjointBit), COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED)
+      ei_assert(   (Mode==UpperTriangular && col>=row)
+                || (Mode==LowerTriangular && col<=row)
+                || (Mode==StrictlyUpperTriangular && col>row)
+                || (Mode==StrictlyLowerTriangular && col<row));
+      return m_matrix.const_cast_derived().coeffRef(row, col);
+    }
+
+    /** \internal */
+    const MatrixType& _expression() const { return m_matrix; }
+
+    /** discard any writes to a row */
+    const Block<Part, 1, ColsAtCompileTime> row(int i) { return Base::row(i); }
+    const Block<Part, 1, ColsAtCompileTime> row(int i) const { return Base::row(i); }
+    /** discard any writes to a column */
+    const Block<Part, RowsAtCompileTime, 1> col(int i) { return Base::col(i); }
+    const Block<Part, RowsAtCompileTime, 1> col(int i) const { return Base::col(i); }
+
+    template<typename OtherDerived>
+    void swap(const MatrixBase<OtherDerived>& other)
+    {
+      Part<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived());
+    }
+
+  protected:
+
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \nonstableyet
+  * \returns an expression of a triangular matrix extracted from the current matrix
+  *
+  * The parameter \a Mode can have the following values: \c UpperTriangular, \c StrictlyUpperTriangular, \c UnitUpperTriangular,
+  * \c LowerTriangular, \c StrictlyLowerTriangular, \c UnitLowerTriangular.
+  *
+  * \addexample PartExample \label How to extract a triangular part of an arbitrary matrix
+  *
+  * Example: \include MatrixBase_extract.cpp
+  * Output: \verbinclude MatrixBase_extract.out
+  *
+  * \sa class Part, part(), marked()
+  */
+template<typename Derived>
+template<unsigned int Mode>
+const Part<Derived, Mode> MatrixBase<Derived>::part() const
+{
+  return derived();
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename Other>
+inline Part<MatrixType, Mode>& Part<MatrixType, Mode>::operator=(const Other& other)
+{
+  if(Other::Flags & EvalBeforeAssigningBit)
+  {
+    typename MatrixBase<Other>::PlainMatrixType other_evaluated(other.rows(), other.cols());
+    other_evaluated.template part<Mode>().lazyAssign(other);
+    lazyAssign(other_evaluated);
+  }
+  else
+    lazyAssign(other.derived());
+  return *this;
+}
+
+template<typename Derived1, typename Derived2, unsigned int Mode, int UnrollCount>
+struct ei_part_assignment_impl
+{
+  enum {
+    col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived1::RowsAtCompileTime
+  };
+
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    ei_part_assignment_impl<Derived1, Derived2, Mode, UnrollCount-1>::run(dst, src);
+
+    if(Mode == SelfAdjoint)
+    {
+      if(row == col)
+        dst.coeffRef(row, col) = ei_real(src.coeff(row, col));
+      else if(row < col)
+        dst.coeffRef(col, row) = ei_conj(dst.coeffRef(row, col) = src.coeff(row, col));
+    }
+    else
+    {
+      ei_assert(Mode == UpperTriangular || Mode == LowerTriangular || Mode == StrictlyUpperTriangular || Mode == StrictlyLowerTriangular);
+      if((Mode == UpperTriangular && row <= col)
+      || (Mode == LowerTriangular && row >= col)
+      || (Mode == StrictlyUpperTriangular && row < col)
+      || (Mode == StrictlyLowerTriangular && row > col))
+        dst.copyCoeff(row, col, src);
+    }
+  }
+};
+
+template<typename Derived1, typename Derived2, unsigned int Mode>
+struct ei_part_assignment_impl<Derived1, Derived2, Mode, 1>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    if(!(Mode & ZeroDiagBit))
+      dst.copyCoeff(0, 0, src);
+  }
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<typename Derived1, typename Derived2, unsigned int Mode>
+struct ei_part_assignment_impl<Derived1, Derived2, Mode, 0>
+{
+  inline static void run(Derived1 &, const Derived2 &) {}
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_part_assignment_impl<Derived1, Derived2, UpperTriangular, Dynamic>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(int j = 0; j < dst.cols(); ++j)
+      for(int i = 0; i <= j; ++i)
+        dst.copyCoeff(i, j, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_part_assignment_impl<Derived1, Derived2, LowerTriangular, Dynamic>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(int j = 0; j < dst.cols(); ++j)
+      for(int i = j; i < dst.rows(); ++i)
+        dst.copyCoeff(i, j, src);
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct ei_part_assignment_impl<Derived1, Derived2, StrictlyUpperTriangular, Dynamic>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(int j = 0; j < dst.cols(); ++j)
+      for(int i = 0; i < j; ++i)
+        dst.copyCoeff(i, j, src);
+  }
+};
+template<typename Derived1, typename Derived2>
+struct ei_part_assignment_impl<Derived1, Derived2, StrictlyLowerTriangular, Dynamic>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(int j = 0; j < dst.cols(); ++j)
+      for(int i = j+1; i < dst.rows(); ++i)
+        dst.copyCoeff(i, j, src);
+  }
+};
+template<typename Derived1, typename Derived2>
+struct ei_part_assignment_impl<Derived1, Derived2, SelfAdjoint, Dynamic>
+{
+  inline static void run(Derived1 &dst, const Derived2 &src)
+  {
+    for(int j = 0; j < dst.cols(); ++j)
+    {
+      for(int i = 0; i < j; ++i)
+        dst.coeffRef(j, i) = ei_conj(dst.coeffRef(i, j) = src.coeff(i, j));
+      dst.coeffRef(j, j) = ei_real(src.coeff(j, j));
+    }
+  }
+};
+
+template<typename MatrixType, unsigned int Mode>
+template<typename Other>
+void Part<MatrixType, Mode>::lazyAssign(const Other& other)
+{
+  const bool unroll = MatrixType::SizeAtCompileTime * Other::CoeffReadCost / 2 <= EIGEN_UNROLLING_LIMIT;
+  ei_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
+
+  ei_part_assignment_impl
+    <MatrixType, Other, Mode,
+    unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic
+    >::run(m_matrix.const_cast_derived(), other.derived());
+}
+
+/** \nonstableyet
+  * \returns a lvalue pseudo-expression allowing to perform special operations on \c *this.
+  *
+  * The \a Mode parameter can have the following values: \c UpperTriangular, \c StrictlyUpperTriangular, \c LowerTriangular,
+  * \c StrictlyLowerTriangular, \c SelfAdjoint.
+  *
+  * \addexample PartExample \label How to write to a triangular part of a matrix
+  *
+  * Example: \include MatrixBase_part.cpp
+  * Output: \verbinclude MatrixBase_part.out
+  *
+  * \sa class Part, MatrixBase::extract(), MatrixBase::marked()
+  */
+template<typename Derived>
+template<unsigned int Mode>
+inline Part<Derived, Mode> MatrixBase<Derived>::part()
+{
+  return Part<Derived, Mode>(derived());
+}
+
+/** \returns true if *this is approximately equal to an upper triangular matrix,
+  *          within the precision given by \a prec.
+  *
+  * \sa isLowerTriangular(), extract(), part(), marked()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
+{
+  if(cols() != rows()) return false;
+  RealScalar maxAbsOnUpperTriangularPart = static_cast<RealScalar>(-1);
+  for(int j = 0; j < cols(); ++j)
+    for(int i = 0; i <= j; ++i)
+    {
+      RealScalar absValue = ei_abs(coeff(i,j));
+      if(absValue > maxAbsOnUpperTriangularPart) maxAbsOnUpperTriangularPart = absValue;
+    }
+  for(int j = 0; j < cols()-1; ++j)
+    for(int i = j+1; i < rows(); ++i)
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperTriangularPart, prec)) return false;
+  return true;
+}
+
+/** \returns true if *this is approximately equal to a lower triangular matrix,
+  *          within the precision given by \a prec.
+  *
+  * \sa isUpperTriangular(), extract(), part(), marked()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
+{
+  if(cols() != rows()) return false;
+  RealScalar maxAbsOnLowerTriangularPart = static_cast<RealScalar>(-1);
+  for(int j = 0; j < cols(); ++j)
+    for(int i = j; i < rows(); ++i)
+    {
+      RealScalar absValue = ei_abs(coeff(i,j));
+      if(absValue > maxAbsOnLowerTriangularPart) maxAbsOnLowerTriangularPart = absValue;
+    }
+  for(int j = 1; j < cols(); ++j)
+    for(int i = 0; i < j; ++i)
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerTriangularPart, prec)) return false;
+  return true;
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename Other>
+inline Part<MatrixType, Mode>& Part<MatrixType, Mode>::operator+=(const Other& other)
+{
+  return *this = m_matrix + other;
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename Other>
+inline Part<MatrixType, Mode>& Part<MatrixType, Mode>::operator-=(const Other& other)
+{
+  return *this = m_matrix - other;
+}
+
+template<typename MatrixType, unsigned int Mode>
+inline Part<MatrixType, Mode>& Part<MatrixType, Mode>::operator*=
+(const typename ei_traits<MatrixType>::Scalar& other)
+{
+  return *this = m_matrix * other;
+}
+
+template<typename MatrixType, unsigned int Mode>
+inline Part<MatrixType, Mode>& Part<MatrixType, Mode>::operator/=
+(const typename ei_traits<MatrixType>::Scalar& other)
+{
+  return *this = m_matrix / other;
+}
+
+#endif // EIGEN_PART_H

Eigen/src/Core/Product.h

@@ -0,0 +1,769 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PRODUCT_H
+#define EIGEN_PRODUCT_H
+
+/***************************
+*** Forward declarations ***
+***************************/
+
+template<int VectorizationMode, int Index, typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl;
+
+template<int StorageOrder, int Index, typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl;
+
+/** \class ProductReturnType
+  *
+  * \brief Helper class to get the correct and optimized returned type of operator*
+  *
+  * \param Lhs the type of the left-hand side
+  * \param Rhs the type of the right-hand side
+  * \param ProductMode the type of the product (determined automatically by ei_product_mode)
+  *
+  * This class defines the typename Type representing the optimized product expression
+  * between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
+  * is the recommended way to define the result type of a function returning an expression
+  * which involve a matrix product. The class Product or DiagonalProduct should never be
+  * used directly.
+  *
+  * \sa class Product, class DiagonalProduct, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+  */
+template<typename Lhs, typename Rhs, int ProductMode>
+struct ProductReturnType
+{
+  typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+  typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+
+  typedef Product<LhsNested, RhsNested, ProductMode> Type;
+};
+
+// cache friendly specialization
+// note that there is a DiagonalProduct specialization in DiagonalProduct.h
+template<typename Lhs, typename Rhs>
+struct ProductReturnType<Lhs,Rhs,CacheFriendlyProduct>
+{
+  typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+
+  typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime,
+                             typename ei_plain_matrix_type_column_major<Rhs>::type
+                   >::type RhsNested;
+
+  typedef Product<LhsNested, RhsNested, CacheFriendlyProduct> Type;
+};
+
+/*  Helper class to determine the type of the product, can be either:
+ *    - NormalProduct
+ *    - CacheFriendlyProduct
+ *    - DiagonalProduct
+ */
+template<typename Lhs, typename Rhs> struct ei_product_mode
+{
+  enum{
+
+    value = ei_is_diagonal<Rhs>::ret || ei_is_diagonal<Lhs>::ret
+          ? DiagonalProduct
+          : Lhs::MaxColsAtCompileTime == Dynamic
+            && ( Lhs::MaxRowsAtCompileTime == Dynamic
+              || Rhs::MaxColsAtCompileTime == Dynamic )
+            && (!(Rhs::IsVectorAtCompileTime && (Lhs::Flags&RowMajorBit)  && (!(Lhs::Flags&DirectAccessBit))))
+            && (!(Lhs::IsVectorAtCompileTime && (!(Rhs::Flags&RowMajorBit)) && (!(Rhs::Flags&DirectAccessBit))))
+            && (ei_is_same_type<typename Lhs::Scalar, typename Rhs::Scalar>::ret)
+          ? CacheFriendlyProduct
+          : NormalProduct };
+};
+
+/** \class Product
+  *
+  * \brief Expression of the product of two matrices
+  *
+  * \param LhsNested the type used to store the left-hand side
+  * \param RhsNested the type used to store the right-hand side
+  * \param ProductMode the type of the product
+  *
+  * This class represents an expression of the product of two matrices.
+  * It is the return type of the operator* between matrices. Its template
+  * arguments are determined automatically by ProductReturnType. Therefore,
+  * Product should never be used direclty. To determine the result type of a
+  * function which involves a matrix product, use ProductReturnType::Type.
+  *
+  * \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
+  */
+template<typename LhsNested, typename RhsNested, int ProductMode>
+struct ei_traits<Product<LhsNested, RhsNested, ProductMode> >
+{
+  // clean the nested types:
+  typedef typename ei_cleantype<LhsNested>::type _LhsNested;
+  typedef typename ei_cleantype<RhsNested>::type _RhsNested;
+  typedef typename ei_scalar_product_traits<typename _LhsNested::Scalar, typename _RhsNested::Scalar>::ReturnType Scalar;
+
+  enum {
+    LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+    RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+
+    RowsAtCompileTime = _LhsNested::RowsAtCompileTime,
+    ColsAtCompileTime = _RhsNested::ColsAtCompileTime,
+    InnerSize = EIGEN_ENUM_MIN(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime),
+
+    MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,
+
+    LhsRowMajor = LhsFlags & RowMajorBit,
+    RhsRowMajor = RhsFlags & RowMajorBit,
+
+    CanVectorizeRhs = RhsRowMajor && (RhsFlags & PacketAccessBit)
+                    && (ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+
+    CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit)
+                    && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+
+    EvalToRowMajor = RhsRowMajor && (ProductMode==(int)CacheFriendlyProduct ? LhsRowMajor : (!CanVectorizeLhs)),
+
+    RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
+
+    Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
+          | EvalBeforeAssigningBit
+          | EvalBeforeNestingBit
+          | (CanVectorizeLhs || CanVectorizeRhs ? PacketAccessBit : 0)
+          | (LhsFlags & RhsFlags & AlignedBit),
+
+    CoeffReadCost = InnerSize == Dynamic ? Dynamic
+                  : InnerSize * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
+                    + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
+
+    /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside
+     * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner
+     * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect
+     * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI.
+     */
+    CanVectorizeInner = LhsRowMajor && (!RhsRowMajor) && (LhsFlags & RhsFlags & ActualPacketAccessBit)
+                      && (InnerSize % ei_packet_traits<Scalar>::size == 0)
+  };
+};
+
+template<typename LhsNested, typename RhsNested, int ProductMode> class Product : ei_no_assignment_operator,
+  public MatrixBase<Product<LhsNested, RhsNested, ProductMode> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+
+  private:
+
+    typedef typename ei_traits<Product>::_LhsNested _LhsNested;
+    typedef typename ei_traits<Product>::_RhsNested _RhsNested;
+
+    enum {
+      PacketSize = ei_packet_traits<Scalar>::size,
+      InnerSize  = ei_traits<Product>::InnerSize,
+      Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
+      CanVectorizeInner = ei_traits<Product>::CanVectorizeInner
+    };
+
+    typedef ei_product_coeff_impl<CanVectorizeInner ? InnerVectorization : NoVectorization,
+                                  Unroll ? InnerSize-1 : Dynamic,
+                                  _LhsNested, _RhsNested, Scalar> ScalarCoeffImpl;
+
+  public:
+
+    template<typename Lhs, typename Rhs>
+    inline Product(const Lhs& lhs, const Rhs& rhs)
+      : m_lhs(lhs), m_rhs(rhs)
+    {
+      // we don't allow taking products of matrices of different real types, as that wouldn't be vectorizable.
+      // We still allow to mix T and complex<T>.
+      EIGEN_STATIC_ASSERT((ei_is_same_type<typename Lhs::RealScalar, typename Rhs::RealScalar>::ret),
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+      ei_assert(lhs.cols() == rhs.rows()
+        && "invalid matrix product"
+        && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
+    }
+
+    /** \internal
+      * compute \a res += \c *this using the cache friendly product.
+      */
+    template<typename DestDerived>
+    void _cacheFriendlyEvalAndAdd(DestDerived& res) const;
+
+    /** \internal
+      * \returns whether it is worth it to use the cache friendly product.
+      */
+    EIGEN_STRONG_INLINE bool _useCacheFriendlyProduct() const
+    {
+      return  m_lhs.cols()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+              && (  rows()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+                 || cols()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD);
+    }
+
+    EIGEN_STRONG_INLINE int rows() const { return m_lhs.rows(); }
+    EIGEN_STRONG_INLINE int cols() const { return m_rhs.cols(); }
+
+    EIGEN_STRONG_INLINE const Scalar coeff(int row, int col) const
+    {
+      Scalar res;
+      ScalarCoeffImpl::run(row, col, m_lhs, m_rhs, res);
+      return res;
+    }
+
+    /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,
+     * which is why we don't set the LinearAccessBit.
+     */
+    EIGEN_STRONG_INLINE const Scalar coeff(int index) const
+    {
+      Scalar res;
+      const int row = RowsAtCompileTime == 1 ? 0 : index;
+      const int col = RowsAtCompileTime == 1 ? index : 0;
+      ScalarCoeffImpl::run(row, col, m_lhs, m_rhs, res);
+      return res;
+    }
+
+    template<int LoadMode>
+    EIGEN_STRONG_INLINE const PacketScalar packet(int row, int col) const
+    {
+      PacketScalar res;
+      ei_product_packet_impl<Flags&RowMajorBit ? RowMajor : ColMajor,
+                                   Unroll ? InnerSize-1 : Dynamic,
+                                   _LhsNested, _RhsNested, PacketScalar, LoadMode>
+        ::run(row, col, m_lhs, m_rhs, res);
+      return res;
+    }
+
+    EIGEN_STRONG_INLINE const _LhsNested& lhs() const { return m_lhs; }
+    EIGEN_STRONG_INLINE const _RhsNested& rhs() const { return m_rhs; }
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+};
+
+/** \returns the matrix product of \c *this and \a other.
+  *
+  * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
+  *
+  * \sa lazy(), operator*=(const MatrixBase&), Cwise::operator*()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline const typename ProductReturnType<Derived,OtherDerived>::Type
+MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+  enum {
+    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
+                   || OtherDerived::RowsAtCompileTime==Dynamic
+                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+  };
+  // note to the lost user:
+  //    * for a dot product use: v1.dot(v2)
+  //    * for a coeff-wise product use: v1.cwise()*v2
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+  return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
+}
+
+/** replaces \c *this by \c *this * \a other.
+  *
+  * \returns a reference to \c *this
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived &
+MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
+{
+  return *this = *this * other;
+}
+
+/***************************************************************************
+* Normal product .coeff() implementation (with meta-unrolling)
+***************************************************************************/
+
+/**************************************
+*** Scalar path  - no vectorization ***
+**************************************/
+
+template<int Index, typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<NoVectorization, Index, Lhs, Rhs, RetScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+  {
+    ei_product_coeff_impl<NoVectorization, Index-1, Lhs, Rhs, RetScalar>::run(row, col, lhs, rhs, res);
+    res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<NoVectorization, 0, Lhs, Rhs, RetScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+  {
+    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<NoVectorization, Dynamic, Lhs, Rhs, RetScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, RetScalar& res)
+  {
+    ei_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = lhs.coeff(row, 0) * rhs.coeff(0, col);
+      for(int i = 1; i < lhs.cols(); ++i)
+        res += lhs.coeff(row, i) * rhs.coeff(i, col);
+  }
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<NoVectorization, -1, Lhs, Rhs, RetScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int, int, const Lhs&, const Rhs&, RetScalar&) {}
+};
+
+/*******************************************
+*** Scalar path with inner vectorization ***
+*******************************************/
+
+template<int Index, typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_product_coeff_vectorized_unroller
+{
+  enum { PacketSize = ei_packet_traits<typename Lhs::Scalar>::size };
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, typename Lhs::PacketScalar &pres)
+  {
+    ei_product_coeff_vectorized_unroller<Index-PacketSize, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, pres);
+    pres = ei_padd(pres, ei_pmul( lhs.template packet<Aligned>(row, Index) , rhs.template packet<Aligned>(Index, col) ));
+  }
+};
+
+template<typename Lhs, typename Rhs, typename PacketScalar>
+struct ei_product_coeff_vectorized_unroller<0, Lhs, Rhs, PacketScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, typename Lhs::PacketScalar &pres)
+  {
+    pres = ei_pmul(lhs.template packet<Aligned>(row, 0) , rhs.template packet<Aligned>(0, col));
+  }
+};
+
+template<int Index, typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<InnerVectorization, Index, Lhs, Rhs, RetScalar>
+{
+  typedef typename Lhs::PacketScalar PacketScalar;
+  enum { PacketSize = ei_packet_traits<typename Lhs::Scalar>::size };
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, RetScalar &res)
+  {
+    PacketScalar pres;
+    ei_product_coeff_vectorized_unroller<Index+1-PacketSize, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, pres);
+    ei_product_coeff_impl<NoVectorization,Index,Lhs,Rhs,RetScalar>::run(row, col, lhs, rhs, res);
+    res = ei_predux(pres);
+  }
+};
+
+template<typename Lhs, typename Rhs, int LhsRows = Lhs::RowsAtCompileTime, int RhsCols = Rhs::ColsAtCompileTime>
+struct ei_product_coeff_vectorized_dyn_selector
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+  {
+    res = ei_dot_impl<
+      Block<Lhs, 1, ei_traits<Lhs>::ColsAtCompileTime>,
+      Block<Rhs, ei_traits<Rhs>::RowsAtCompileTime, 1>,
+      LinearVectorization, NoUnrolling>::run(lhs.row(row), rhs.col(col));
+  }
+};
+
+// NOTE the 3 following specializations are because taking .col(0) on a vector is a bit slower
+// NOTE maybe they are now useless since we have a specialization for Block<Matrix>
+template<typename Lhs, typename Rhs, int RhsCols>
+struct ei_product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,RhsCols>
+{
+  EIGEN_STRONG_INLINE static void run(int /*row*/, int col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+  {
+    res = ei_dot_impl<
+      Lhs,
+      Block<Rhs, ei_traits<Rhs>::RowsAtCompileTime, 1>,
+      LinearVectorization, NoUnrolling>::run(lhs, rhs.col(col));
+  }
+};
+
+template<typename Lhs, typename Rhs, int LhsRows>
+struct ei_product_coeff_vectorized_dyn_selector<Lhs,Rhs,LhsRows,1>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int /*col*/, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+  {
+    res = ei_dot_impl<
+      Block<Lhs, 1, ei_traits<Lhs>::ColsAtCompileTime>,
+      Rhs,
+      LinearVectorization, NoUnrolling>::run(lhs.row(row), rhs);
+  }
+};
+
+template<typename Lhs, typename Rhs>
+struct ei_product_coeff_vectorized_dyn_selector<Lhs,Rhs,1,1>
+{
+  EIGEN_STRONG_INLINE static void run(int /*row*/, int /*col*/, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+  {
+    res = ei_dot_impl<
+      Lhs,
+      Rhs,
+      LinearVectorization, NoUnrolling>::run(lhs, rhs);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename RetScalar>
+struct ei_product_coeff_impl<InnerVectorization, Dynamic, Lhs, Rhs, RetScalar>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, typename Lhs::Scalar &res)
+  {
+    ei_product_coeff_vectorized_dyn_selector<Lhs,Rhs>::run(row, col, lhs, rhs, res);
+  }
+};
+
+/*******************
+*** Packet path  ***
+*******************/
+
+template<int Index, typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<RowMajor, Index, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    ei_product_packet_impl<RowMajor, Index-1, Lhs, Rhs, PacketScalar, LoadMode>::run(row, col, lhs, rhs, res);
+    res =  ei_pmadd(ei_pset1(lhs.coeff(row, Index)), rhs.template packet<LoadMode>(Index, col), res);
+  }
+};
+
+template<int Index, typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<ColMajor, Index, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    ei_product_packet_impl<ColMajor, Index-1, Lhs, Rhs, PacketScalar, LoadMode>::run(row, col, lhs, rhs, res);
+    res =  ei_pmadd(lhs.template packet<LoadMode>(row, Index), ei_pset1(rhs.coeff(Index, col)), res);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<RowMajor, 0, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
+  }
+};
+
+template<typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<ColMajor, 0, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
+  {
+    res = ei_pmul(lhs.template packet<LoadMode>(row, 0), ei_pset1(rhs.coeff(0, col)));
+  }
+};
+
+template<typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar& res)
+  {
+    ei_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.template packet<LoadMode>(0, col));
+      for(int i = 1; i < lhs.cols(); ++i)
+        res =  ei_pmadd(ei_pset1(lhs.coeff(row, i)), rhs.template packet<LoadMode>(i, col), res);
+  }
+};
+
+template<typename Lhs, typename Rhs, typename PacketScalar, int LoadMode>
+struct ei_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, PacketScalar, LoadMode>
+{
+  EIGEN_STRONG_INLINE static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar& res)
+  {
+    ei_assert(lhs.cols()>0 && "you are using a non initialized matrix");
+    res = ei_pmul(lhs.template packet<LoadMode>(row, 0), ei_pset1(rhs.coeff(0, col)));
+      for(int i = 1; i < lhs.cols(); ++i)
+        res =  ei_pmadd(lhs.template packet<LoadMode>(row, i), ei_pset1(rhs.coeff(i, col)), res);
+  }
+};
+
+/***************************************************************************
+* Cache friendly product callers and specific nested evaluation strategies
+***************************************************************************/
+
+template<typename Scalar, typename RhsType>
+static void ei_cache_friendly_product_colmajor_times_vector(
+  int size, const Scalar* lhs, int lhsStride, const RhsType& rhs, Scalar* res);
+
+template<typename Scalar, typename ResType>
+static void ei_cache_friendly_product_rowmajor_times_vector(
+  const Scalar* lhs, int lhsStride, const Scalar* rhs, int rhsSize, ResType& res);
+
+template<typename ProductType,
+  int LhsRows  = ei_traits<ProductType>::RowsAtCompileTime,
+  int LhsOrder = int(ei_traits<ProductType>::LhsFlags)&RowMajorBit ? RowMajor : ColMajor,
+  int LhsHasDirectAccess = int(ei_traits<ProductType>::LhsFlags)&DirectAccessBit? HasDirectAccess : NoDirectAccess,
+  int RhsCols  = ei_traits<ProductType>::ColsAtCompileTime,
+  int RhsOrder = int(ei_traits<ProductType>::RhsFlags)&RowMajorBit ? RowMajor : ColMajor,
+  int RhsHasDirectAccess = int(ei_traits<ProductType>::RhsFlags)&DirectAccessBit? HasDirectAccess : NoDirectAccess>
+struct ei_cache_friendly_product_selector
+{
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    product._cacheFriendlyEvalAndAdd(res);
+  }
+};
+
+// optimized colmajor * vector path
+template<typename ProductType, int LhsRows, int RhsOrder, int RhsAccess>
+struct ei_cache_friendly_product_selector<ProductType,LhsRows,ColMajor,NoDirectAccess,1,RhsOrder,RhsAccess>
+{
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    const int size = product.rhs().rows();
+    for (int k=0; k<size; ++k)
+        res += product.rhs().coeff(k) * product.lhs().col(k);
+  }
+};
+
+// optimized cache friendly colmajor * vector path for matrix with direct access flag
+// NOTE this path could also be enabled for expressions if we add runtime align queries
+template<typename ProductType, int LhsRows, int RhsOrder, int RhsAccess>
+struct ei_cache_friendly_product_selector<ProductType,LhsRows,ColMajor,HasDirectAccess,1,RhsOrder,RhsAccess>
+{
+  typedef typename ProductType::Scalar Scalar;
+
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    enum {
+      EvalToRes = (ei_packet_traits<Scalar>::size==1)
+                ||((DestDerived::Flags&ActualPacketAccessBit) && (!(DestDerived::Flags & RowMajorBit))) };
+    Scalar* EIGEN_RESTRICT _res;
+    if (EvalToRes)
+       _res = &res.coeffRef(0);
+    else
+    {
+      _res = ei_aligned_stack_new(Scalar,res.size());
+      Map<Matrix<Scalar,DestDerived::RowsAtCompileTime,1> >(_res, res.size()) = res;
+    }
+    ei_cache_friendly_product_colmajor_times_vector(res.size(),
+      &product.lhs().const_cast_derived().coeffRef(0,0), product.lhs().stride(),
+      product.rhs(), _res);
+
+    if (!EvalToRes)
+    {
+      res = Map<Matrix<Scalar,DestDerived::SizeAtCompileTime,1> >(_res, res.size());
+      ei_aligned_stack_delete(Scalar, _res, res.size());
+    }
+  }
+};
+
+// optimized vector * rowmajor path
+template<typename ProductType, int LhsOrder, int LhsAccess, int RhsCols>
+struct ei_cache_friendly_product_selector<ProductType,1,LhsOrder,LhsAccess,RhsCols,RowMajor,NoDirectAccess>
+{
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    const int cols = product.lhs().cols();
+    for (int j=0; j<cols; ++j)
+      res += product.lhs().coeff(j) * product.rhs().row(j);
+  }
+};
+
+// optimized cache friendly vector * rowmajor path for matrix with direct access flag
+// NOTE this path coul also be enabled for expressions if we add runtime align queries
+template<typename ProductType, int LhsOrder, int LhsAccess, int RhsCols>
+struct ei_cache_friendly_product_selector<ProductType,1,LhsOrder,LhsAccess,RhsCols,RowMajor,HasDirectAccess>
+{
+  typedef typename ProductType::Scalar Scalar;
+
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    enum {
+      EvalToRes = (ei_packet_traits<Scalar>::size==1)
+                ||((DestDerived::Flags & ActualPacketAccessBit) && (DestDerived::Flags & RowMajorBit)) };
+    Scalar* EIGEN_RESTRICT _res;
+    if (EvalToRes)
+       _res = &res.coeffRef(0);
+    else
+    {
+      _res = ei_aligned_stack_new(Scalar, res.size());
+      Map<Matrix<Scalar,DestDerived::SizeAtCompileTime,1> >(_res, res.size()) = res;
+    }
+    ei_cache_friendly_product_colmajor_times_vector(res.size(),
+      &product.rhs().const_cast_derived().coeffRef(0,0), product.rhs().stride(),
+      product.lhs().transpose(), _res);
+
+    if (!EvalToRes)
+    {
+      res = Map<Matrix<Scalar,DestDerived::SizeAtCompileTime,1> >(_res, res.size());
+      ei_aligned_stack_delete(Scalar, _res, res.size());
+    }
+  }
+};
+
+// optimized rowmajor - vector product
+template<typename ProductType, int LhsRows, int RhsOrder, int RhsAccess>
+struct ei_cache_friendly_product_selector<ProductType,LhsRows,RowMajor,HasDirectAccess,1,RhsOrder,RhsAccess>
+{
+  typedef typename ProductType::Scalar Scalar;
+  typedef typename ei_traits<ProductType>::_RhsNested Rhs;
+  enum {
+      UseRhsDirectly = ((ei_packet_traits<Scalar>::size==1) || (Rhs::Flags&ActualPacketAccessBit))
+                     && (!(Rhs::Flags & RowMajorBit)) };
+
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    Scalar* EIGEN_RESTRICT _rhs;
+    if (UseRhsDirectly)
+       _rhs = &product.rhs().const_cast_derived().coeffRef(0);
+    else
+    {
+      _rhs = ei_aligned_stack_new(Scalar, product.rhs().size());
+      Map<Matrix<Scalar,Rhs::SizeAtCompileTime,1> >(_rhs, product.rhs().size()) = product.rhs();
+    }
+    ei_cache_friendly_product_rowmajor_times_vector(&product.lhs().const_cast_derived().coeffRef(0,0), product.lhs().stride(),
+                                                    _rhs, product.rhs().size(), res);
+
+    if (!UseRhsDirectly) ei_aligned_stack_delete(Scalar, _rhs, product.rhs().size());
+  }
+};
+
+// optimized vector - colmajor product
+template<typename ProductType, int LhsOrder, int LhsAccess, int RhsCols>
+struct ei_cache_friendly_product_selector<ProductType,1,LhsOrder,LhsAccess,RhsCols,ColMajor,HasDirectAccess>
+{
+  typedef typename ProductType::Scalar Scalar;
+  typedef typename ei_traits<ProductType>::_LhsNested Lhs;
+  enum {
+      UseLhsDirectly = ((ei_packet_traits<Scalar>::size==1) || (Lhs::Flags&ActualPacketAccessBit))
+                     && (Lhs::Flags & RowMajorBit) };
+
+  template<typename DestDerived>
+  inline static void run(DestDerived& res, const ProductType& product)
+  {
+    Scalar* EIGEN_RESTRICT _lhs;
+    if (UseLhsDirectly)
+       _lhs = &product.lhs().const_cast_derived().coeffRef(0);
+    else
+    {
+      _lhs = ei_aligned_stack_new(Scalar, product.lhs().size());
+      Map<Matrix<Scalar,Lhs::SizeAtCompileTime,1> >(_lhs, product.lhs().size()) = product.lhs();
+    }
+    ei_cache_friendly_product_rowmajor_times_vector(&product.rhs().const_cast_derived().coeffRef(0,0), product.rhs().stride(),
+                                                    _lhs, product.lhs().size(), res);
+
+    if(!UseLhsDirectly) ei_aligned_stack_delete(Scalar, _lhs, product.lhs().size());
+  }
+};
+
+// discard this case which has to be handled by the default path
+// (we keep it to be sure to hit a compilation error if this is not the case)
+template<typename ProductType, int LhsRows, int RhsOrder, int RhsAccess>
+struct ei_cache_friendly_product_selector<ProductType,LhsRows,RowMajor,NoDirectAccess,1,RhsOrder,RhsAccess>
+{};
+
+// discard this case which has to be handled by the default path
+// (we keep it to be sure to hit a compilation error if this is not the case)
+template<typename ProductType, int LhsOrder, int LhsAccess, int RhsCols>
+struct ei_cache_friendly_product_selector<ProductType,1,LhsOrder,LhsAccess,RhsCols,ColMajor,NoDirectAccess>
+{};
+
+
+/** \internal */
+template<typename Derived>
+template<typename Lhs,typename Rhs>
+inline Derived&
+MatrixBase<Derived>::operator+=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProduct>, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>& other)
+{
+  if (other._expression()._useCacheFriendlyProduct())
+    ei_cache_friendly_product_selector<Product<Lhs,Rhs,CacheFriendlyProduct> >::run(const_cast_derived(), other._expression());
+  else
+    lazyAssign(derived() + other._expression());
+  return derived();
+}
+
+template<typename Derived>
+template<typename Lhs, typename Rhs>
+inline Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)
+{
+  if (product._useCacheFriendlyProduct())
+  {
+    setZero();
+    ei_cache_friendly_product_selector<Product<Lhs,Rhs,CacheFriendlyProduct> >::run(const_cast_derived(), product);
+  }
+  else
+  {
+    lazyAssign<Product<Lhs,Rhs,CacheFriendlyProduct> >(product);
+  }
+  return derived();
+}
+
+template<typename T> struct ei_product_copy_rhs
+{
+  typedef typename ei_meta_if<
+         (ei_traits<T>::Flags & RowMajorBit)
+      || (!(ei_traits<T>::Flags & DirectAccessBit)),
+      typename ei_plain_matrix_type_column_major<T>::type,
+      const T&
+    >::ret type;
+};
+
+template<typename T> struct ei_product_copy_lhs
+{
+  typedef typename ei_meta_if<
+      (!(int(ei_traits<T>::Flags) & DirectAccessBit)),
+      typename ei_plain_matrix_type<T>::type,
+      const T&
+    >::ret type;
+};
+
+template<typename Lhs, typename Rhs, int ProductMode>
+template<typename DestDerived>
+inline void Product<Lhs,Rhs,ProductMode>::_cacheFriendlyEvalAndAdd(DestDerived& res) const
+{
+  typedef typename ei_product_copy_lhs<_LhsNested>::type LhsCopy;
+  typedef typename ei_unref<LhsCopy>::type _LhsCopy;
+  typedef typename ei_product_copy_rhs<_RhsNested>::type RhsCopy;
+  typedef typename ei_unref<RhsCopy>::type _RhsCopy;
+  LhsCopy lhs(m_lhs);
+  RhsCopy rhs(m_rhs);
+  ei_cache_friendly_product<Scalar>(
+    rows(), cols(), lhs.cols(),
+    _LhsCopy::Flags&RowMajorBit, (const Scalar*)&(lhs.const_cast_derived().coeffRef(0,0)), lhs.stride(),
+    _RhsCopy::Flags&RowMajorBit, (const Scalar*)&(rhs.const_cast_derived().coeffRef(0,0)), rhs.stride(),
+    Flags&RowMajorBit, (Scalar*)&(res.coeffRef(0,0)), res.stride()
+  );
+}
+
+#endif // EIGEN_PRODUCT_H

Eigen/src/Core/Redux.h

@@ -0,0 +1,371 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_REDUX_H
+#define EIGEN_REDUX_H
+
+// TODO
+//  * implement other kind of vectorization
+//  * factorize code
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Func, typename Derived>
+struct ei_redux_traits
+{
+private:
+  enum {
+    PacketSize = ei_packet_traits<typename Derived::Scalar>::size,
+    InnerMaxSize = int(Derived::Flags)&RowMajorBit
+                 ? Derived::MaxColsAtCompileTime
+                 : Derived::MaxRowsAtCompileTime
+  };
+
+  enum {
+    MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
+                  && (ei_functor_traits<Func>::PacketAccess),
+    MayLinearVectorize = MightVectorize && (int(Derived::Flags)&LinearAccessBit),
+    MaySliceVectorize  = MightVectorize && int(InnerMaxSize)>=3*PacketSize 
+  };
+
+public:
+  enum {
+    Vectorization = int(MayLinearVectorize) ? int(LinearVectorization)
+                  : int(MaySliceVectorize)  ? int(SliceVectorization)
+                                            : int(NoVectorization)
+  };
+  
+private:
+  enum {
+    Cost = Derived::SizeAtCompileTime * Derived::CoeffReadCost
+           + (Derived::SizeAtCompileTime-1) * NumTraits<typename Derived::Scalar>::AddCost,
+    UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Vectorization) == int(NoVectorization) ? 1 : int(PacketSize))
+  };
+
+public:
+  enum {
+    Unrolling = Cost <= UnrollingLimit
+              ? CompleteUnrolling
+              : NoUnrolling
+  };
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Func, typename Derived, int Start, int Length>
+struct ei_redux_novec_unroller
+{
+  enum {
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func& func)
+  {
+    return func(ei_redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+                ei_redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
+  }
+};
+
+template<typename Func, typename Derived, int Start>
+struct ei_redux_novec_unroller<Func, Derived, Start, 1>
+{
+  enum {
+    col = Start / Derived::RowsAtCompileTime,
+    row = Start % Derived::RowsAtCompileTime
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func&)
+  {
+    return mat.coeff(row, col);
+  }
+};
+
+/*** vectorization ***/
+  
+template<typename Func, typename Derived, int Start, int Length>
+struct ei_redux_vec_unroller
+{
+  enum {
+    PacketSize = ei_packet_traits<typename Derived::Scalar>::size,
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func& func)
+  {
+    return func.packetOp(
+            ei_redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
+            ei_redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
+  }
+};
+
+template<typename Func, typename Derived, int Start>
+struct ei_redux_vec_unroller<Func, Derived, Start, 1>
+{
+  enum {
+    index = Start * ei_packet_traits<typename Derived::Scalar>::size,
+    row = int(Derived::Flags)&RowMajorBit
+        ? index / int(Derived::ColsAtCompileTime)
+        : index % Derived::RowsAtCompileTime,
+    col = int(Derived::Flags)&RowMajorBit
+        ? index % int(Derived::ColsAtCompileTime)
+        : index / Derived::RowsAtCompileTime,
+    alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func&)
+  {
+    return mat.template packet<alignment>(row, col);
+  }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Func, typename Derived,
+         int Vectorization = ei_redux_traits<Func, Derived>::Vectorization,
+         int Unrolling = ei_redux_traits<Func, Derived>::Unrolling
+>
+struct ei_redux_impl;
+
+template<typename Func, typename Derived>
+struct ei_redux_impl<Func, Derived, NoVectorization, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  static Scalar run(const Derived& mat, const Func& func)
+  {
+    ei_assert(mat.rows()>0 && mat.cols()>0 && "you are using a non initialized matrix");
+    Scalar res;
+    res = mat.coeff(0, 0);
+    for(int i = 1; i < mat.rows(); ++i)
+      res = func(res, mat.coeff(i, 0));
+    for(int j = 1; j < mat.cols(); ++j)
+      for(int i = 0; i < mat.rows(); ++i)
+        res = func(res, mat.coeff(i, j));
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct ei_redux_impl<Func,Derived, NoVectorization, CompleteUnrolling>
+  : public ei_redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
+{};
+
+template<typename Func, typename Derived>
+struct ei_redux_impl<Func, Derived, LinearVectorization, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  static Scalar run(const Derived& mat, const Func& func)
+  {
+    const int size = mat.size();
+    const int packetSize = ei_packet_traits<Scalar>::size;
+    const int alignedStart =  (Derived::Flags & AlignedBit)
+                           || !(Derived::Flags & DirectAccessBit)
+                           ? 0
+                           : ei_alignmentOffset(&mat.const_cast_derived().coeffRef(0), size);
+    enum {
+      alignment = (Derived::Flags & DirectAccessBit) || (Derived::Flags & AlignedBit)
+                ? Aligned : Unaligned
+    };
+    const int alignedSize = ((size-alignedStart)/packetSize)*packetSize;
+    const int alignedEnd = alignedStart + alignedSize;
+    Scalar res;
+    if(alignedSize)
+    {
+      PacketScalar packet_res = mat.template packet<alignment>(alignedStart);
+      for(int index = alignedStart + packetSize; index < alignedEnd; index += packetSize)
+        packet_res = func.packetOp(packet_res, mat.template packet<alignment>(index));
+      res = func.predux(packet_res);
+      
+      for(int index = 0; index < alignedStart; ++index)
+        res = func(res,mat.coeff(index));
+
+      for(int index = alignedEnd; index < size; ++index)
+        res = func(res,mat.coeff(index));
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = mat.coeff(0);
+      for(int index = 1; index < size; ++index)
+        res = func(res,mat.coeff(index));
+    }
+
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct ei_redux_impl<Func, Derived, SliceVectorization, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  static Scalar run(const Derived& mat, const Func& func)
+  {
+    const int innerSize = mat.innerSize();
+    const int outerSize = mat.outerSize();
+    enum {
+      packetSize = ei_packet_traits<Scalar>::size,
+      isRowMajor = Derived::Flags&RowMajorBit?1:0
+    };
+    const int packetedInnerSize = ((innerSize)/packetSize)*packetSize;
+    Scalar res;
+    if(packetedInnerSize)
+    {
+      PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
+      for(int j=0; j<outerSize; ++j)
+        for(int i=0; i<packetedInnerSize; i+=int(packetSize))
+          packet_res = func.packetOp(packet_res, mat.template packet<Unaligned>
+                                                 (isRowMajor?j:i, isRowMajor?i:j));
+      
+      res = func.predux(packet_res);
+      for(int j=0; j<outerSize; ++j)
+        for(int i=packetedInnerSize; i<innerSize; ++i)
+          res = func(res, mat.coeff(isRowMajor?j:i, isRowMajor?i:j));
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = ei_redux_impl<Func, Derived, NoVectorization, NoUnrolling>::run(mat, func);
+    }
+
+    return res;
+  }
+};
+
+template<typename Func, typename Derived>
+struct ei_redux_impl<Func, Derived, LinearVectorization, CompleteUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  enum {
+    PacketSize = ei_packet_traits<Scalar>::size,
+    Size = Derived::SizeAtCompileTime,
+    VectorizationSize = (Size / PacketSize) * PacketSize
+  };
+  EIGEN_STRONG_INLINE static Scalar run(const Derived& mat, const Func& func)
+  {
+    Scalar res = func.predux(ei_redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
+    if (VectorizationSize != Size)
+      res = func(res,ei_redux_novec_unroller<Func, Derived, VectorizationSize, Size-VectorizationSize>::run(mat,func));
+    return res;
+  }
+};
+
+
+/** \returns the result of a full redux operation on the whole matrix or vector using \a func
+  *
+  * The template parameter \a BinaryOp is the type of the functor \a func which must be
+  * an assiociative operator. Both current STL and TR1 functor styles are handled.
+  *
+  * \sa MatrixBase::sum(), MatrixBase::minCoeff(), MatrixBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
+  */
+template<typename Derived>
+template<typename Func>
+inline typename ei_result_of<Func(typename ei_traits<Derived>::Scalar)>::type
+MatrixBase<Derived>::redux(const Func& func) const
+{
+  typename Derived::Nested nested(derived());
+  typedef typename ei_cleantype<typename Derived::Nested>::type ThisNested;
+  return ei_redux_impl<Func, ThisNested>
+            ::run(nested, func);
+}
+
+/** \returns the minimum of all coefficients of *this
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::minCoeff() const
+{
+  return this->redux(Eigen::ei_scalar_min_op<Scalar>());
+}
+
+/** \returns the maximum of all coefficients of *this
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::maxCoeff() const
+{
+  return this->redux(Eigen::ei_scalar_max_op<Scalar>());
+}
+
+/** \returns the sum of all coefficients of *this
+  *
+  * \sa trace(), prod()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::sum() const
+{
+  return this->redux(Eigen::ei_scalar_sum_op<Scalar>());
+}
+
+/** \returns the product of all coefficients of *this
+  *
+  * Example: \include MatrixBase_prod.cpp
+  * Output: \verbinclude MatrixBase_prod.out
+  *
+  * \sa sum()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::prod() const
+{
+  return this->redux(Eigen::ei_scalar_product_op<Scalar>());
+}
+
+/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
+  *
+  * \c *this can be any matrix, not necessarily square.
+  *
+  * \sa diagonal(), sum()
+  */
+template<typename Derived>
+EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::trace() const
+{
+  return diagonal().sum();
+}
+
+#endif // EIGEN_REDUX_H

Eigen/src/Core/ReturnByValue.h

@@ -0,0 +1,73 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_RETURNBYVALUE_H
+#define EIGEN_RETURNBYVALUE_H
+
+/** \class ReturnByValue
+  *
+  */
+template<typename Functor, typename _Scalar,int _Rows,int _Cols,int _Options,int _MaxRows,int _MaxCols>
+struct ei_traits<ReturnByValue<Functor,Matrix<_Scalar,_Rows,_Cols,_Options,_MaxRows,_MaxCols> > >
+  : public ei_traits<Matrix<_Scalar,_Rows,_Cols,_Options,_MaxRows,_MaxCols> >
+{
+  enum {
+    Flags = ei_traits<Matrix<_Scalar,_Rows,_Cols,_Options,_MaxRows,_MaxCols> >::Flags | EvalBeforeNestingBit
+  };
+};
+
+template<typename Functor,typename EvalTypeDerived,int n>
+struct ei_nested<ReturnByValue<Functor,MatrixBase<EvalTypeDerived> >, n, EvalTypeDerived>
+{
+  typedef EvalTypeDerived type;
+};
+
+template<typename Functor, typename EvalType> class ReturnByValue
+{
+  public:
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const
+    { static_cast<const Functor*>(this)->evalTo(dst); }
+};
+
+template<typename Functor, typename _Scalar,int _Rows,int _Cols,int _Options,int _MaxRows,int _MaxCols>
+  class ReturnByValue<Functor,Matrix<_Scalar,_Rows,_Cols,_Options,_MaxRows,_MaxCols> >
+  : public MatrixBase<ReturnByValue<Functor,Matrix<_Scalar,_Rows,_Cols,_Options,_MaxRows,_MaxCols> > >
+{
+  public:
+    EIGEN_GENERIC_PUBLIC_INTERFACE(ReturnByValue)
+    template<typename Dest>
+    inline void evalTo(Dest& dst) const
+    { static_cast<const Functor* const>(this)->evalTo(dst); }
+};
+
+template<typename Derived>
+template<typename OtherDerived,typename OtherEvalType>
+Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived,OtherEvalType>& other)
+{
+  other.evalTo(derived());
+  return derived();
+}
+
+#endif // EIGEN_RETURNBYVALUE_H

Eigen/src/Core/SolveTriangular.h

@@ -0,0 +1,297 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SOLVETRIANGULAR_H
+#define EIGEN_SOLVETRIANGULAR_H
+
+template<typename XprType> struct ei_is_part { enum {value=false}; };
+template<typename XprType, unsigned int Mode> struct ei_is_part<Part<XprType,Mode> > { enum {value=true}; };
+
+template<typename Lhs, typename Rhs,
+  int TriangularPart = (int(Lhs::Flags) & LowerTriangularBit)
+                     ? LowerTriangular
+                     : (int(Lhs::Flags) & UpperTriangularBit)
+                     ? UpperTriangular
+                     : 0xffffff,
+  int StorageOrder = ei_is_part<Lhs>::value ? 0xffffff  // this is to solve ambiguous specializations
+                   : int(Lhs::Flags) & (RowMajorBit|SparseBit)
+  >
+struct ei_solve_triangular_selector;
+
+// transform a Part xpr to a Flagged xpr
+template<typename Lhs, unsigned int LhsMode, typename Rhs, int UpLo, int StorageOrder>
+struct ei_solve_triangular_selector<Part<Lhs,LhsMode>,Rhs,UpLo,StorageOrder>
+{
+  static void run(const Part<Lhs,LhsMode>& lhs, Rhs& other)
+  {
+    ei_solve_triangular_selector<Flagged<Lhs,LhsMode,0>,Rhs>::run(lhs._expression(), other);
+  }
+};
+
+// forward substitution, row-major
+template<typename Lhs, typename Rhs, int UpLo>
+struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense>
+{
+  typedef typename Rhs::Scalar Scalar;
+  static void run(const Lhs& lhs, Rhs& other)
+  {
+    const bool IsLowerTriangular = (UpLo==LowerTriangular);
+    const int size = lhs.cols();
+    /* We perform the inverse product per block of 4 rows such that we perfectly match
+     * our optimized matrix * vector product. blockyStart represents the number of rows
+     * we have process first using the non-block version.
+     */
+    int blockyStart = (std::max(size-5,0)/4)*4;
+    if (IsLowerTriangular)
+      blockyStart = size - blockyStart;
+    else
+      blockyStart -= 1;
+    for(int c=0 ; c<other.cols() ; ++c)
+    {
+      // process first rows using the non block version
+      if(!(Lhs::Flags & UnitDiagBit))
+      {
+        if (IsLowerTriangular)
+          other.coeffRef(0,c) = other.coeff(0,c)/lhs.coeff(0, 0);
+        else
+          other.coeffRef(size-1,c) = other.coeff(size-1, c)/lhs.coeff(size-1, size-1);
+      }
+      for(int i=(IsLowerTriangular ? 1 : size-2); IsLowerTriangular ? i<blockyStart : i>blockyStart; i += (IsLowerTriangular ? 1 : -1) )
+      {
+        Scalar tmp = other.coeff(i,c)
+          - (IsLowerTriangular ? ((lhs.row(i).start(i)) * other.col(c).start(i)).coeff(0,0)
+                     : ((lhs.row(i).end(size-i-1)) * other.col(c).end(size-i-1)).coeff(0,0));
+        if (Lhs::Flags & UnitDiagBit)
+          other.coeffRef(i,c) = tmp;
+        else
+          other.coeffRef(i,c) = tmp/lhs.coeff(i,i);
+      }
+
+      // now let's process the remaining rows 4 at once
+      for(int i=blockyStart; IsLowerTriangular ? i<size : i>0; )
+      {
+        int startBlock = i;
+        int endBlock = startBlock + (IsLowerTriangular ? 4 : -4);
+
+        /* Process the i cols times 4 rows block, and keep the result in a temporary vector */
+        // FIXME use fixed size block but take care to small fixed size matrices...
+        Matrix<Scalar,Dynamic,1> btmp(4);
+        if (IsLowerTriangular)
+          btmp = lhs.block(startBlock,0,4,i) * other.col(c).start(i);
+        else
+          btmp = lhs.block(i-3,i+1,4,size-1-i) * other.col(c).end(size-1-i);
+
+        /* Let's process the 4x4 sub-matrix as usual.
+         * btmp stores the diagonal coefficients used to update the remaining part of the result.
+         */
+        {
+          Scalar tmp = other.coeff(startBlock,c)-btmp.coeff(IsLowerTriangular?0:3);
+          if (Lhs::Flags & UnitDiagBit)
+            other.coeffRef(i,c) = tmp;
+          else
+            other.coeffRef(i,c) = tmp/lhs.coeff(i,i);
+        }
+
+        i += IsLowerTriangular ? 1 : -1;
+        for (;IsLowerTriangular ? i<endBlock : i>endBlock; i += IsLowerTriangular ? 1 : -1)
+        {
+          int remainingSize = IsLowerTriangular ? i-startBlock : startBlock-i;
+          Scalar tmp = other.coeff(i,c)
+            - btmp.coeff(IsLowerTriangular ? remainingSize : 3-remainingSize)
+            - (   lhs.row(i).segment(IsLowerTriangular ? startBlock : i+1, remainingSize)
+              * other.col(c).segment(IsLowerTriangular ? startBlock : i+1, remainingSize)).coeff(0,0);
+
+          if (Lhs::Flags & UnitDiagBit)
+            other.coeffRef(i,c) = tmp;
+          else
+            other.coeffRef(i,c) = tmp/lhs.coeff(i,i);
+        }
+      }
+    }
+  }
+};
+
+// Implements the following configurations:
+//  - inv(LowerTriangular,         ColMajor) * Column vector
+//  - inv(LowerTriangular,UnitDiag,ColMajor) * Column vector
+//  - inv(UpperTriangular,         ColMajor) * Column vector
+//  - inv(UpperTriangular,UnitDiag,ColMajor) * Column vector
+template<typename Lhs, typename Rhs, int UpLo>
+struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense>
+{
+  typedef typename Rhs::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  enum { PacketSize =  ei_packet_traits<Scalar>::size };
+
+  static void run(const Lhs& lhs, Rhs& other)
+  {
+    static const bool IsLowerTriangular = (UpLo==LowerTriangular);
+    const int size = lhs.cols();
+    for(int c=0 ; c<other.cols() ; ++c)
+    {
+      /* let's perform the inverse product per block of 4 columns such that we perfectly match
+       * our optimized matrix * vector product. blockyEnd represents the number of rows
+       * we can process using the block version.
+       */
+      int blockyEnd = (std::max(size-5,0)/4)*4;
+      if (!IsLowerTriangular)
+        blockyEnd = size-1 - blockyEnd;
+      for(int i=IsLowerTriangular ? 0 : size-1; IsLowerTriangular ? i<blockyEnd : i>blockyEnd;)
+      {
+        /* Let's process the 4x4 sub-matrix as usual.
+         * btmp stores the diagonal coefficients used to update the remaining part of the result.
+         */
+        int startBlock = i;
+        int endBlock = startBlock + (IsLowerTriangular ? 4 : -4);
+        Matrix<Scalar,4,1> btmp;
+        for (;IsLowerTriangular ? i<endBlock : i>endBlock;
+             i += IsLowerTriangular ? 1 : -1)
+        {
+          if(!(Lhs::Flags & UnitDiagBit))
+            other.coeffRef(i,c) /= lhs.coeff(i,i);
+          int remainingSize = IsLowerTriangular ? endBlock-i-1 : i-endBlock-1;
+          if (remainingSize>0)
+            other.col(c).segment((IsLowerTriangular ? i : endBlock) + 1, remainingSize) -=
+                other.coeffRef(i,c)
+              * Block<Lhs,Dynamic,1>(lhs, (IsLowerTriangular ? i : endBlock) + 1, i, remainingSize, 1);
+          btmp.coeffRef(IsLowerTriangular ? i-startBlock : remainingSize) = -other.coeffRef(i,c);
+        }
+
+        /* Now we can efficiently update the remaining part of the result as a matrix * vector product.
+         * NOTE in order to reduce both compilation time and binary size, let's directly call
+         * the fast product implementation. It is equivalent to the following code:
+         *   other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock)
+         *                                       * other.col(c).block(startBlock,endBlock-startBlock)).lazy();
+         */
+        // FIXME this is cool but what about conjugate/adjoint expressions ? do we want to evaluate them ?
+        // this is a more general problem though.
+        ei_cache_friendly_product_colmajor_times_vector(
+          IsLowerTriangular ? size-endBlock : endBlock+1,
+          &(lhs.const_cast_derived().coeffRef(IsLowerTriangular ? endBlock : 0, IsLowerTriangular ? startBlock : endBlock+1)),
+          lhs.stride(),
+          btmp, &(other.coeffRef(IsLowerTriangular ? endBlock : 0, c)));
+// 				if (IsLowerTriangular)
+//           other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock)
+//                                           * other.col(c).block(startBlock,endBlock-startBlock)).lazy();
+// 				else
+//           other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock)
+//                                           * other.col(c).block(startBlock,endBlock-startBlock)).lazy();
+      }
+
+      /* Now we have to process the remaining part as usual */
+      int i;
+      for(i=blockyEnd; IsLowerTriangular ? i<size-1 : i>0; i += (IsLowerTriangular ? 1 : -1) )
+      {
+        if(!(Lhs::Flags & UnitDiagBit))
+          other.coeffRef(i,c) /= lhs.coeff(i,i);
+
+        /* NOTE we cannot use lhs.col(i).end(size-i-1) because Part::coeffRef gets called by .col() to
+         * get the address of the start of the row
+         */
+        if(IsLowerTriangular)
+          other.col(c).end(size-i-1) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, i+1,i, size-i-1,1);
+        else
+          other.col(c).start(i) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, 0,i, i, 1);
+      }
+      if(!(Lhs::Flags & UnitDiagBit))
+        other.coeffRef(i,c) /= lhs.coeff(i,i);
+    }
+  }
+};
+
+/** "in-place" version of MatrixBase::solveTriangular() where the result is written in \a other
+  *
+  * \nonstableyet
+  *
+  * The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
+  * This function will const_cast it, so constness isn't honored here.
+  *
+  * See MatrixBase:solveTriangular() for the details.
+  */
+template<typename Derived>
+template<typename OtherDerived>
+void MatrixBase<Derived>::solveTriangularInPlace(const MatrixBase<OtherDerived>& _other) const
+{
+  MatrixBase<OtherDerived>& other = _other.const_cast_derived();
+  ei_assert(derived().cols() == derived().rows());
+  ei_assert(derived().cols() == other.rows());
+  ei_assert(!(Flags & ZeroDiagBit));
+  ei_assert(Flags & (UpperTriangularBit|LowerTriangularBit));
+
+  enum { copy = ei_traits<OtherDerived>::Flags & RowMajorBit };
+
+  typedef typename ei_meta_if<copy,
+    typename ei_plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::ret OtherCopy;
+  OtherCopy otherCopy(other.derived());
+
+  ei_solve_triangular_selector<Derived, typename ei_unref<OtherCopy>::type>::run(derived(), otherCopy);
+
+  if (copy)
+    other = otherCopy;
+}
+
+/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
+  *
+  * \nonstableyet
+  *
+  * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other.
+  * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
+  * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
+  * is an upper (resp. lower) triangular matrix.
+  *
+  * It is required that \c *this be marked as either an upper or a lower triangular matrix, which
+  * can be done by marked(), and that is automatically the case with expressions such as those returned
+  * by extract().
+  *
+  * \addexample SolveTriangular \label How to solve a triangular system (aka. how to multiply the inverse of a triangular matrix by another one)
+  *
+  * Example: \include MatrixBase_marked.cpp
+  * Output: \verbinclude MatrixBase_marked.out
+  *
+  * This function is essentially a wrapper to the faster solveTriangularInPlace() function creating
+  * a temporary copy of \a other, calling solveTriangularInPlace() on the copy and returning it.
+  * Therefore, if \a other is not needed anymore, it is quite faster to call solveTriangularInPlace()
+  * instead of solveTriangular().
+  *
+  * For users coming from BLAS, this function (and more specifically solveTriangularInPlace()) offer
+  * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
+  *
+  * \b Tips: to perform a \em "right-inverse-multiply" you can simply transpose the operation, e.g.:
+  * \code
+  * M * T^1  <=>  T.transpose().solveTriangularInPlace(M.transpose());
+  * \endcode
+  *
+  * \sa solveTriangularInPlace(), marked(), extract()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+typename ei_plain_matrix_type_column_major<OtherDerived>::type
+MatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const
+{
+  typename ei_plain_matrix_type_column_major<OtherDerived>::type res(other);
+  solveTriangularInPlace(res);
+  return res;
+}
+
+#endif // EIGEN_SOLVETRIANGULAR_H

Eigen/src/Core/Swap.h

@@ -0,0 +1,142 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SWAP_H
+#define EIGEN_SWAP_H
+
+/** \class SwapWrapper
+  *
+  * \internal
+  *
+  * \brief Internal helper class for swapping two expressions
+  */
+template<typename ExpressionType>
+struct ei_traits<SwapWrapper<ExpressionType> >
+{
+  typedef typename ExpressionType::Scalar Scalar;
+  enum {
+    RowsAtCompileTime = ExpressionType::RowsAtCompileTime,
+    ColsAtCompileTime = ExpressionType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = ExpressionType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = ExpressionType::MaxColsAtCompileTime,
+    Flags = ExpressionType::Flags,
+    CoeffReadCost = ExpressionType::CoeffReadCost
+  };
+};
+
+template<typename ExpressionType> class SwapWrapper
+  : public MatrixBase<SwapWrapper<ExpressionType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(SwapWrapper)
+    typedef typename ei_packet_traits<Scalar>::type Packet;
+
+    inline SwapWrapper(ExpressionType& xpr) : m_expression(xpr) {}
+
+    inline int rows() const { return m_expression.rows(); }
+    inline int cols() const { return m_expression.cols(); }
+    inline int stride() const { return m_expression.stride(); }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_expression.const_cast_derived().coeffRef(row, col);
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_expression.const_cast_derived().coeffRef(index);
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(int row, int col, const MatrixBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      ei_internal_assert(row >= 0 && row < rows()
+                         && col >= 0 && col < cols());
+      Scalar tmp = m_expression.coeff(row, col);
+      m_expression.coeffRef(row, col) = _other.coeff(row, col);
+      _other.coeffRef(row, col) = tmp;
+    }
+
+    template<typename OtherDerived>
+    void copyCoeff(int index, const MatrixBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      ei_internal_assert(index >= 0 && index < m_expression.size());
+      Scalar tmp = m_expression.coeff(index);
+      m_expression.coeffRef(index) = _other.coeff(index);
+      _other.coeffRef(index) = tmp;
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(int row, int col, const MatrixBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      ei_internal_assert(row >= 0 && row < rows()
+                        && col >= 0 && col < cols());
+      Packet tmp = m_expression.template packet<StoreMode>(row, col);
+      m_expression.template writePacket<StoreMode>(row, col,
+        _other.template packet<LoadMode>(row, col)
+      );
+      _other.template writePacket<LoadMode>(row, col, tmp);
+    }
+
+    template<typename OtherDerived, int StoreMode, int LoadMode>
+    void copyPacket(int index, const MatrixBase<OtherDerived>& other)
+    {
+      OtherDerived& _other = other.const_cast_derived();
+      ei_internal_assert(index >= 0 && index < m_expression.size());
+      Packet tmp = m_expression.template packet<StoreMode>(index);
+      m_expression.template writePacket<StoreMode>(index,
+        _other.template packet<LoadMode>(index)
+      );
+      _other.template writePacket<LoadMode>(index, tmp);
+    }
+
+  protected:
+    ExpressionType& m_expression;
+};
+
+/** swaps *this with the expression \a other.
+  *
+  * \note \a other is only marked for internal reasons, but of course
+  * it gets const-casted. One reason is that one will often call swap
+  * on temporary objects (hence non-const references are forbidden).
+  * Another reason is that lazyAssign takes a const argument anyway.
+  */
+template<typename Derived>
+template<typename OtherDerived>
+void MatrixBase<Derived>::swap(const MatrixBase<OtherDerived>& other)
+{
+  (SwapWrapper<Derived>(derived())).lazyAssign(other);
+}
+
+#endif // EIGEN_SWAP_H
+
+
+
+
+
+

Eigen/src/Core/Transpose.h

@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_TRANSPOSE_H
+#define EIGEN_TRANSPOSE_H
+
+/** \class Transpose
+  *
+  * \brief Expression of the transpose of a matrix
+  *
+  * \param MatrixType the type of the object of which we are taking the transpose
+  *
+  * This class represents an expression of the transpose of a matrix.
+  * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::transpose(), MatrixBase::adjoint()
+  */
+template<typename MatrixType>
+struct ei_traits<Transpose<MatrixType> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsAtCompileTime = MatrixType::ColsAtCompileTime,
+    ColsAtCompileTime = MatrixType::RowsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    Flags = ((int(_MatrixTypeNested::Flags) ^ RowMajorBit)
+          & ~(LowerTriangularBit | UpperTriangularBit))
+          | (int(_MatrixTypeNested::Flags)&UpperTriangularBit ? LowerTriangularBit : 0)
+          | (int(_MatrixTypeNested::Flags)&LowerTriangularBit ? UpperTriangularBit : 0),
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType> class Transpose
+  : public MatrixBase<Transpose<MatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
+
+    inline Transpose(const MatrixType& matrix) : m_matrix(matrix) {}
+
+    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
+
+    inline int rows() const { return m_matrix.cols(); }
+    inline int cols() const { return m_matrix.rows(); }
+    inline int nonZeros() const { return m_matrix.nonZeros(); }
+    inline int stride(void) const { return m_matrix.stride(); }
+
+    inline Scalar& coeffRef(int row, int col)
+    {
+      return m_matrix.const_cast_derived().coeffRef(col, row);
+    }
+
+    inline Scalar& coeffRef(int index)
+    {
+      return m_matrix.const_cast_derived().coeffRef(index);
+    }
+
+    inline const CoeffReturnType coeff(int row, int col) const
+    {
+      return m_matrix.coeff(col, row);
+    }
+
+    inline const CoeffReturnType coeff(int index) const
+    {
+      return m_matrix.coeff(index);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int row, int col) const
+    {
+      return m_matrix.template packet<LoadMode>(col, row);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int row, int col, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(col, row, x);
+    }
+
+    template<int LoadMode>
+    inline const PacketScalar packet(int index) const
+    {
+      return m_matrix.template packet<LoadMode>(index);
+    }
+
+    template<int LoadMode>
+    inline void writePacket(int index, const PacketScalar& x)
+    {
+      m_matrix.const_cast_derived().template writePacket<LoadMode>(index, x);
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \returns an expression of the transpose of *this.
+  *
+  * Example: \include MatrixBase_transpose.cpp
+  * Output: \verbinclude MatrixBase_transpose.out
+  *
+  * \warning If you want to replace a matrix by its own transpose, do \b NOT do this:
+  * \code
+  * m = m.transpose(); // bug!!! caused by aliasing effect
+  * \endcode
+  * Instead, use the transposeInPlace() method:
+  * \code
+  * m.transposeInPlace();
+  * \endcode
+  * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+  * \code
+  * m = m.transpose().eval();
+  * \endcode
+  *
+  * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline Transpose<Derived>
+MatrixBase<Derived>::transpose()
+{
+  return derived();
+}
+
+/** This is the const version of transpose().
+  *
+  * Make sure you read the warning for transpose() !
+  *
+  * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+inline const Transpose<Derived>
+MatrixBase<Derived>::transpose() const
+{
+  return derived();
+}
+
+/** \returns an expression of the adjoint (i.e. conjugate transpose) of *this.
+  *
+  * Example: \include MatrixBase_adjoint.cpp
+  * Output: \verbinclude MatrixBase_adjoint.out
+  *
+  * \warning If you want to replace a matrix by its own adjoint, do \b NOT do this:
+  * \code
+  * m = m.adjoint(); // bug!!! caused by aliasing effect
+  * \endcode
+  * Instead, use the adjointInPlace() method:
+  * \code
+  * m.adjointInPlace();
+  * \endcode
+  * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+  * \code
+  * m = m.adjoint().eval();
+  * \endcode
+  *
+  * \sa adjointInPlace(), transpose(), conjugate(), class Transpose, class ei_scalar_conjugate_op */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::AdjointReturnType
+MatrixBase<Derived>::adjoint() const
+{
+  return conjugate().nestByValue();
+}
+
+/***************************************************************************
+* "in place" transpose implementation
+***************************************************************************/
+
+template<typename MatrixType,
+  bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic>
+struct ei_inplace_transpose_selector;
+
+template<typename MatrixType>
+struct ei_inplace_transpose_selector<MatrixType,true> { // square matrix
+  static void run(MatrixType& m) {
+    m.template part<StrictlyUpperTriangular>().swap(m.transpose());
+  }
+};
+
+template<typename MatrixType>
+struct ei_inplace_transpose_selector<MatrixType,false> { // non square matrix
+  static void run(MatrixType& m) {
+    if (m.rows()==m.cols())
+      m.template part<StrictlyUpperTriangular>().swap(m.transpose());
+    else
+      m = m.transpose().eval();
+  }
+};
+
+/** This is the "in place" version of transpose(): it replaces \c *this by its own transpose.
+  * Thus, doing
+  * \code
+  * m.transposeInPlace();
+  * \endcode
+  * has the same effect on m as doing
+  * \code
+  * m = m.transpose().eval();
+  * \endcode
+  * and is faster and also safer because in the latter line of code, forgetting the eval() results
+  * in a bug caused by aliasing.
+  *
+  * Notice however that this method is only useful if you want to replace a matrix by its own transpose.
+  * If you just need the transpose of a matrix, use transpose().
+  *
+  * \note if the matrix is not square, then \c *this must be a resizable matrix.
+  *
+  * \sa transpose(), adjoint(), adjointInPlace() */
+template<typename Derived>
+inline void MatrixBase<Derived>::transposeInPlace()
+{
+  ei_inplace_transpose_selector<Derived>::run(derived());
+}
+
+/***************************************************************************
+* "in place" adjoint implementation
+***************************************************************************/
+
+/** This is the "in place" version of adjoint(): it replaces \c *this by its own transpose.
+  * Thus, doing
+  * \code
+  * m.adjointInPlace();
+  * \endcode
+  * has the same effect on m as doing
+  * \code
+  * m = m.adjoint().eval();
+  * \endcode
+  * and is faster and also safer because in the latter line of code, forgetting the eval() results
+  * in a bug caused by aliasing.
+  *
+  * Notice however that this method is only useful if you want to replace a matrix by its own adjoint.
+  * If you just need the adjoint of a matrix, use adjoint().
+  *
+  * \note if the matrix is not square, then \c *this must be a resizable matrix.
+  *
+  * \sa transpose(), adjoint(), transposeInPlace() */
+template<typename Derived>
+inline void MatrixBase<Derived>::adjointInPlace()
+{
+  derived() = adjoint().eval();
+}
+
+#endif // EIGEN_TRANSPOSE_H

Eigen/src/Core/Visitor.h

@@ -0,0 +1,197 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_VISITOR_H
+#define EIGEN_VISITOR_H
+
+template<typename Visitor, typename Derived, int UnrollCount>
+struct ei_visitor_impl
+{
+  enum {
+    col = (UnrollCount-1) / Derived::RowsAtCompileTime,
+    row = (UnrollCount-1) % Derived::RowsAtCompileTime
+  };
+
+  inline static void run(const Derived &mat, Visitor& visitor)
+  {
+    ei_visitor_impl<Visitor, Derived, UnrollCount-1>::run(mat, visitor);
+    visitor(mat.coeff(row, col), row, col);
+  }
+};
+
+template<typename Visitor, typename Derived>
+struct ei_visitor_impl<Visitor, Derived, 1>
+{
+  inline static void run(const Derived &mat, Visitor& visitor)
+  {
+    return visitor.init(mat.coeff(0, 0), 0, 0);
+  }
+};
+
+template<typename Visitor, typename Derived>
+struct ei_visitor_impl<Visitor, Derived, Dynamic>
+{
+  inline static void run(const Derived& mat, Visitor& visitor)
+  {
+    visitor.init(mat.coeff(0,0), 0, 0);
+    for(int i = 1; i < mat.rows(); ++i)
+      visitor(mat.coeff(i, 0), i, 0);
+    for(int j = 1; j < mat.cols(); ++j)
+      for(int i = 0; i < mat.rows(); ++i)
+        visitor(mat.coeff(i, j), i, j);
+  }
+};
+
+
+/** Applies the visitor \a visitor to the whole coefficients of the matrix or vector.
+  *
+  * The template parameter \a Visitor is the type of the visitor and provides the following interface:
+  * \code
+  * struct MyVisitor {
+  *   // called for the first coefficient
+  *   void init(const Scalar& value, int i, int j);
+  *   // called for all other coefficients
+  *   void operator() (const Scalar& value, int i, int j);
+  * };
+  * \endcode
+  *
+  * \note compared to one or two \em for \em loops, visitors offer automatic
+  * unrolling for small fixed size matrix.
+  *
+  * \sa minCoeff(int*,int*), maxCoeff(int*,int*), MatrixBase::redux()
+  */
+template<typename Derived>
+template<typename Visitor>
+void MatrixBase<Derived>::visit(Visitor& visitor) const
+{
+  const bool unroll = SizeAtCompileTime * CoeffReadCost
+                    + (SizeAtCompileTime-1) * ei_functor_traits<Visitor>::Cost
+                    <= EIGEN_UNROLLING_LIMIT;
+  return ei_visitor_impl<Visitor, Derived,
+      unroll ? int(SizeAtCompileTime) : Dynamic
+    >::run(derived(), visitor);
+}
+
+/** \internal
+  * \brief Base class to implement min and max visitors
+  */
+template <typename Scalar>
+struct ei_coeff_visitor
+{
+  int row, col;
+  Scalar res;
+  inline void init(const Scalar& value, int i, int j)
+  {
+    res = value;
+    row = i;
+    col = j;
+  }
+};
+
+/** \internal
+  * \brief Visitor computing the min coefficient with its value and coordinates
+  *
+  * \sa MatrixBase::minCoeff(int*, int*)
+  */
+template <typename Scalar>
+struct ei_min_coeff_visitor : ei_coeff_visitor<Scalar>
+{
+  void operator() (const Scalar& value, int i, int j)
+  {
+    if(value < this->res)
+    {
+      this->res = value;
+      this->row = i;
+      this->col = j;
+    }
+  }
+};
+
+template<typename Scalar>
+struct ei_functor_traits<ei_min_coeff_visitor<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost
+  };
+};
+
+/** \internal
+  * \brief Visitor computing the max coefficient with its value and coordinates
+  *
+  * \sa MatrixBase::maxCoeff(int*, int*)
+  */
+template <typename Scalar>
+struct ei_max_coeff_visitor : ei_coeff_visitor<Scalar>
+{
+  void operator() (const Scalar& value, int i, int j)
+  {
+    if(value > this->res)
+    {
+      this->res = value;
+      this->row = i;
+      this->col = j;
+    }
+  }
+};
+
+template<typename Scalar>
+struct ei_functor_traits<ei_max_coeff_visitor<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::AddCost
+  };
+};
+
+/** \returns the minimum of all coefficients of *this
+  * and puts in *row and *col its location.
+  *
+  * \sa MatrixBase::maxCoeff(int*,int*), MatrixBase::visitor(), MatrixBase::minCoeff()
+  */
+template<typename Derived>
+typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::minCoeff(int* row, int* col) const
+{
+  ei_min_coeff_visitor<Scalar> minVisitor;
+  this->visit(minVisitor);
+  *row = minVisitor.row;
+  if (col) *col = minVisitor.col;
+  return minVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this
+  * and puts in *row and *col its location.
+  *
+  * \sa MatrixBase::minCoeff(int*,int*), MatrixBase::visitor(), MatrixBase::maxCoeff()
+  */
+template<typename Derived>
+typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::maxCoeff(int* row, int* col) const
+{
+  ei_max_coeff_visitor<Scalar> maxVisitor;
+  this->visit(maxVisitor);
+  *row = maxVisitor.row;
+  if (col) *col = maxVisitor.col;
+  return maxVisitor.res;
+}
+
+
+#endif // EIGEN_VISITOR_H

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

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

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

@@ -0,0 +1,433 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Konstantinos Margaritis <markos@codex.gr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
+#define EIGEN_PACKET_MATH_ALTIVEC_H
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
+#endif
+
+typedef __vector float          v4f;
+typedef __vector int            v4i;
+typedef __vector unsigned int   v4ui;
+typedef __vector __bool int     v4bi;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+
+#define USE_CONST_v0i     const v4i   v0i   = vec_splat_s32(0)
+#define USE_CONST_v1i     const v4i   v1i   = vec_splat_s32(1)
+#define USE_CONST_v16i_   const v4i   v16i_ = vec_splat_s32(-16)
+#define USE_CONST_v0f     USE_CONST_v0i; const v4f v0f = (v4f) v0i
+#define USE_CONST_v1f     USE_CONST_v1i; const v4f v1f = vec_ctf(v1i, 0)
+#define USE_CONST_v1i_    const v4ui  v1i_  = vec_splat_u32(-1)
+#define USE_CONST_v0f_    USE_CONST_v1i_; const v4f v0f_ = (v4f) vec_sl(v1i_, v1i_)
+
+template<> struct ei_packet_traits<float> : ei_default_packet_traits
+{ typedef v4f type; enum {size=4}; };
+template<> struct ei_packet_traits<int>   : ei_default_packet_traits
+{ typedef v4i type; enum {size=4}; };
+
+template<> struct ei_unpacket_traits<v4f>  { typedef float  type; enum {size=4}; };
+template<> struct ei_unpacket_traits<v4i>  { typedef int    type; enum {size=4}; };
+
+inline std::ostream & operator <<(std::ostream & s, const v4f & v)
+{
+  union {
+    v4f   v;
+    float n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const v4i & v)
+{
+  union {
+    v4i   v;
+    int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const v4ui & v)
+{
+  union {
+    v4ui   v;
+    unsigned int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const v4bi & v)
+{
+  union {
+    __vector __bool int v;
+    unsigned int n[4];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+  return s;
+}
+
+template<> inline v4f  ei_padd(const v4f&   a, const v4f&   b) { return vec_add(a,b); }
+template<> inline v4i  ei_padd(const v4i&   a, const v4i&   b) { return vec_add(a,b); }
+
+template<> inline v4f  ei_psub(const v4f&   a, const v4f&   b) { return vec_sub(a,b); }
+template<> inline v4i  ei_psub(const v4i&   a, const v4i&   b) { return vec_sub(a,b); }
+
+template<> EIGEN_STRONG_INLINE v4f ei_pnegate(const v4f& a)
+{
+  v4i mask = {0x80000000, 0x80000000, 0x80000000, 0x80000000};
+  return vec_xor(a,(v4f) mask);
+}
+
+template<> EIGEN_STRONG_INLINE v4i ei_pnegate(const v4i& a)
+{
+  USE_CONST_v0i;
+  return ei_psub(v0i, a);
+}
+
+template<> inline v4f  ei_pmul(const v4f&   a, const v4f&   b) { USE_CONST_v0f; return vec_madd(a,b, v0f); }
+template<> inline v4i  ei_pmul(const v4i&   a, const v4i&   b)
+{
+  // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
+  //Set up constants, variables
+  v4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
+  USE_CONST_v0i;
+  USE_CONST_v1i;
+  USE_CONST_v16i_;
+
+  // Get the absolute values
+  a1  = vec_abs(a);
+  b1  = vec_abs(b);
+
+  // Get the signs using xor
+  v4bi sgn = (v4bi) vec_cmplt(vec_xor(a, b), v0i);
+
+  // Do the multiplication for the asbolute values.
+  bswap = (v4i) vec_rl((v4ui) b1, (v4ui) v16i_ );
+  low_prod = vec_mulo((__vector short)a1, (__vector short)b1);
+  high_prod = vec_msum((__vector short)a1, (__vector short)bswap, v0i);
+  high_prod = (v4i) vec_sl((v4ui) high_prod, (v4ui) v16i_);
+  prod = vec_add( low_prod, high_prod );
+
+  // NOR the product and select only the negative elements according to the sign mask
+  prod_ = vec_nor(prod, prod);
+  prod_ = vec_sel(v0i, prod_, sgn);
+
+  // Add 1 to the result to get the negative numbers
+  v1sel = vec_sel(v0i, v1i, sgn);
+  prod_ = vec_add(prod_, v1sel);
+
+  // Merge the results back to the final vector.
+  prod = vec_sel(prod, prod_, sgn);
+
+  return prod;
+}
+
+template<> inline v4f  ei_pdiv(const v4f&   a, const v4f&   b) {
+  v4f t, y_0, y_1, res;
+  USE_CONST_v0f;
+  USE_CONST_v1f;
+
+  // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
+  y_0 = vec_re(b);
+
+  // Do one Newton-Raphson iteration to get the needed accuracy
+  t = vec_nmsub(y_0, b, v1f);
+  y_1 = vec_madd(y_0, t, y_0);
+
+  res = vec_madd(a, y_1, v0f);
+  return res;
+}
+
+template<> inline v4f  ei_pmadd(const v4f&  a, const v4f&   b, const v4f&  c) { return vec_madd(a, b, c); }
+
+template<> inline v4f  ei_pmin(const v4f&   a, const v4f&   b) { return vec_min(a,b); }
+template<> inline v4i  ei_pmin(const v4i&   a, const v4i&   b) { return vec_min(a,b); }
+
+template<> inline v4f  ei_pmax(const v4f&   a, const v4f&   b) { return vec_max(a,b); }
+template<> inline v4i  ei_pmax(const v4i&   a, const v4i&   b) { return vec_max(a,b); }
+
+template<> EIGEN_STRONG_INLINE v4f ei_pabs(const v4f& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE v4i ei_pabs(const v4i& a) { return vec_abs(a); }
+
+template<> inline v4f  ei_pload(const float* from) { return vec_ld(0, from); }
+template<> inline v4i  ei_pload(const int*   from) { return vec_ld(0, from); }
+
+template<> inline v4f  ei_ploadu(const float*  from)
+{
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  __vector unsigned char MSQ, LSQ;
+  __vector unsigned char mask;
+  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
+  mask = vec_lvsl(0, from);                        // create the permute mask
+  return (v4f) vec_perm(MSQ, LSQ, mask);           // align the data
+}
+
+template<> inline v4i  ei_ploadu(const int*    from)
+{
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  __vector unsigned char MSQ, LSQ;
+  __vector unsigned char mask;
+  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
+  mask = vec_lvsl(0, from);                        // create the permute mask
+  return (v4i) vec_perm(MSQ, LSQ, mask);    // align the data
+}
+
+template<> inline v4f  ei_pset1(const float&  from)
+{
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  float __attribute__(aligned(16)) af[4];
+  af[0] = from;
+  v4f vc = vec_ld(0, af);
+  vc = vec_splat(vc, 0);
+  return vc;
+}
+
+template<> inline v4i  ei_pset1(const int&    from)
+{
+  int __attribute__(aligned(16)) ai[4];
+  ai[0] = from;
+  v4i vc = vec_ld(0, ai);
+  vc = vec_splat(vc, 0);
+  return vc;
+}
+
+template<> inline void ei_pstore(float*   to, const v4f&   from) { vec_st(from, 0, to); }
+template<> inline void ei_pstore(int*     to, const v4i&   from) { vec_st(from, 0, to); }
+
+template<> inline void ei_pstoreu(float*  to, const v4f&   from)
+{
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  // Warning: not thread safe!
+  __vector unsigned char MSQ, LSQ, edges;
+  __vector unsigned char edgeAlign, align;
+
+  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
+  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
+  edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
+  align = vec_lvsr( 0, to );                                // permute map to misalign data
+  MSQ = vec_perm(edges,(__vector unsigned char)from,align);   // misalign the data (MSQ)
+  LSQ = vec_perm((__vector unsigned char)from,edges,align);   // misalign the data (LSQ)
+  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
+  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
+}
+
+template<> inline void ei_pstoreu(int*    to , const v4i&    from )
+{
+  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+  // Warning: not thread safe!
+  __vector unsigned char MSQ, LSQ, edges;
+  __vector unsigned char edgeAlign, align;
+
+  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
+  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
+  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
+  edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
+  align = vec_lvsr( 0, to );                                // permute map to misalign data
+  MSQ = vec_perm(edges,(__vector unsigned char)from,align);   // misalign the data (MSQ)
+  LSQ = vec_perm((__vector unsigned char)from,edges,align);   // misalign the data (LSQ)
+  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
+  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
+}
+
+template<> inline float  ei_pfirst(const v4f&  a)
+{
+  float EIGEN_ALIGN_128 af[4];
+  vec_st(a, 0, af);
+  return af[0];
+}
+
+template<> inline int    ei_pfirst(const v4i&  a)
+{
+  int EIGEN_ALIGN_128 ai[4];
+  vec_st(a, 0, ai);
+  return ai[0];
+}
+
+template<> EIGEN_STRONG_INLINE v4f ei_preverse(const v4f& a)
+{
+  static const __vector unsigned char reverse_mask =
+    {12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
+  return (v4f)vec_perm((__vector unsigned char)a,(__vector unsigned char)a,reverse_mask);
+}
+template<> EIGEN_STRONG_INLINE v4i ei_preverse(const v4i& a)
+{
+  static const __vector unsigned char __attribute__(aligned(16)) reverse_mask =
+    {12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
+  return (v4i)vec_perm((__vector unsigned char)a,(__vector unsigned char)a,reverse_mask);
+}
+
+inline v4f ei_preduxp(const v4f* vecs)
+{
+  v4f v[4], sum[4];
+
+  // It's easier and faster to transpose then add as columns
+  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+  // Do the transpose, first set of moves
+  v[0] = vec_mergeh(vecs[0], vecs[2]);
+  v[1] = vec_mergel(vecs[0], vecs[2]);
+  v[2] = vec_mergeh(vecs[1], vecs[3]);
+  v[3] = vec_mergel(vecs[1], vecs[3]);
+  // Get the resulting vectors
+  sum[0] = vec_mergeh(v[0], v[2]);
+  sum[1] = vec_mergel(v[0], v[2]);
+  sum[2] = vec_mergeh(v[1], v[3]);
+  sum[3] = vec_mergel(v[1], v[3]);
+
+  // Now do the summation:
+  // Lines 0+1
+  sum[0] = vec_add(sum[0], sum[1]);
+  // Lines 2+3
+  sum[1] = vec_add(sum[2], sum[3]);
+  // Add the results
+  sum[0] = vec_add(sum[0], sum[1]);
+  return sum[0];
+}
+
+inline v4i  ei_preduxp(const v4i* vecs)
+{
+  v4i v[4], sum[4];
+
+  // It's easier and faster to transpose then add as columns
+  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+  // Do the transpose, first set of moves
+  v[0] = vec_mergeh(vecs[0], vecs[2]);
+  v[1] = vec_mergel(vecs[0], vecs[2]);
+  v[2] = vec_mergeh(vecs[1], vecs[3]);
+  v[3] = vec_mergel(vecs[1], vecs[3]);
+  // Get the resulting vectors
+  sum[0] = vec_mergeh(v[0], v[2]);
+  sum[1] = vec_mergel(v[0], v[2]);
+  sum[2] = vec_mergeh(v[1], v[3]);
+  sum[3] = vec_mergel(v[1], v[3]);
+
+  // Now do the summation:
+  // Lines 0+1
+  sum[0] = vec_add(sum[0], sum[1]);
+  // Lines 2+3
+  sum[1] = vec_add(sum[2], sum[3]);
+  // Add the results
+  sum[0] = vec_add(sum[0], sum[1]);
+  return sum[0];
+}
+
+inline float ei_predux(const v4f& a)
+{
+  v4f b, sum;
+  b = (v4f)vec_sld(a, a, 8);
+  sum = vec_add(a, b);
+  b = (v4f)vec_sld(sum, sum, 4);
+  sum = vec_add(sum, b);
+  return ei_pfirst(sum);
+}
+
+inline int ei_predux(const v4i& a)
+{
+  USE_CONST_v0i;
+  v4i sum;
+  sum = vec_sums(a, v0i);
+  sum = vec_sld(sum, v0i, 12);
+  return ei_pfirst(sum);
+}
+
+// implement other reductions operators
+inline float ei_predux_mul(const v4f& a)
+{
+  v4f prod;
+  prod = ei_pmul(a, (v4f)vec_sld(a, a, 8));
+  return ei_pfirst(ei_pmul(prod, (v4f)vec_sld(prod, prod, 4)));
+}
+
+inline int ei_predux_mul(const v4i& a)
+{
+  EIGEN_ALIGN_128 int aux[4];
+  ei_pstore(aux, a);
+  return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+inline float ei_predux_min(const v4f& a)
+{
+  v4f b, res;
+  b = vec_min(a, vec_sld(a, a, 8));
+  res = vec_min(b, vec_sld(b, b, 4));
+  return ei_pfirst(res);
+}
+
+inline int ei_predux_min(const v4i& a)
+{
+  v4i b, res;
+  b = vec_min(a, vec_sld(a, a, 8));
+  res = vec_min(b, vec_sld(b, b, 4));
+  return ei_pfirst(res);
+}
+
+inline float ei_predux_max(const v4f& a)
+{
+  v4f b, res;
+  b = vec_max(a, vec_sld(a, a, 8));
+  res = vec_max(b, vec_sld(b, b, 4));
+  return ei_pfirst(res);
+}
+
+inline int ei_predux_max(const v4i& a)
+{
+  v4i b, res;
+  b = vec_max(a, vec_sld(a, a, 8));
+  res = vec_max(b, vec_sld(b, b, 4));
+  return ei_pfirst(res);
+}
+
+
+
+template<int Offset>
+struct ei_palign_impl<Offset, v4f>
+{
+  inline static void run(v4f& first, const v4f& second)
+  {
+    first = vec_sld(first, second, Offset*4);
+  }
+};
+
+template<int Offset>
+struct ei_palign_impl<Offset, v4i>
+{
+  inline static void run(v4i& first, const v4i& second)
+  {
+    first = vec_sld(first, second, Offset*4);
+  }
+};
+
+#endif // EIGEN_PACKET_MATH_ALTIVEC_H

Eigen/src/Core/arch/CMakeLists.txt

@@ -0,0 +1,2 @@
+ADD_SUBDIRECTORY(SSE)
+ADD_SUBDIRECTORY(AltiVec)

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

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

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

@@ -0,0 +1,376 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+/* The sin, cos, exp, and log functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
+#define EIGEN_MATH_FUNCTIONS_SSE_H
+
+static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_plog(Packet4f x)
+{
+  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+
+  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
+
+  /* the smallest non denormalized float number */
+  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);
+
+  /* natural logarithm computed for 4 simultaneous float
+    return NaN for x <= 0
+  */
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+
+
+  Packet4i emm0;
+
+  Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
+
+  x = ei_pmax(x, ei_p4f_min_norm_pos);  /* cut off denormalized stuff */
+  emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
+
+  /* keep only the fractional part */
+  x = _mm_and_ps(x, ei_p4f_inv_mant_mask);
+  x = _mm_or_ps(x, ei_p4f_half);
+
+  emm0 = _mm_sub_epi32(emm0, ei_p4i_0x7f);
+  Packet4f e = ei_padd(_mm_cvtepi32_ps(emm0), ei_p4f_1);
+
+  /* part2:
+     if( x < SQRTHF ) {
+       e -= 1;
+       x = x + x - 1.0;
+     } else { x = x - 1.0; }
+  */
+  Packet4f mask = _mm_cmplt_ps(x, ei_p4f_cephes_SQRTHF);
+  Packet4f tmp = _mm_and_ps(x, mask);
+  x = ei_psub(x, ei_p4f_1);
+  e = ei_psub(e, _mm_and_ps(ei_p4f_1, mask));
+  x = ei_padd(x, tmp);
+
+  Packet4f x2 = ei_pmul(x,x);
+  Packet4f x3 = ei_pmul(x2,x);
+
+  Packet4f y, y1, y2;
+  y  = ei_pmadd(ei_p4f_cephes_log_p0, x, ei_p4f_cephes_log_p1);
+  y1 = ei_pmadd(ei_p4f_cephes_log_p3, x, ei_p4f_cephes_log_p4);
+  y2 = ei_pmadd(ei_p4f_cephes_log_p6, x, ei_p4f_cephes_log_p7);
+  y  = ei_pmadd(y , x, ei_p4f_cephes_log_p2);
+  y1 = ei_pmadd(y1, x, ei_p4f_cephes_log_p5);
+  y2 = ei_pmadd(y2, x, ei_p4f_cephes_log_p8);
+  y = ei_pmadd(y, x3, y1);
+  y = ei_pmadd(y, x3, y2);
+  y = ei_pmul(y, x3);
+
+  y1 = ei_pmul(e, ei_p4f_cephes_log_q1);
+  tmp = ei_pmul(x2, ei_p4f_half);
+  y = ei_padd(y, y1);
+  x = ei_psub(x, tmp);
+  y2 = ei_pmul(e, ei_p4f_cephes_log_q2);
+  x = ei_padd(x, y);
+  x = ei_padd(x, y2);
+  return _mm_or_ps(x, invalid_mask); // negative arg will be NAN
+}
+
+static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_pexp(Packet4f x)
+{
+  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+
+
+  _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647949f);
+  _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
+
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
+
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
+
+  Packet4f tmp = _mm_setzero_ps(), fx;
+  Packet4i emm0;
+
+  // clamp x
+  x = ei_pmax(ei_pmin(x, ei_p4f_exp_hi), ei_p4f_exp_lo);
+
+  /* express exp(x) as exp(g + n*log(2)) */
+  fx = ei_pmadd(x, ei_p4f_cephes_LOG2EF, ei_p4f_half);
+
+  /* how to perform a floorf with SSE: just below */
+  emm0 = _mm_cvttps_epi32(fx);
+  tmp  = _mm_cvtepi32_ps(emm0);
+  /* if greater, substract 1 */
+  Packet4f mask = _mm_cmpgt_ps(tmp, fx);
+  mask = _mm_and_ps(mask, ei_p4f_1);
+  fx = ei_psub(tmp, mask);
+
+  tmp = ei_pmul(fx, ei_p4f_cephes_exp_C1);
+  Packet4f z = ei_pmul(fx, ei_p4f_cephes_exp_C2);
+  x = ei_psub(x, tmp);
+  x = ei_psub(x, z);
+
+  z = ei_pmul(x,x);
+
+  Packet4f y = ei_p4f_cephes_exp_p0;
+  y = ei_pmadd(y, x, ei_p4f_cephes_exp_p1);
+  y = ei_pmadd(y, x, ei_p4f_cephes_exp_p2);
+  y = ei_pmadd(y, x, ei_p4f_cephes_exp_p3);
+  y = ei_pmadd(y, x, ei_p4f_cephes_exp_p4);
+  y = ei_pmadd(y, x, ei_p4f_cephes_exp_p5);
+  y = ei_pmadd(y, z, x);
+  y = ei_padd(y, ei_p4f_1);
+
+  /* build 2^n */
+  emm0 = _mm_cvttps_epi32(fx);
+  emm0 = _mm_add_epi32(emm0, ei_p4i_0x7f);
+  emm0 = _mm_slli_epi32(emm0, 23);
+  return ei_pmul(y, _mm_castsi128_ps(emm0));
+}
+
+/* evaluation of 4 sines at onces, using SSE2 intrinsics.
+
+   The code is the exact rewriting of the cephes sinf function.
+   Precision is excellent as long as x < 8192 (I did not bother to
+   take into account the special handling they have for greater values
+   -- it does not return garbage for arguments over 8192, though, but
+   the extra precision is missing).
+
+   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+   surprising but correct result.
+*/
+
+static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_psin(Packet4f x)
+{
+  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+
+  _EIGEN_DECLARE_CONST_Packet4i(1, 1);
+  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
+  _EIGEN_DECLARE_CONST_Packet4i(2, 2);
+  _EIGEN_DECLARE_CONST_Packet4i(4, 4);
+
+  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
+
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1,  8.3321608736E-3f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0,  2.443315711809948E-005f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
+
+  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
+
+  Packet4i emm0, emm2;
+  sign_bit = x;
+  /* take the absolute value */
+  x = ei_pabs(x);
+
+  /* take the modulo */
+
+  /* extract the sign bit (upper one) */
+  sign_bit = _mm_and_ps(sign_bit, ei_p4f_sign_mask);
+
+  /* scale by 4/Pi */
+  y = ei_pmul(x, ei_p4f_cephes_FOPI);
+
+  /* store the integer part of y in mm0 */
+  emm2 = _mm_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = _mm_add_epi32(emm2, ei_p4i_1);
+  emm2 = _mm_and_si128(emm2, ei_p4i_not1);
+  y = _mm_cvtepi32_ps(emm2);
+  /* get the swap sign flag */
+  emm0 = _mm_and_si128(emm2, ei_p4i_4);
+  emm0 = _mm_slli_epi32(emm0, 29);
+  /* get the polynom selection mask
+     there is one polynom for 0 <= x <= Pi/4
+     and another one for Pi/4<x<=Pi/2
+
+     Both branches will be computed.
+  */
+  emm2 = _mm_and_si128(emm2, ei_p4i_2);
+  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+
+  Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
+  Packet4f poly_mask = _mm_castsi128_ps(emm2);
+  sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
+
+  /* The magic pass: "Extended precision modular arithmetic"
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = ei_pmul(y, ei_p4f_minus_cephes_DP1);
+  xmm2 = ei_pmul(y, ei_p4f_minus_cephes_DP2);
+  xmm3 = ei_pmul(y, ei_p4f_minus_cephes_DP3);
+  x = ei_padd(x, xmm1);
+  x = ei_padd(x, xmm2);
+  x = ei_padd(x, xmm3);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = ei_p4f_coscof_p0;
+  Packet4f z = _mm_mul_ps(x,x);
+
+  y = ei_pmadd(y, z, ei_p4f_coscof_p1);
+  y = ei_pmadd(y, z, ei_p4f_coscof_p2);
+  y = ei_pmul(y, z);
+  y = ei_pmul(y, z);
+  Packet4f tmp = ei_pmul(z, ei_p4f_half);
+  y = ei_psub(y, tmp);
+  y = ei_padd(y, ei_p4f_1);
+
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  Packet4f y2 = ei_p4f_sincof_p0;
+  y2 = ei_pmadd(y2, z, ei_p4f_sincof_p1);
+  y2 = ei_pmadd(y2, z, ei_p4f_sincof_p2);
+  y2 = ei_pmul(y2, z);
+  y2 = ei_pmul(y2, x);
+  y2 = ei_padd(y2, x);
+
+  /* select the correct result from the two polynoms */
+  y2 = _mm_and_ps(poly_mask, y2);
+  y = _mm_andnot_ps(poly_mask, y);
+  y = _mm_or_ps(y,y2);
+  /* update the sign */
+  return _mm_xor_ps(y, sign_bit);
+}
+
+/* almost the same as ei_psin */
+static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_pcos(Packet4f x)
+{
+  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+
+  _EIGEN_DECLARE_CONST_Packet4i(1, 1);
+  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
+  _EIGEN_DECLARE_CONST_Packet4i(2, 2);
+  _EIGEN_DECLARE_CONST_Packet4i(4, 4);
+
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1,  8.3321608736E-3f);
+  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0,  2.443315711809948E-005f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
+  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);
+  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
+
+  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
+  Packet4i emm0, emm2;
+
+  x = ei_pabs(x);
+
+  /* scale by 4/Pi */
+  y = ei_pmul(x, ei_p4f_cephes_FOPI);
+
+  /* get the integer part of y */
+  emm2 = _mm_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = _mm_add_epi32(emm2, ei_p4i_1);
+  emm2 = _mm_and_si128(emm2, ei_p4i_not1);
+  y = _mm_cvtepi32_ps(emm2);
+
+  emm2 = _mm_sub_epi32(emm2, ei_p4i_2);
+
+  /* get the swap sign flag */
+  emm0 = _mm_andnot_si128(emm2, ei_p4i_4);
+  emm0 = _mm_slli_epi32(emm0, 29);
+  /* get the polynom selection mask */
+  emm2 = _mm_and_si128(emm2, ei_p4i_2);
+  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+
+  Packet4f sign_bit = _mm_castsi128_ps(emm0);
+  Packet4f poly_mask = _mm_castsi128_ps(emm2);
+
+  /* The magic pass: "Extended precision modular arithmetic"
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = ei_pmul(y, ei_p4f_minus_cephes_DP1);
+  xmm2 = ei_pmul(y, ei_p4f_minus_cephes_DP2);
+  xmm3 = ei_pmul(y, ei_p4f_minus_cephes_DP3);
+  x = ei_padd(x, xmm1);
+  x = ei_padd(x, xmm2);
+  x = ei_padd(x, xmm3);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = ei_p4f_coscof_p0;
+  Packet4f z = ei_pmul(x,x);
+
+  y = ei_pmadd(y,z,ei_p4f_coscof_p1);
+  y = ei_pmadd(y,z,ei_p4f_coscof_p2);
+  y = ei_pmul(y, z);
+  y = ei_pmul(y, z);
+  Packet4f tmp = _mm_mul_ps(z, ei_p4f_half);
+  y = ei_psub(y, tmp);
+  y = ei_padd(y, ei_p4f_1);
+
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+  Packet4f y2 = ei_p4f_sincof_p0;
+  y2 = ei_pmadd(y2, z, ei_p4f_sincof_p1);
+  y2 = ei_pmadd(y2, z, ei_p4f_sincof_p2);
+  y2 = ei_pmul(y2, z);
+  y2 = ei_pmadd(y2, x, x);
+
+  /* select the correct result from the two polynoms */
+  y2 = _mm_and_ps(poly_mask, y2);
+  y  = _mm_andnot_ps(poly_mask, y);
+  y  = _mm_or_ps(y,y2);
+
+  /* update the sign */
+  return _mm_xor_ps(y, sign_bit);
+}
+
+static EIGEN_UNUSED Packet4f ei_psqrt(Packet4f _x)
+{
+  Packet4f half = ei_pmul(_x, ei_pset1(.5f));
+  Packet4f x = _mm_rsqrt_ps(_x);
+  x = ei_pmul(x, ei_psub(ei_pset1(1.5f), ei_pmul(half, ei_pmul(x,x))));
+  return ei_pmul(_x,x);
+}
+
+#endif // EIGEN_MATH_FUNCTIONS_SSE_H

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

@@ -0,0 +1,480 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PACKET_MATH_SSE_H
+#define EIGEN_PACKET_MATH_SSE_H
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
+#endif
+
+typedef __m128  Packet4f;
+typedef __m128i Packet4i;
+typedef __m128d Packet2d;
+
+#define ei_vec4f_swizzle1(v,p,q,r,s) \
+  (_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), ((s)<<6|(r)<<4|(q)<<2|(p)))))
+
+#define ei_vec4i_swizzle1(v,p,q,r,s) \
+  (_mm_shuffle_epi32( v, ((s)<<6|(r)<<4|(q)<<2|(p))))
+
+#define ei_vec4f_swizzle2(a,b,p,q,r,s) \
+  (_mm_shuffle_ps( (a), (b), ((s)<<6|(r)<<4|(q)<<2|(p))))
+
+#define ei_vec4i_swizzle2(a,b,p,q,r,s) \
+  (_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), ((s)<<6|(r)<<4|(q)<<2|(p))))))
+  
+#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+  const Packet4f ei_p4f_##NAME = ei_pset1<float>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+  const Packet4f ei_p4f_##NAME = _mm_castsi128_ps(ei_pset1<int>(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+  const Packet4i ei_p4i_##NAME = ei_pset1<int>(X)
+
+template<> struct ei_packet_traits<float>  : ei_default_packet_traits
+{
+  typedef Packet4f type; enum {size=4};
+  enum {
+    HasSin  = 1,
+    HasCos  = 1,
+    HasLog  = 1,
+    HasExp  = 1,
+    HasSqrt = 1
+  };
+};
+template<> struct ei_packet_traits<double> : ei_default_packet_traits
+{ typedef Packet2d type; enum {size=2}; };
+template<> struct ei_packet_traits<int>    : ei_default_packet_traits
+{ typedef Packet4i type; enum {size=4}; };
+
+template<> struct ei_unpacket_traits<Packet4f> { typedef float  type; enum {size=4}; };
+template<> struct ei_unpacket_traits<Packet2d> { typedef double type; enum {size=2}; };
+template<> struct ei_unpacket_traits<Packet4i> { typedef int    type; enum {size=4}; };
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pset1<float>(const float&  from) { return _mm_set1_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pset1<double>(const double& from) { return _mm_set1_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pset1<int>(const int&    from) { return _mm_set1_epi32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pnegate(const Packet4f& a)
+{
+  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
+  return _mm_xor_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d ei_pnegate(const Packet2d& a)
+{
+  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
+  return _mm_xor_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ei_pnegate(const Packet4i& a)
+{
+  return ei_psub(_mm_setr_epi32(0,0,0,0), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+  // this version is slightly faster than 4 scalar products
+  return ei_vec4i_swizzle1(
+            ei_vec4i_swizzle2(
+              _mm_mul_epu32(a,b),
+              _mm_mul_epu32(ei_vec4i_swizzle1(a,1,0,3,2),
+                            ei_vec4i_swizzle1(b,1,0,3,2)),
+              0,2,0,2),
+            0,2,1,3);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ ei_assert(false && "packet integer division are not supported by SSE");
+  return ei_pset1<int>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4i ei_pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return ei_padd(ei_pmul(a,b), c); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_min_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+  // after some bench, this version *is* faster than a scalar implementation
+  Packet4i mask = _mm_cmplt_epi32(a,b);
+  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+  // after some bench, this version *is* faster than a scalar implementation
+  Packet4i mask = _mm_cmpgt_epi32(a,b);
+  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pload<float>(const float*    from) { return _mm_load_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_pload<double>(const double*  from) { return _mm_load_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_pload<int>(const int* from) { return _mm_load_si128(reinterpret_cast<const Packet4i*>(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_ploadu(const float*   from) {
+  Packet4f r;
+  r = _mm_castpd_ps(_mm_load_sd((double*)(from)));
+  r = _mm_loadh_pi(r, (const __m64*)(from+2));
+  return r;
+}
+template<> EIGEN_STRONG_INLINE Packet2d ei_ploadu<double>(const double*  from) { return _mm_castps_pd(ei_ploadu((const float*)(from))); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_ploadu<int>(const int* from) { return _mm_castpd_si128(ei_ploadu((const double*)(from))); }
+
+template<> EIGEN_STRONG_INLINE void ei_pstore<float>(float*   to, const Packet4f& from) { _mm_store_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void ei_pstore<double>(double* to, const Packet2d& from) { _mm_store_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void ei_pstore<int>(int*       to, const Packet4i& from) { _mm_store_si128(reinterpret_cast<Packet4i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void ei_pstoreu<double>(double* to, const Packet2d& from) {
+  _mm_storel_pd((to), from);
+  _mm_storeh_pd((to+1), from);
+}
+template<> EIGEN_STRONG_INLINE void ei_pstoreu<float>(float*  to, const Packet4f& from) { ei_pstoreu((double*)to, _mm_castps_pd(from)); }
+template<> EIGEN_STRONG_INLINE void ei_pstoreu<int>(int*      to, const Packet4i& from) { ei_pstoreu((double*)to, _mm_castsi128_pd(from)); }
+
+#ifdef _MSC_VER
+// this fix internal compilation error
+template<> EIGEN_STRONG_INLINE float  ei_pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
+template<> EIGEN_STRONG_INLINE double ei_pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
+template<> EIGEN_STRONG_INLINE int    ei_pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#else
+template<> EIGEN_STRONG_INLINE float  ei_pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
+template<> EIGEN_STRONG_INLINE double ei_pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
+template<> EIGEN_STRONG_INLINE int    ei_pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_preverse(const Packet4f& a)
+{ return _mm_shuffle_ps(a,a,0x1B); }
+template<> EIGEN_STRONG_INLINE Packet2d ei_preverse(const Packet2d& a)
+{ return _mm_shuffle_pd(a,a,0x1); }
+template<> EIGEN_STRONG_INLINE Packet4i ei_preverse(const Packet4i& a)
+{ return _mm_shuffle_epi32(a,0x1B); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_pabs(const Packet4f& a)
+{
+  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
+  return _mm_and_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d ei_pabs(const Packet2d& a)
+{
+  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
+  return _mm_and_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ei_pabs(const Packet4i& a)
+{
+  #ifdef __SSSE3__
+  return _mm_abs_epi32(a);
+  #else
+  Packet4i aux = _mm_srai_epi32(a,31);
+  return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
+  #endif
+}
+
+
+#ifdef __SSE3__
+// TODO implement SSE2 versions as well as integer versions
+template<> EIGEN_STRONG_INLINE Packet4f ei_preduxp<Packet4f>(const Packet4f* vecs)
+{
+  return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));
+}
+template<> EIGEN_STRONG_INLINE Packet2d ei_preduxp<Packet2d>(const Packet2d* vecs)
+{
+  return _mm_hadd_pd(vecs[0], vecs[1]);
+}
+// SSSE3 version:
+// EIGEN_STRONG_INLINE Packet4i ei_preduxp(const Packet4i* vecs)
+// {
+//   return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));
+// }
+
+template<> EIGEN_STRONG_INLINE float ei_predux<Packet4f>(const Packet4f& a)
+{
+  Packet4f tmp0 = _mm_hadd_ps(a,a);
+  return ei_pfirst(_mm_hadd_ps(tmp0, tmp0));
+}
+
+template<> EIGEN_STRONG_INLINE double ei_predux<Packet2d>(const Packet2d& a) { return ei_pfirst(_mm_hadd_pd(a, a)); }
+
+// SSSE3 version:
+// EIGEN_STRONG_INLINE float ei_predux(const Packet4i& a)
+// {
+//   Packet4i tmp0 = _mm_hadd_epi32(a,a);
+//   return ei_pfirst(_mm_hadd_epi32(tmp0, tmp0));
+// }
+#else
+// SSE2 versions
+template<> EIGEN_STRONG_INLINE float ei_predux<Packet4f>(const Packet4f& a)
+{
+  Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
+  return ei_pfirst(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double ei_predux<Packet2d>(const Packet2d& a)
+{
+  return ei_pfirst(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ei_preduxp<Packet4f>(const Packet4f* vecs)
+{
+  Packet4f tmp0, tmp1, tmp2;
+  tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);
+  tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);
+  tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);
+  tmp0 = _mm_add_ps(tmp0, tmp1);
+  tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);
+  tmp1 = _mm_add_ps(tmp1, tmp2);
+  tmp2 = _mm_movehl_ps(tmp1, tmp0);
+  tmp0 = _mm_movelh_ps(tmp0, tmp1);
+  return _mm_add_ps(tmp0, tmp2);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d ei_preduxp<Packet2d>(const Packet2d* vecs)
+{
+  return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));
+}
+#endif  // SSE3
+
+template<> EIGEN_STRONG_INLINE int ei_predux<Packet4i>(const Packet4i& a)
+{
+  Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
+  return ei_pfirst(tmp) + ei_pfirst(_mm_shuffle_epi32(tmp, 1));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i ei_preduxp<Packet4i>(const Packet4i* vecs)
+{
+  Packet4i tmp0, tmp1, tmp2;
+  tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);
+  tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);
+  tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);
+  tmp0 = _mm_add_epi32(tmp0, tmp1);
+  tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);
+  tmp1 = _mm_add_epi32(tmp1, tmp2);
+  tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);
+  tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);
+  return _mm_add_epi32(tmp0, tmp2);
+}
+
+// Other reduction functions:
+
+// mul
+template<> EIGEN_STRONG_INLINE float ei_predux_mul<Packet4f>(const Packet4f& a)
+{
+  Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
+  return ei_pfirst(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double ei_predux_mul<Packet2d>(const Packet2d& a)
+{
+  return ei_pfirst(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int ei_predux_mul<Packet4i>(const Packet4i& a)
+{
+  // after some experiments, it is seems this is the fastest way to implement it
+  // for GCC (eg., reusing ei_pmul is very slow !)
+  // TODO try to call _mm_mul_epu32 directly
+  EIGEN_ALIGN_128 int aux[4];
+  ei_pstore(aux, a);
+  return  (aux[0] * aux[1]) * (aux[2] * aux[3]);;
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float ei_predux_min<Packet4f>(const Packet4f& a)
+{
+  Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
+  return ei_pfirst(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double ei_predux_min<Packet2d>(const Packet2d& a)
+{
+  return ei_pfirst(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int ei_predux_min<Packet4i>(const Packet4i& a)
+{
+  // after some experiments, it is seems this is the fastest way to implement it
+  // for GCC (eg., it does not like using std::min after the ei_pstore !!)
+  EIGEN_ALIGN_128 int aux[4];
+  ei_pstore(aux, a);
+  register int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
+  register int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
+  return aux0<aux2 ? aux0 : aux2;
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float ei_predux_max<Packet4f>(const Packet4f& a)
+{
+  Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
+  return ei_pfirst(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double ei_predux_max<Packet2d>(const Packet2d& a)
+{
+  return ei_pfirst(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int ei_predux_max<Packet4i>(const Packet4i& a)
+{
+  // after some experiments, it is seems this is the fastest way to implement it
+  // for GCC (eg., it does not like using std::min after the ei_pstore !!)
+  EIGEN_ALIGN_128 int aux[4];
+  ei_pstore(aux, a);
+  register int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
+  register int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
+  return aux0>aux2 ? aux0 : aux2;
+}
+
+#if (defined __GNUC__)
+// template <> EIGEN_STRONG_INLINE Packet4f ei_pmadd(const Packet4f&  a, const Packet4f&  b, const Packet4f&  c)
+// {
+//   Packet4f res = b;
+//   asm("mulps %[a], %[b] \n\taddps %[c], %[b]" : [b] "+x" (res) : [a] "x" (a), [c] "x" (c));
+//   return res;
+// }
+// EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i&  a, const Packet4i&  b, const int i)
+// {
+//   Packet4i res = a;
+//   asm("palignr %[i], %[a], %[b] " : [b] "+x" (res) : [a] "x" (a), [i] "i" (i));
+//   return res;
+// }
+#endif
+
+#ifdef __SSSE3__
+// SSSE3 versions
+template<int Offset>
+struct ei_palign_impl<Offset,Packet4f>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4f& first, const Packet4f& second)
+  {
+    if (Offset!=0)
+      first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));
+  }
+};
+
+template<int Offset>
+struct ei_palign_impl<Offset,Packet4i>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4i& first, const Packet4i& second)
+  {
+    if (Offset!=0)
+      first = _mm_alignr_epi8(second,first, Offset*4);
+  }
+};
+
+template<int Offset>
+struct ei_palign_impl<Offset,Packet2d>
+{
+  EIGEN_STRONG_INLINE static void run(Packet2d& first, const Packet2d& second)
+  {
+    if (Offset==1)
+      first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));
+  }
+};
+#else
+// SSE2 versions
+template<int Offset>
+struct ei_palign_impl<Offset,Packet4f>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4f& first, const Packet4f& second)
+  {
+    if (Offset==1)
+    {
+      first = _mm_move_ss(first,second);
+      first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));
+    }
+    else if (Offset==2)
+    {
+      first = _mm_movehl_ps(first,first);
+      first = _mm_movelh_ps(first,second);
+    }
+    else if (Offset==3)
+    {
+      first = _mm_move_ss(first,second);
+      first = _mm_shuffle_ps(first,second,0x93);
+    }
+  }
+};
+
+template<int Offset>
+struct ei_palign_impl<Offset,Packet4i>
+{
+  EIGEN_STRONG_INLINE static void run(Packet4i& first, const Packet4i& second)
+  {
+    if (Offset==1)
+    {
+      first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+      first = _mm_shuffle_epi32(first,0x39);
+    }
+    else if (Offset==2)
+    {
+      first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));
+      first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+    }
+    else if (Offset==3)
+    {
+      first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
+      first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));
+    }
+  }
+};
+
+template<int Offset>
+struct ei_palign_impl<Offset,Packet2d>
+{
+  EIGEN_STRONG_INLINE static void run(Packet2d& first, const Packet2d& second)
+  {
+    if (Offset==1)
+    {
+      first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));
+      first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));
+    }
+  }
+};
+#endif
+
+#endif // EIGEN_PACKET_MATH_SSE_H

Eigen/src/Core/products/GeneralMatrixMatrix.h

@@ -0,0 +1,490 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_H
+
+template <int L2MemorySize,typename Scalar>
+struct ei_L2_block_traits {
+  enum {width = 8 * ei_meta_sqrt<L2MemorySize/(64*sizeof(Scalar))>::ret };
+};
+
+#ifndef EIGEN_EXTERN_INSTANTIATIONS
+
+template<typename Scalar>
+static void ei_cache_friendly_product(
+  int _rows, int _cols, int depth,
+  bool _lhsRowMajor, const Scalar* _lhs, int _lhsStride,
+  bool _rhsRowMajor, const Scalar* _rhs, int _rhsStride,
+  bool resRowMajor, Scalar* res, int resStride)
+{
+  const Scalar* EIGEN_RESTRICT lhs;
+  const Scalar* EIGEN_RESTRICT rhs;
+  int lhsStride, rhsStride, rows, cols;
+  bool lhsRowMajor;
+
+  if (resRowMajor)
+  {
+    lhs = _rhs;
+    rhs = _lhs;
+    lhsStride = _rhsStride;
+    rhsStride = _lhsStride;
+    cols = _rows;
+    rows = _cols;
+    lhsRowMajor = !_rhsRowMajor;
+    ei_assert(_lhsRowMajor);
+  }
+  else
+  {
+    lhs = _lhs;
+    rhs = _rhs;
+    lhsStride = _lhsStride;
+    rhsStride = _rhsStride;
+    rows = _rows;
+    cols = _cols;
+    lhsRowMajor = _lhsRowMajor;
+    ei_assert(!_rhsRowMajor);
+  }
+
+  typedef typename ei_packet_traits<Scalar>::type PacketType;
+
+
+
+#ifndef EIGEN_USE_ALT_PRODUCT
+
+  enum {
+    PacketSize = sizeof(PacketType)/sizeof(Scalar),
+    #if (defined __i386__)
+    HalfRegisterCount = 4,
+    #else
+    HalfRegisterCount = 8,
+    #endif
+
+    // register block size along the N direction
+    nr = HalfRegisterCount/2,
+
+    // register block size along the M direction
+    mr = 2 * PacketSize,
+
+    // max cache block size along the K direction
+    Max_kc = ei_L2_block_traits<EIGEN_TUNE_FOR_CPU_CACHE_SIZE,Scalar>::width,
+
+    // max cache block size along the M direction
+    Max_mc = 2*Max_kc
+  };
+
+  int kc = std::min<int>(Max_kc,depth);  // cache block size along the K direction
+  int mc = std::min<int>(Max_mc,rows);   // cache block size along the M direction
+
+  Scalar* blockA = ei_aligned_stack_new(Scalar, kc*mc);
+  Scalar* blockB = ei_aligned_stack_new(Scalar, kc*cols*PacketSize);
+
+  // number of columns which can be processed by packet of nr columns
+  int packet_cols = (cols/nr)*nr;
+
+  // GEMM_VAR1
+  for(int k2=0; k2<depth; k2+=kc)
+  {
+    const int actual_kc = std::min(k2+kc,depth)-k2;
+
+    // we have selected one row panel of rhs and one column panel of lhs
+    // pack rhs's panel into a sequential chunk of memory
+    // and expand each coeff to a constant packet for further reuse
+    {
+      int count = 0;
+      for(int j2=0; j2<packet_cols; j2+=nr)
+      {
+        const Scalar* b0 = &rhs[(j2+0)*rhsStride + k2];
+        const Scalar* b1 = &rhs[(j2+1)*rhsStride + k2];
+        const Scalar* b2 = &rhs[(j2+2)*rhsStride + k2];
+        const Scalar* b3 = &rhs[(j2+3)*rhsStride + k2];
+        for(int k=0; k<actual_kc; k++)
+        {
+          ei_pstore(&blockB[count+0*PacketSize], ei_pset1(b0[k]));
+          ei_pstore(&blockB[count+1*PacketSize], ei_pset1(b1[k]));
+          if (nr==4)
+          {
+            ei_pstore(&blockB[count+2*PacketSize], ei_pset1(b2[k]));
+            ei_pstore(&blockB[count+3*PacketSize], ei_pset1(b3[k]));
+          }
+          count += nr*PacketSize;
+        }
+      }
+    }
+
+    // => GEPP_VAR1
+    for(int i2=0; i2<rows; i2+=mc)
+    {
+      const int actual_mc = std::min(i2+mc,rows)-i2;
+
+      // We have selected a mc x kc block of lhs
+      // Let's pack it in a clever order for further purely sequential access
+      int count = 0;
+      const int peeled_mc = (actual_mc/mr)*mr;
+      if (lhsRowMajor)
+      {
+        for(int i=0; i<peeled_mc; i+=mr)
+          for(int k=0; k<actual_kc; k++)
+            for(int w=0; w<mr; w++)
+              blockA[count++] = lhs[(k2+k) + (i2+i+w)*lhsStride];
+        for(int i=peeled_mc; i<actual_mc; i++)
+        {
+          const Scalar* llhs = &lhs[(k2) + (i2+i)*lhsStride];
+          for(int k=0; k<actual_kc; k++)
+            blockA[count++] = llhs[k];
+        }
+      }
+      else
+      {
+        for(int i=0; i<peeled_mc; i+=mr)
+          for(int k=0; k<actual_kc; k++)
+            for(int w=0; w<mr; w++)
+              blockA[count++] = lhs[(k2+k)*lhsStride + i2+i+w];
+        for(int i=peeled_mc; i<actual_mc; i++)
+          for(int k=0; k<actual_kc; k++)
+            blockA[count++] = lhs[(k2+k)*lhsStride + i2+i];
+      }
+
+      // GEBP
+      // loops on each cache friendly block of the result/rhs
+      for(int j2=0; j2<packet_cols; j2+=nr)
+      {
+        // loops on each register blocking of lhs/res
+        const int peeled_mc = (actual_mc/mr)*mr;
+        for(int i=0; i<peeled_mc; i+=mr)
+        {
+          const Scalar* blA = &blockA[i*actual_kc];
+          #ifdef EIGEN_VECTORIZE_SSE
+          _mm_prefetch((const char*)(&blA[0]), _MM_HINT_T0);
+          #endif
+
+          // TODO move the res loads to the stores
+
+          // gets res block as register
+          PacketType C0, C1, C2, C3, C4, C5, C6, C7;
+                    C0 = ei_ploadu(&res[(j2+0)*resStride + i2 + i]);
+                    C1 = ei_ploadu(&res[(j2+1)*resStride + i2 + i]);
+          if(nr==4) C2 = ei_ploadu(&res[(j2+2)*resStride + i2 + i]);
+          if(nr==4) C3 = ei_ploadu(&res[(j2+3)*resStride + i2 + i]);
+                    C4 = ei_ploadu(&res[(j2+0)*resStride + i2 + i + PacketSize]);
+                    C5 = ei_ploadu(&res[(j2+1)*resStride + i2 + i + PacketSize]);
+          if(nr==4) C6 = ei_ploadu(&res[(j2+2)*resStride + i2 + i + PacketSize]);
+          if(nr==4) C7 = ei_ploadu(&res[(j2+3)*resStride + i2 + i + PacketSize]);
+
+          // performs "inner" product
+          // TODO let's check wether the flowing peeled loop could not be
+          //      optimized via optimal prefetching from one loop to the other
+          const Scalar* blB = &blockB[j2*actual_kc*PacketSize];
+          const int peeled_kc = (actual_kc/4)*4;
+          for(int k=0; k<peeled_kc; k+=4)
+          {
+            PacketType B0, B1, B2, B3, A0, A1;
+
+                      A0 = ei_pload(&blA[0*PacketSize]);
+                      A1 = ei_pload(&blA[1*PacketSize]);
+                      B0 = ei_pload(&blB[0*PacketSize]);
+                      B1 = ei_pload(&blB[1*PacketSize]);
+                      C0 = ei_pmadd(B0, A0, C0);
+            if(nr==4) B2 = ei_pload(&blB[2*PacketSize]);
+                      C4 = ei_pmadd(B0, A1, C4);
+            if(nr==4) B3 = ei_pload(&blB[3*PacketSize]);
+                      B0 = ei_pload(&blB[(nr==4 ? 4 : 2)*PacketSize]);
+                      C1 = ei_pmadd(B1, A0, C1);
+                      C5 = ei_pmadd(B1, A1, C5);
+                      B1 = ei_pload(&blB[(nr==4 ? 5 : 3)*PacketSize]);
+            if(nr==4) C2 = ei_pmadd(B2, A0, C2);
+            if(nr==4) C6 = ei_pmadd(B2, A1, C6);
+            if(nr==4) B2 = ei_pload(&blB[6*PacketSize]);
+            if(nr==4) C3 = ei_pmadd(B3, A0, C3);
+                      A0 = ei_pload(&blA[2*PacketSize]);
+            if(nr==4) C7 = ei_pmadd(B3, A1, C7);
+                      A1 = ei_pload(&blA[3*PacketSize]);
+            if(nr==4) B3 = ei_pload(&blB[7*PacketSize]);
+                      C0 = ei_pmadd(B0, A0, C0);
+                      C4 = ei_pmadd(B0, A1, C4);
+                      B0 = ei_pload(&blB[(nr==4 ? 8 : 4)*PacketSize]);
+                      C1 = ei_pmadd(B1, A0, C1);
+                      C5 = ei_pmadd(B1, A1, C5);
+                      B1 = ei_pload(&blB[(nr==4 ? 9 : 5)*PacketSize]);
+            if(nr==4) C2 = ei_pmadd(B2, A0, C2);
+            if(nr==4) C6 = ei_pmadd(B2, A1, C6);
+            if(nr==4) B2 = ei_pload(&blB[10*PacketSize]);
+            if(nr==4) C3 = ei_pmadd(B3, A0, C3);
+                      A0 = ei_pload(&blA[4*PacketSize]);
+            if(nr==4) C7 = ei_pmadd(B3, A1, C7);
+                      A1 = ei_pload(&blA[5*PacketSize]);
+            if(nr==4) B3 = ei_pload(&blB[11*PacketSize]);
+
+                      C0 = ei_pmadd(B0, A0, C0);
+                      C4 = ei_pmadd(B0, A1, C4);
+                      B0 = ei_pload(&blB[(nr==4 ? 12 : 6)*PacketSize]);
+                      C1 = ei_pmadd(B1, A0, C1);
+                      C5 = ei_pmadd(B1, A1, C5);
+                      B1 = ei_pload(&blB[(nr==4 ? 13 : 7)*PacketSize]);
+            if(nr==4) C2 = ei_pmadd(B2, A0, C2);
+            if(nr==4) C6 = ei_pmadd(B2, A1, C6);
+            if(nr==4) B2 = ei_pload(&blB[14*PacketSize]);
+            if(nr==4) C3 = ei_pmadd(B3, A0, C3);
+                      A0 = ei_pload(&blA[6*PacketSize]);
+            if(nr==4) C7 = ei_pmadd(B3, A1, C7);
+                      A1 = ei_pload(&blA[7*PacketSize]);
+            if(nr==4) B3 = ei_pload(&blB[15*PacketSize]);
+                      C0 = ei_pmadd(B0, A0, C0);
+                      C4 = ei_pmadd(B0, A1, C4);
+                      C1 = ei_pmadd(B1, A0, C1);
+                      C5 = ei_pmadd(B1, A1, C5);
+            if(nr==4) C2 = ei_pmadd(B2, A0, C2);
+            if(nr==4) C6 = ei_pmadd(B2, A1, C6);
+            if(nr==4) C3 = ei_pmadd(B3, A0, C3);
+            if(nr==4) C7 = ei_pmadd(B3, A1, C7);
+
+            blB += 4*nr*PacketSize;
+            blA += 4*mr;
+          }
+          // process remaining peeled loop
+          for(int k=peeled_kc; k<actual_kc; k++)
+          {
+            PacketType B0, B1, B2, B3, A0, A1;
+
+                      A0 = ei_pload(&blA[0*PacketSize]);
+                      A1 = ei_pload(&blA[1*PacketSize]);
+                      B0 = ei_pload(&blB[0*PacketSize]);
+                      B1 = ei_pload(&blB[1*PacketSize]);
+                      C0 = ei_pmadd(B0, A0, C0);
+            if(nr==4) B2 = ei_pload(&blB[2*PacketSize]);
+                      C4 = ei_pmadd(B0, A1, C4);
+            if(nr==4) B3 = ei_pload(&blB[3*PacketSize]);
+                      C1 = ei_pmadd(B1, A0, C1);
+                      C5 = ei_pmadd(B1, A1, C5);
+            if(nr==4) C2 = ei_pmadd(B2, A0, C2);
+            if(nr==4) C6 = ei_pmadd(B2, A1, C6);
+            if(nr==4) C3 = ei_pmadd(B3, A0, C3);
+            if(nr==4) C7 = ei_pmadd(B3, A1, C7);
+
+            blB += nr*PacketSize;
+            blA += mr;
+          }
+
+                    ei_pstoreu(&res[(j2+0)*resStride + i2 + i], C0);
+                    ei_pstoreu(&res[(j2+1)*resStride + i2 + i], C1);
+          if(nr==4) ei_pstoreu(&res[(j2+2)*resStride + i2 + i], C2);
+          if(nr==4) ei_pstoreu(&res[(j2+3)*resStride + i2 + i], C3);
+                    ei_pstoreu(&res[(j2+0)*resStride + i2 + i + PacketSize], C4);
+                    ei_pstoreu(&res[(j2+1)*resStride + i2 + i + PacketSize], C5);
+          if(nr==4) ei_pstoreu(&res[(j2+2)*resStride + i2 + i + PacketSize], C6);
+          if(nr==4) ei_pstoreu(&res[(j2+3)*resStride + i2 + i + PacketSize], C7);
+        }
+        for(int i=peeled_mc; i<actual_mc; i++)
+        {
+          const Scalar* blA = &blockA[i*actual_kc];
+          #ifdef EIGEN_VECTORIZE_SSE
+          _mm_prefetch((const char*)(&blA[0]), _MM_HINT_T0);
+          #endif
+
+          // gets a 1 x nr res block as registers
+          Scalar C0(0), C1(0), C2(0), C3(0);
+          const Scalar* blB = &blockB[j2*actual_kc*PacketSize];
+          for(int k=0; k<actual_kc; k++)
+          {
+            Scalar B0, B1, B2, B3, A0;
+
+                      A0 =  blA[k];
+                      B0 =  blB[0*PacketSize];
+                      B1 =  blB[1*PacketSize];
+                      C0 += B0 * A0;
+            if(nr==4) B2 =  blB[2*PacketSize];
+            if(nr==4) B3 =  blB[3*PacketSize];
+                      C1 += B1 * A0;
+            if(nr==4) C2 += B2 * A0;
+            if(nr==4) C3 += B3 * A0;
+
+            blB += nr*PacketSize;
+          }
+          res[(j2+0)*resStride + i2 + i] += C0;
+          res[(j2+1)*resStride + i2 + i] += C1;
+          if(nr==4) res[(j2+2)*resStride + i2 + i] += C2;
+          if(nr==4) res[(j2+3)*resStride + i2 + i] += C3;
+        }
+      }
+      // remaining rhs/res columns (<nr)
+      for(int j2=packet_cols; j2<cols; j2++)
+      {
+        for(int i=0; i<actual_mc; i++)
+        {
+          Scalar c0 = res[(j2)*resStride + i2+i];
+          if (lhsRowMajor)
+            for(int k=0; k<actual_kc; k++)
+              c0 += lhs[(k2+k)+(i2+i)*lhsStride] * rhs[j2*rhsStride + k2 + k];
+          else
+            for(int k=0; k<actual_kc; k++)
+              c0 += lhs[(k2+k)*lhsStride + i2+i] * rhs[j2*rhsStride + k2 + k];
+          res[(j2)*resStride + i2+i] = c0;
+        }
+      }
+    }
+  }
+
+  ei_aligned_stack_delete(Scalar, blockA, kc*mc);
+  ei_aligned_stack_delete(Scalar, blockB, kc*cols*PacketSize);
+
+#else // alternate product from cylmor
+
+  enum {
+    PacketSize = sizeof(PacketType)/sizeof(Scalar),
+    #if (defined __i386__)
+    // i386 architecture provides only 8 xmm registers,
+    // so let's reduce the max number of rows processed at once.
+    MaxBlockRows = 4,
+    MaxBlockRows_ClampingMask = 0xFFFFFC,
+    #else
+    MaxBlockRows = 8,
+    MaxBlockRows_ClampingMask = 0xFFFFF8,
+    #endif
+    // maximal size of the blocks fitted in L2 cache
+    MaxL2BlockSize = ei_L2_block_traits<EIGEN_TUNE_FOR_CPU_CACHE_SIZE,Scalar>::width
+  };
+
+  const bool resIsAligned = (PacketSize==1) || (((resStride%PacketSize) == 0) && (size_t(res)%16==0));
+
+  const int remainingSize = depth % PacketSize;
+  const int size = depth - remainingSize; // third dimension of the product clamped to packet boundaries
+
+  const int l2BlockRows = MaxL2BlockSize > rows ? rows : 512;
+  const int l2BlockCols = MaxL2BlockSize > cols ? cols : 128;
+  const int l2BlockSize = MaxL2BlockSize > size ? size : 256;
+  const int l2BlockSizeAligned = (1 + std::max(l2BlockSize,l2BlockCols)/PacketSize)*PacketSize;
+  const bool needRhsCopy = (PacketSize>1) && ((rhsStride%PacketSize!=0) || (size_t(rhs)%16!=0));
+
+  Scalar* EIGEN_RESTRICT block = new Scalar[l2BlockRows*size];
+//   for(int i=0; i<l2BlockRows*l2BlockSize; ++i)
+//     block[i] = 0;
+  // loops on each L2 cache friendly blocks of lhs
+  for(int l2k=0; l2k<depth; l2k+=l2BlockSize)
+  {
+    for(int l2i=0; l2i<rows; l2i+=l2BlockRows)
+    {
+      // We have selected a block of lhs
+      // Packs this block into 'block'
+      int count = 0;
+      for(int k=0; k<l2BlockSize; k+=MaxBlockRows)
+      {
+        for(int i=0; i<l2BlockRows; i+=2*PacketSize)
+          for (int w=0; w<MaxBlockRows; ++w)
+            for (int y=0; y<2*PacketSize; ++y)
+              block[count++] = lhs[(k+l2k+w)*lhsStride + l2i+i+ y];
+      }
+
+      // loops on each L2 cache firendly block of the result/rhs
+      for(int l2j=0; l2j<cols; l2j+=l2BlockCols)
+      {
+        for(int k=0; k<l2BlockSize; k+=MaxBlockRows)
+        {
+          for(int j=0; j<l2BlockCols; ++j)
+          {
+            PacketType A0, A1, A2, A3, A4, A5, A6, A7;
+
+            // Load the packets from rhs and reorder them
+
+            // Here we need some vector reordering
+            // Right now its hardcoded to packets of 4 elements
+            const Scalar* lrhs = &rhs[(j+l2j)*rhsStride+(k+l2k)];
+            A0 = ei_pset1(lrhs[0]);
+            A1 = ei_pset1(lrhs[1]);
+            A2 = ei_pset1(lrhs[2]);
+            A3 = ei_pset1(lrhs[3]);
+            if (MaxBlockRows==8)
+            {
+              A4 = ei_pset1(lrhs[4]);
+              A5 = ei_pset1(lrhs[5]);
+              A6 = ei_pset1(lrhs[6]);
+              A7 = ei_pset1(lrhs[7]);
+            }
+
+            Scalar * lb = &block[l2BlockRows * k];
+            for(int i=0; i<l2BlockRows; i+=2*PacketSize)
+            {
+              PacketType R0, R1, L0, L1, T0, T1;
+
+              // We perform "cross products" of vectors to avoid
+              // reductions (horizontal ops) afterwards
+              T0 = ei_pload(&res[(j+l2j)*resStride+l2i+i]);
+              T1 = ei_pload(&res[(j+l2j)*resStride+l2i+i+PacketSize]);
+
+              R0 = ei_pload(&lb[0*PacketSize]);
+              L0 = ei_pload(&lb[1*PacketSize]);
+              R1 = ei_pload(&lb[2*PacketSize]);
+              L1 = ei_pload(&lb[3*PacketSize]);
+              T0 = ei_pmadd(R0, A0, T0);
+              T1 = ei_pmadd(L0, A0, T1);
+              R0 = ei_pload(&lb[4*PacketSize]);
+              L0 = ei_pload(&lb[5*PacketSize]);
+              T0 = ei_pmadd(R1, A1, T0);
+              T1 = ei_pmadd(L1, A1, T1);
+              R1 = ei_pload(&lb[6*PacketSize]);
+              L1 = ei_pload(&lb[7*PacketSize]);
+              T0 = ei_pmadd(R0, A2, T0);
+              T1 = ei_pmadd(L0, A2, T1);
+              if(MaxBlockRows==8)
+              {
+                R0 = ei_pload(&lb[8*PacketSize]);
+                L0 = ei_pload(&lb[9*PacketSize]);
+              }
+              T0 = ei_pmadd(R1, A3, T0);
+              T1 = ei_pmadd(L1, A3, T1);
+              if(MaxBlockRows==8)
+              {
+                R1 = ei_pload(&lb[10*PacketSize]);
+                L1 = ei_pload(&lb[11*PacketSize]);
+                T0 = ei_pmadd(R0, A4, T0);
+                T1 = ei_pmadd(L0, A4, T1);
+                R0 = ei_pload(&lb[12*PacketSize]);
+                L0 = ei_pload(&lb[13*PacketSize]);
+                T0 = ei_pmadd(R1, A5, T0);
+                T1 = ei_pmadd(L1, A5, T1);
+                R1 = ei_pload(&lb[14*PacketSize]);
+                L1 = ei_pload(&lb[15*PacketSize]);
+                T0 = ei_pmadd(R0, A6, T0);
+                T1 = ei_pmadd(L0, A6, T1);
+                T0 = ei_pmadd(R1, A7, T0);
+                T1 = ei_pmadd(L1, A7, T1);
+              }
+              lb += MaxBlockRows*2*PacketSize;
+
+              ei_pstore(&res[(j+l2j)*resStride+l2i+i], T0);
+              ei_pstore(&res[(j+l2j)*resStride+l2i+i+PacketSize], T1);
+            }
+          }
+        }
+      }
+    }
+  }
+  delete[] block;
+#endif
+
+
+}
+
+#endif // EIGEN_EXTERN_INSTANTIATIONS
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_H

Eigen/src/Core/products/GeneralMatrixVector.h

@@ -0,0 +1,434 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_H
+
+/* Optimized col-major matrix * vector product:
+ * This algorithm processes 4 columns at onces that allows to both reduce
+ * the number of load/stores of the result by a factor 4 and to reduce
+ * the instruction dependency. Moreover, we know that all bands have the
+ * same alignment pattern.
+ * TODO: since rhs gets evaluated only once, no need to evaluate it
+ */
+template<typename Scalar, typename RhsType>
+static EIGEN_DONT_INLINE void ei_cache_friendly_product_colmajor_times_vector(
+  int size,
+  const Scalar* lhs, int lhsStride,
+  const RhsType& rhs,
+  Scalar* res)
+{
+  #ifdef _EIGEN_ACCUMULATE_PACKETS
+  #error _EIGEN_ACCUMULATE_PACKETS has already been defined
+  #endif
+  #define _EIGEN_ACCUMULATE_PACKETS(A0,A13,A2) \
+    ei_pstore(&res[j], \
+      ei_padd(ei_pload(&res[j]), \
+        ei_padd( \
+          ei_padd(ei_pmul(ptmp0,EIGEN_CAT(ei_ploa , A0)(&lhs0[j])), \
+                  ei_pmul(ptmp1,EIGEN_CAT(ei_ploa , A13)(&lhs1[j]))), \
+          ei_padd(ei_pmul(ptmp2,EIGEN_CAT(ei_ploa , A2)(&lhs2[j])), \
+                  ei_pmul(ptmp3,EIGEN_CAT(ei_ploa , A13)(&lhs3[j]))) )))
+
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  const int PacketSize = sizeof(Packet)/sizeof(Scalar);
+
+  enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };
+  const int columnsAtOnce = 4;
+  const int peels = 2;
+  const int PacketAlignedMask = PacketSize-1;
+  const int PeelAlignedMask = PacketSize*peels-1;
+
+  // How many coeffs of the result do we have to skip to be aligned.
+  // Here we assume data are at least aligned on the base scalar type that is mandatory anyway.
+  const int alignedStart = ei_alignmentOffset(res,size);
+  const int alignedSize = PacketSize>1 ? alignedStart + ((size-alignedStart) & ~PacketAlignedMask) : 0;
+  const int peeledSize  = peels>1 ? alignedStart + ((alignedSize-alignedStart) & ~PeelAlignedMask) : alignedStart;
+
+  const int alignmentStep = PacketSize>1 ? (PacketSize - lhsStride % PacketSize) & PacketAlignedMask : 0;
+  int alignmentPattern = alignmentStep==0 ? AllAligned
+                       : alignmentStep==(PacketSize/2) ? EvenAligned
+                       : FirstAligned;
+
+  // we cannot assume the first element is aligned because of sub-matrices
+  const int lhsAlignmentOffset = ei_alignmentOffset(lhs,size);
+
+  // find how many columns do we have to skip to be aligned with the result (if possible)
+  int skipColumns = 0;
+  if (PacketSize>1)
+  {
+    ei_internal_assert(size_t(lhs+lhsAlignmentOffset)%sizeof(Packet)==0 || size<PacketSize);
+
+    while (skipColumns<PacketSize &&
+           alignedStart != ((lhsAlignmentOffset + alignmentStep*skipColumns)%PacketSize))
+      ++skipColumns;
+    if (skipColumns==PacketSize)
+    {
+      // nothing can be aligned, no need to skip any column
+      alignmentPattern = NoneAligned;
+      skipColumns = 0;
+    }
+    else
+    {
+      skipColumns = std::min(skipColumns,rhs.size());
+      // note that the skiped columns are processed later.
+    }
+
+    ei_internal_assert((alignmentPattern==NoneAligned) || (size_t(lhs+alignedStart+lhsStride*skipColumns)%sizeof(Packet))==0);
+  }
+
+  int offset1 = (FirstAligned && alignmentStep==1?3:1);
+  int offset3 = (FirstAligned && alignmentStep==1?1:3);
+
+  int columnBound = ((rhs.size()-skipColumns)/columnsAtOnce)*columnsAtOnce + skipColumns;
+  for (int i=skipColumns; i<columnBound; i+=columnsAtOnce)
+  {
+    Packet ptmp0 = ei_pset1(rhs[i]),   ptmp1 = ei_pset1(rhs[i+offset1]),
+           ptmp2 = ei_pset1(rhs[i+2]), ptmp3 = ei_pset1(rhs[i+offset3]);
+
+    // this helps a lot generating better binary code
+    const Scalar *lhs0 = lhs + i*lhsStride, *lhs1 = lhs + (i+offset1)*lhsStride,
+                 *lhs2 = lhs + (i+2)*lhsStride, *lhs3 = lhs + (i+offset3)*lhsStride;
+
+    if (PacketSize>1)
+    {
+      /* explicit vectorization */
+      // process initial unaligned coeffs
+      for (int j=0; j<alignedStart; ++j)
+        res[j] += ei_pfirst(ptmp0)*lhs0[j] + ei_pfirst(ptmp1)*lhs1[j] + ei_pfirst(ptmp2)*lhs2[j] + ei_pfirst(ptmp3)*lhs3[j];
+
+      if (alignedSize>alignedStart)
+      {
+        switch(alignmentPattern)
+        {
+          case AllAligned:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,d,d);
+            break;
+          case EvenAligned:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,du,d);
+            break;
+          case FirstAligned:
+            if(peels>1)
+            {
+              Packet A00, A01, A02, A03, A10, A11, A12, A13;
+
+              A01 = ei_pload(&lhs1[alignedStart-1]);
+              A02 = ei_pload(&lhs2[alignedStart-2]);
+              A03 = ei_pload(&lhs3[alignedStart-3]);
+
+              for (int j = alignedStart; j<peeledSize; j+=peels*PacketSize)
+              {
+                A11 = ei_pload(&lhs1[j-1+PacketSize]);  ei_palign<1>(A01,A11);
+                A12 = ei_pload(&lhs2[j-2+PacketSize]);  ei_palign<2>(A02,A12);
+                A13 = ei_pload(&lhs3[j-3+PacketSize]);  ei_palign<3>(A03,A13);
+
+                A00 = ei_pload (&lhs0[j]);
+                A10 = ei_pload (&lhs0[j+PacketSize]);
+                A00 = ei_pmadd(ptmp0, A00, ei_pload(&res[j]));
+                A10 = ei_pmadd(ptmp0, A10, ei_pload(&res[j+PacketSize]));
+
+                A00 = ei_pmadd(ptmp1, A01, A00);
+                A01 = ei_pload(&lhs1[j-1+2*PacketSize]);  ei_palign<1>(A11,A01);
+                A00 = ei_pmadd(ptmp2, A02, A00);
+                A02 = ei_pload(&lhs2[j-2+2*PacketSize]);  ei_palign<2>(A12,A02);
+                A00 = ei_pmadd(ptmp3, A03, A00);
+                ei_pstore(&res[j],A00);
+                A03 = ei_pload(&lhs3[j-3+2*PacketSize]);  ei_palign<3>(A13,A03);
+                A10 = ei_pmadd(ptmp1, A11, A10);
+                A10 = ei_pmadd(ptmp2, A12, A10);
+                A10 = ei_pmadd(ptmp3, A13, A10);
+                ei_pstore(&res[j+PacketSize],A10);
+              }
+            }
+            for (int j = peeledSize; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,du,du);
+            break;
+          default:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(du,du,du);
+            break;
+        }
+      }
+    } // end explicit vectorization
+
+    /* process remaining coeffs (or all if there is no explicit vectorization) */
+    for (int j=alignedSize; j<size; ++j)
+	  res[j] += ei_pfirst(ptmp0)*lhs0[j] + ei_pfirst(ptmp1)*lhs1[j] + ei_pfirst(ptmp2)*lhs2[j] + ei_pfirst(ptmp3)*lhs3[j];
+  }
+
+  // process remaining first and last columns (at most columnsAtOnce-1)
+  int end = rhs.size();
+  int start = columnBound;
+  do
+  {
+    for (int i=start; i<end; ++i)
+    {
+      Packet ptmp0 = ei_pset1(rhs[i]);
+      const Scalar* lhs0 = lhs + i*lhsStride;
+
+      if (PacketSize>1)
+      {
+        /* explicit vectorization */
+        // process first unaligned result's coeffs
+        for (int j=0; j<alignedStart; ++j)
+          res[j] += ei_pfirst(ptmp0) * lhs0[j];
+
+        // process aligned result's coeffs
+        if ((size_t(lhs0+alignedStart)%sizeof(Packet))==0)
+          for (int j = alignedStart;j<alignedSize;j+=PacketSize)
+            ei_pstore(&res[j], ei_pmadd(ptmp0,ei_pload(&lhs0[j]),ei_pload(&res[j])));
+        else
+          for (int j = alignedStart;j<alignedSize;j+=PacketSize)
+            ei_pstore(&res[j], ei_pmadd(ptmp0,ei_ploadu(&lhs0[j]),ei_pload(&res[j])));
+      }
+
+      // process remaining scalars (or all if no explicit vectorization)
+      for (int j=alignedSize; j<size; ++j)
+        res[j] += ei_pfirst(ptmp0) * lhs0[j];
+    }
+    if (skipColumns)
+    {
+      start = 0;
+      end = skipColumns;
+      skipColumns = 0;
+    }
+    else
+      break;
+  } while(PacketSize>1);
+  #undef _EIGEN_ACCUMULATE_PACKETS
+}
+
+// TODO add peeling to mask unaligned load/stores
+template<typename Scalar, typename ResType>
+static EIGEN_DONT_INLINE void ei_cache_friendly_product_rowmajor_times_vector(
+  const Scalar* lhs, int lhsStride,
+  const Scalar* rhs, int rhsSize,
+  ResType& res)
+{
+  #ifdef _EIGEN_ACCUMULATE_PACKETS
+  #error _EIGEN_ACCUMULATE_PACKETS has already been defined
+  #endif
+
+  #define _EIGEN_ACCUMULATE_PACKETS(A0,A13,A2) {\
+    Packet b = ei_pload(&rhs[j]); \
+    ptmp0 = ei_pmadd(b, EIGEN_CAT(ei_ploa,A0) (&lhs0[j]), ptmp0); \
+    ptmp1 = ei_pmadd(b, EIGEN_CAT(ei_ploa,A13)(&lhs1[j]), ptmp1); \
+    ptmp2 = ei_pmadd(b, EIGEN_CAT(ei_ploa,A2) (&lhs2[j]), ptmp2); \
+    ptmp3 = ei_pmadd(b, EIGEN_CAT(ei_ploa,A13)(&lhs3[j]), ptmp3); }
+
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  const int PacketSize = sizeof(Packet)/sizeof(Scalar);
+
+  enum { AllAligned=0, EvenAligned=1, FirstAligned=2, NoneAligned=3 };
+  const int rowsAtOnce = 4;
+  const int peels = 2;
+  const int PacketAlignedMask = PacketSize-1;
+  const int PeelAlignedMask = PacketSize*peels-1;
+  const int size = rhsSize;
+
+  // How many coeffs of the result do we have to skip to be aligned.
+  // Here we assume data are at least aligned on the base scalar type that is mandatory anyway.
+  const int alignedStart = ei_alignmentOffset(rhs, size);
+  const int alignedSize = PacketSize>1 ? alignedStart + ((size-alignedStart) & ~PacketAlignedMask) : 0;
+  const int peeledSize  = peels>1 ? alignedStart + ((alignedSize-alignedStart) & ~PeelAlignedMask) : alignedStart;
+
+  const int alignmentStep = PacketSize>1 ? (PacketSize - lhsStride % PacketSize) & PacketAlignedMask : 0;
+  int alignmentPattern = alignmentStep==0 ? AllAligned
+                       : alignmentStep==(PacketSize/2) ? EvenAligned
+                       : FirstAligned;
+
+  // we cannot assume the first element is aligned because of sub-matrices
+  const int lhsAlignmentOffset = ei_alignmentOffset(lhs,size);
+
+  // find how many rows do we have to skip to be aligned with rhs (if possible)
+  int skipRows = 0;
+  if (PacketSize>1)
+  {
+    ei_internal_assert(size_t(lhs+lhsAlignmentOffset)%sizeof(Packet)==0  || size<PacketSize);
+
+    while (skipRows<PacketSize &&
+           alignedStart != ((lhsAlignmentOffset + alignmentStep*skipRows)%PacketSize))
+      ++skipRows;
+    if (skipRows==PacketSize)
+    {
+      // nothing can be aligned, no need to skip any column
+      alignmentPattern = NoneAligned;
+      skipRows = 0;
+    }
+    else
+    {
+      skipRows = std::min(skipRows,res.size());
+      // note that the skiped columns are processed later.
+    }
+    ei_internal_assert((alignmentPattern==NoneAligned) || PacketSize==1
+      || (size_t(lhs+alignedStart+lhsStride*skipRows)%sizeof(Packet))==0);
+  }
+
+  int offset1 = (FirstAligned && alignmentStep==1?3:1);
+  int offset3 = (FirstAligned && alignmentStep==1?1:3);
+
+  int rowBound = ((res.size()-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;
+  for (int i=skipRows; i<rowBound; i+=rowsAtOnce)
+  {
+    Scalar tmp0 = Scalar(0), tmp1 = Scalar(0), tmp2 = Scalar(0), tmp3 = Scalar(0);
+
+    // this helps the compiler generating good binary code
+    const Scalar *lhs0 = lhs + i*lhsStride,     *lhs1 = lhs + (i+offset1)*lhsStride,
+                 *lhs2 = lhs + (i+2)*lhsStride, *lhs3 = lhs + (i+offset3)*lhsStride;
+
+    if (PacketSize>1)
+    {
+      /* explicit vectorization */
+      Packet ptmp0 = ei_pset1(Scalar(0)), ptmp1 = ei_pset1(Scalar(0)), ptmp2 = ei_pset1(Scalar(0)), ptmp3 = ei_pset1(Scalar(0));
+
+      // process initial unaligned coeffs
+      // FIXME this loop get vectorized by the compiler !
+      for (int j=0; j<alignedStart; ++j)
+      {
+        Scalar b = rhs[j];
+        tmp0 += b*lhs0[j]; tmp1 += b*lhs1[j]; tmp2 += b*lhs2[j]; tmp3 += b*lhs3[j];
+      }
+
+      if (alignedSize>alignedStart)
+      {
+        switch(alignmentPattern)
+        {
+          case AllAligned:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,d,d);
+            break;
+          case EvenAligned:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,du,d);
+            break;
+          case FirstAligned:
+            if (peels>1)
+            {
+              /* Here we proccess 4 rows with with two peeled iterations to hide
+               * tghe overhead of unaligned loads. Moreover unaligned loads are handled
+               * using special shift/move operations between the two aligned packets
+               * overlaping the desired unaligned packet. This is *much* more efficient
+               * than basic unaligned loads.
+               */
+              Packet A01, A02, A03, b, A11, A12, A13;
+              A01 = ei_pload(&lhs1[alignedStart-1]);
+              A02 = ei_pload(&lhs2[alignedStart-2]);
+              A03 = ei_pload(&lhs3[alignedStart-3]);
+
+              for (int j = alignedStart; j<peeledSize; j+=peels*PacketSize)
+              {
+                b = ei_pload(&rhs[j]);
+                A11 = ei_pload(&lhs1[j-1+PacketSize]);  ei_palign<1>(A01,A11);
+                A12 = ei_pload(&lhs2[j-2+PacketSize]);  ei_palign<2>(A02,A12);
+                A13 = ei_pload(&lhs3[j-3+PacketSize]);  ei_palign<3>(A03,A13);
+
+                ptmp0 = ei_pmadd(b, ei_pload (&lhs0[j]), ptmp0);
+                ptmp1 = ei_pmadd(b, A01, ptmp1);
+                A01 = ei_pload(&lhs1[j-1+2*PacketSize]);  ei_palign<1>(A11,A01);
+                ptmp2 = ei_pmadd(b, A02, ptmp2);
+                A02 = ei_pload(&lhs2[j-2+2*PacketSize]);  ei_palign<2>(A12,A02);
+                ptmp3 = ei_pmadd(b, A03, ptmp3);
+                A03 = ei_pload(&lhs3[j-3+2*PacketSize]);  ei_palign<3>(A13,A03);
+
+                b = ei_pload(&rhs[j+PacketSize]);
+                ptmp0 = ei_pmadd(b, ei_pload (&lhs0[j+PacketSize]), ptmp0);
+                ptmp1 = ei_pmadd(b, A11, ptmp1);
+                ptmp2 = ei_pmadd(b, A12, ptmp2);
+                ptmp3 = ei_pmadd(b, A13, ptmp3);
+              }
+            }
+            for (int j = peeledSize; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(d,du,du);
+            break;
+          default:
+            for (int j = alignedStart; j<alignedSize; j+=PacketSize)
+              _EIGEN_ACCUMULATE_PACKETS(du,du,du);
+            break;
+        }
+        tmp0 += ei_predux(ptmp0);
+        tmp1 += ei_predux(ptmp1);
+        tmp2 += ei_predux(ptmp2);
+        tmp3 += ei_predux(ptmp3);
+      }
+    } // end explicit vectorization
+
+    // process remaining coeffs (or all if no explicit vectorization)
+    // FIXME this loop get vectorized by the compiler !
+    for (int j=alignedSize; j<size; ++j)
+    {
+      Scalar b = rhs[j];
+      tmp0 += b*lhs0[j]; tmp1 += b*lhs1[j]; tmp2 += b*lhs2[j]; tmp3 += b*lhs3[j];
+    }
+    res[i] += tmp0; res[i+offset1] += tmp1; res[i+2] += tmp2; res[i+offset3] += tmp3;
+  }
+
+  // process remaining first and last rows (at most columnsAtOnce-1)
+  int end = res.size();
+  int start = rowBound;
+  do
+  {
+    for (int i=start; i<end; ++i)
+    {
+      Scalar tmp0 = Scalar(0);
+      Packet ptmp0 = ei_pset1(tmp0);
+      const Scalar* lhs0 = lhs + i*lhsStride;
+      // process first unaligned result's coeffs
+      // FIXME this loop get vectorized by the compiler !
+      for (int j=0; j<alignedStart; ++j)
+        tmp0 += rhs[j] * lhs0[j];
+
+      if (alignedSize>alignedStart)
+      {
+        // process aligned rhs coeffs
+        if ((size_t(lhs0+alignedStart)%sizeof(Packet))==0)
+          for (int j = alignedStart;j<alignedSize;j+=PacketSize)
+            ptmp0 = ei_pmadd(ei_pload(&rhs[j]), ei_pload(&lhs0[j]), ptmp0);
+        else
+          for (int j = alignedStart;j<alignedSize;j+=PacketSize)
+            ptmp0 = ei_pmadd(ei_pload(&rhs[j]), ei_ploadu(&lhs0[j]), ptmp0);
+        tmp0 += ei_predux(ptmp0);
+      }
+
+      // process remaining scalars
+      // FIXME this loop get vectorized by the compiler !
+      for (int j=alignedSize; j<size; ++j)
+        tmp0 += rhs[j] * lhs0[j];
+      res[i] += tmp0;
+    }
+    if (skipRows)
+    {
+      start = 0;
+      end = skipRows;
+      skipRows = 0;
+    }
+    else
+      break;
+  } while(PacketSize>1);
+
+  #undef _EIGEN_ACCUMULATE_PACKETS
+}
+
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_H

Eigen/src/Core/products/SelfadjointMatrixVector.h

@@ -0,0 +1,146 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+
+template<bool Conjugate> struct ei_conj_if {
+  template<typename Scalar> Scalar operator() (const Scalar& x) const { return ei_conj(x); }
+};
+
+template<> struct ei_conj_if<false> {
+  template<typename Scalar> Scalar& operator() (Scalar& x) const { return x; }
+};
+
+/* Optimized col-major selfadjoint matrix * vector product:
+ * This algorithm processes 2 columns at onces that allows to both reduce
+ * the number of load/stores of the result by a factor 2 and to reduce
+ * the instruction dependency.
+ */
+template<typename Scalar, int StorageOrder, int UpLo>
+static EIGEN_DONT_INLINE void ei_product_selfadjoint_vector(
+  int size,
+  const Scalar* lhs, int lhsStride,
+  const Scalar* rhs, //int rhsIncr,
+  Scalar* res)
+{
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  const int PacketSize = sizeof(Packet)/sizeof(Scalar);
+
+  enum {
+    IsRowMajor = StorageOrder==RowMajorBit ? 1 : 0,
+    IsLower = UpLo == LowerTriangularBit ? 1 : 0,
+    FirstTriangular = IsRowMajor == IsLower
+  };
+
+  ei_conj_if<NumTraits<Scalar>::IsComplex && IsRowMajor> conj0;
+  ei_conj_if<NumTraits<Scalar>::IsComplex && !IsRowMajor> conj1;
+
+  for (int i=0;i<size;i++)
+    res[i] = 0;
+
+  int bound = std::max(0,size-8) & 0xfffffffE;
+  if (FirstTriangular)
+    bound = size - bound;
+
+  for (int j=FirstTriangular ? bound : 0;
+       j<(FirstTriangular ? size : bound);j+=2)
+  {
+    register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+    register const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
+
+    Scalar t0 = rhs[j];
+    Packet ptmp0 = ei_pset1(t0);
+    Scalar t1 = rhs[j+1];
+    Packet ptmp1 = ei_pset1(t1);
+
+    Scalar t2 = 0;
+    Packet ptmp2 = ei_pset1(t2);
+    Scalar t3 = 0;
+    Packet ptmp3 = ei_pset1(t3);
+
+    size_t starti = FirstTriangular ? 0 : j+2;
+    size_t endi   = FirstTriangular ? j : size;
+    size_t alignedEnd = starti;
+    size_t alignedStart = (starti) + ei_alignmentOffset(&res[starti], endi-starti);
+    alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
+
+    res[j]   += t0 * conj0(A0[j]);
+    if(FirstTriangular)
+    {
+      res[j+1]   += t1 * conj0(A1[j+1]);
+      res[j] += t1 * conj0(A1[j]);
+      t3 += conj1(A1[j]) * rhs[j];
+    }
+    else
+    {
+      res[j+1] += t0 * conj0(A0[j+1]) + t1 * conj0(A1[j+1]);
+      t2 += conj1(A0[j+1]) * rhs[j+1];
+    }
+
+    for (size_t i=starti; i<alignedStart; ++i)
+    {
+      res[i] += t0 * A0[i] + t1 * A1[i];
+      t2 += ei_conj(A0[i]) * rhs[i];
+      t3 += ei_conj(A1[i]) * rhs[i];
+    }
+    for (size_t i=alignedStart; i<alignedEnd; i+=PacketSize)
+    {
+      Packet A0i = ei_ploadu(&A0[i]);
+      Packet A1i = ei_ploadu(&A1[i]);
+      Packet Bi = ei_ploadu(&rhs[i]); // FIXME should be aligned in most cases
+      Packet Xi = ei_pload(&res[i]);
+
+      Xi = ei_padd(ei_padd(Xi, ei_pmul(ptmp0, conj0(A0i))), ei_pmul(ptmp1, conj0(A1i)));
+      ptmp2 = ei_padd(ptmp2, ei_pmul(conj1(A0i), Bi));
+      ptmp3 = ei_padd(ptmp3, ei_pmul(conj1(A1i), Bi));
+      ei_pstore(&res[i],Xi);
+    }
+    for (size_t i=alignedEnd; i<endi; i++)
+    {
+      res[i] += t0 * conj0(A0[i]) + t1 * conj0(A1[i]);
+      t2 += conj1(A0[i]) * rhs[i];
+      t3 += conj1(A1[i]) * rhs[i];
+    }
+
+    res[j]   += t2 + ei_predux(ptmp2);
+    res[j+1] += t3 + ei_predux(ptmp3);
+  }
+  for (int j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
+  {
+    register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+
+    Scalar t1 = rhs[j];
+    Scalar t2 = 0;
+    res[j] += t1 * conj0(A0[j]);
+    for (int i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++) {
+      res[i] += t1 * conj0(A0[i]);
+      t2 += conj1(A0[i]) * rhs[i];
+    }
+    res[j] += t2;
+  }
+}
+
+
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H

Eigen/src/Core/util/CMakeLists.txt

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

Eigen/src/Core/util/Constants.h

@@ -0,0 +1,270 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CONSTANTS_H
+#define EIGEN_CONSTANTS_H
+
+/** This value means that a quantity is not known at compile-time, and that instead the value is
+  * stored in some runtime variable.
+  *
+  * Explanation for the choice of this value:
+  * - It should be positive and larger than the number of entries in any reasonable fixed-size matrix.
+  *   This allows to simplify many compile-time conditions throughout Eigen.
+  * - It should be smaller than the sqrt of INT_MAX. Indeed, we often multiply a number of rows with a number
+  *   of columns in order to compute a number of coefficients. Even if we guard that with an "if" checking whether
+  *   the values are Dynamic, we still get a compiler warning "integer overflow". So the only way to get around
+  *   it would be a meta-selector. Doing this everywhere would reduce code readability and lenghten compilation times.
+  *   Also, disabling compiler warnings for integer overflow, sounds like a bad idea.
+  * - It should be a prime number, because for example the old value 10000 led to bugs with 100x100 matrices.
+  *
+  * If you wish to port Eigen to a platform where sizeof(int)==2, it is perfectly possible to set Dynamic to, say, 97.
+  * However, changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
+  */
+const int Dynamic = 33331;
+
+/** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
+  * The value Infinity there means the L-infinity norm.
+  */
+const int Infinity = -1;
+
+/** \defgroup flags flags
+  * \ingroup Core_Module
+  *
+  * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
+  * expression.
+  *
+  * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
+  * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
+  * runtime overhead.
+  *
+  * \sa MatrixBase::Flags
+  */
+
+/** \ingroup flags
+  *
+  * for a matrix, this means that the storage order is row-major.
+  * If this bit is not set, the storage order is column-major.
+  * For an expression, this determines the storage order of
+  * the matrix created by evaluation of that expression. */
+const unsigned int RowMajorBit = 0x1;
+
+/** \ingroup flags
+  *
+  * means the expression should be evaluated by the calling expression */
+const unsigned int EvalBeforeNestingBit = 0x2;
+
+/** \ingroup flags
+  *
+  * means the expression should be evaluated before any assignement */
+const unsigned int EvalBeforeAssigningBit = 0x4;
+
+/** \ingroup flags
+  *
+  * Short version: means the expression might be vectorized
+  *
+  * Long version: means that the coefficients can be handled by packets
+  * and start at a memory location whose alignment meets the requirements
+  * of the present CPU architecture for optimized packet access. In the fixed-size
+  * case, there is the additional condition that the total size of the coefficients
+  * array is a multiple of the packet size, so that it is possible to access all the
+  * coefficients by packets. In the dynamic-size case, there is no such condition
+  * on the total size, so it might not be possible to access the few last coeffs
+  * by packets.
+  *
+  * \note This bit can be set regardless of whether vectorization is actually enabled.
+  *       To check for actual vectorizability, see \a ActualPacketAccessBit.
+  */
+const unsigned int PacketAccessBit = 0x8;
+
+#ifdef EIGEN_VECTORIZE
+/** \ingroup flags
+  *
+  * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
+  * is set to the value \a PacketAccessBit.
+  *
+  * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
+  * is set to the value 0.
+  */
+const unsigned int ActualPacketAccessBit = PacketAccessBit;
+#else
+const unsigned int ActualPacketAccessBit = 0x0;
+#endif
+
+/** \ingroup flags
+  *
+  * Short version: means the expression can be seen as 1D vector.
+  *
+  * Long version: means that one can access the coefficients
+  * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
+  * index-based access methods are guaranteed
+  * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
+  * is guaranteed that whenever it is available, index-based access is at least as fast as
+  * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
+  *
+  * If both PacketAccessBit and LinearAccessBit are set, then the
+  * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
+  * lvalue expression.
+  *
+  * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
+  * Product expressions don't have it, because it would be troublesome for vectorization, even when the
+  * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
+  * not index-based packet access, so they don't have the LinearAccessBit.
+  */
+const unsigned int LinearAccessBit = 0x10;
+
+/** \ingroup flags
+  *
+  * Means that the underlying array of coefficients can be directly accessed. This means two things.
+  * First, references to the coefficients must be available through coeffRef(int, int). This rules out read-only
+  * expressions whose coefficients are computed on demand by coeff(int, int). Second, the memory layout of the
+  * array of coefficients must be exactly the natural one suggested by rows(), cols(), stride(), and the RowMajorBit.
+  * This rules out expressions such as Diagonal, whose coefficients, though referencable, do not have
+  * such a regular memory layout.
+  */
+const unsigned int DirectAccessBit = 0x20;
+
+/** \ingroup flags
+  *
+  * means the first coefficient packet is guaranteed to be aligned */
+const unsigned int AlignedBit = 0x40;
+
+/** \ingroup flags
+  *
+  * means all diagonal coefficients are equal to 0 */
+const unsigned int ZeroDiagBit = 0x80;
+
+/** \ingroup flags
+  *
+  * means all diagonal coefficients are equal to 1 */
+const unsigned int UnitDiagBit = 0x100;
+
+/** \ingroup flags
+  *
+  * means the matrix is selfadjoint (M=M*). */
+const unsigned int SelfAdjointBit = 0x200;
+
+/** \ingroup flags
+  *
+  * means the strictly lower triangular part is 0 */
+const unsigned int UpperTriangularBit = 0x400;
+
+/** \ingroup flags
+  *
+  * means the strictly upper triangular part is 0 */
+const unsigned int LowerTriangularBit = 0x800;
+
+/** \ingroup flags
+  *
+  * means the expression includes sparse matrices and the sparse path has to be taken. */
+const unsigned int SparseBit = 0x1000;
+
+// list of flags that are inherited by default
+const unsigned int HereditaryBits = RowMajorBit
+                                  | EvalBeforeNestingBit
+                                  | EvalBeforeAssigningBit
+                                  | SparseBit;
+
+// diagonal means both upper and lower triangular
+const unsigned DiagonalBits = UpperTriangularBit | LowerTriangularBit;
+    
+// Possible values for the Mode parameter of part()
+const unsigned int UpperTriangular = UpperTriangularBit;
+const unsigned int StrictlyUpperTriangular = UpperTriangularBit | ZeroDiagBit;
+const unsigned int LowerTriangular = LowerTriangularBit;
+const unsigned int StrictlyLowerTriangular = LowerTriangularBit | ZeroDiagBit;
+const unsigned int SelfAdjoint = SelfAdjointBit;
+const unsigned int UnitUpperTriangular = UpperTriangularBit | UnitDiagBit;
+const unsigned int UnitLowerTriangular = LowerTriangularBit | UnitDiagBit;
+
+template<typename T> struct ei_is_diagonal
+{
+  enum {
+    ret = ( (unsigned int)(T::Flags) & DiagonalBits ) == DiagonalBits
+  };
+};
+
+enum { Aligned, Unaligned };
+enum { ForceAligned, AsRequested };
+enum { ConditionalJumpCost = 5 };
+enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
+enum DirectionType { Vertical, Horizontal, BothDirections };
+enum ProductEvaluationMode { NormalProduct, CacheFriendlyProduct, DiagonalProduct, SparseTimeSparseProduct, SparseTimeDenseProduct, DenseTimeSparseProduct };
+
+enum {
+  /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
+    * and good size */
+  InnerVectorization,
+  /** \internal Vectorization path using a single loop plus scalar loops for the
+    * unaligned boundaries */
+  LinearVectorization,
+  /** \internal Generic vectorization path using one vectorized loop per row/column with some
+    * scalar loops to handle the unaligned boundaries */
+  SliceVectorization,
+  NoVectorization
+};
+
+enum {
+  NoUnrolling,
+  InnerUnrolling,
+  CompleteUnrolling
+};
+
+enum {
+  ColMajor = 0,
+  RowMajor = 0x1,  // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
+  /** \internal Align the matrix itself if it is vectorizable fixed-size */
+  AutoAlign = 0,
+  /** \internal Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be
+                requested to be aligned) */
+  DontAlign = 0x2
+};
+
+enum {
+  IsDense         = 0,
+  IsSparse        = SparseBit,
+  NoDirectAccess  = 0,
+  HasDirectAccess = DirectAccessBit
+};
+
+enum TransformTraits {
+  Isometry      = 0x1,
+  Affine        = 0x2,
+  AffineCompact = 0x10 | Affine,
+  Projective    = 0x20
+};
+
+const int EiArch_Generic = 0x0;
+const int EiArch_SSE     = 0x1;
+const int EiArch_AltiVec = 0x2;
+
+#if defined EIGEN_VECTORIZE_SSE
+  const int EiArch = EiArch_SSE;
+#elif defined EIGEN_VECTORIZE_ALTIVEC
+  const int EiArch = EiArch_AltiVec;
+#else
+  const int EiArch = EiArch_Generic;
+#endif
+
+#endif // EIGEN_CONSTANTS_H

Eigen/src/Core/util/DisableMSVCWarnings.h

@@ -0,0 +1,5 @@
+
+#ifdef _MSC_VER
+  #pragma warning( push )
+  #pragma warning( disable : 4181 4244 4127 4211 4717 )
+#endif

Eigen/src/Core/util/EnableMSVCWarnings.h

@@ -0,0 +1,4 @@
+
+#ifdef _MSC_VER
+  #pragma warning( pop )
+#endif

Eigen/src/Core/util/ForwardDeclarations.h

@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_FORWARDDECLARATIONS_H
+#define EIGEN_FORWARDDECLARATIONS_H
+
+template<typename T> struct ei_traits;
+template<typename T> struct NumTraits;
+
+template<typename _Scalar, int _Rows, int _Cols,
+         int _Options = EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION | AutoAlign,
+         int _MaxRows = _Rows, int _MaxCols = _Cols> class Matrix;
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged;
+template<typename ExpressionType> class NestByValue;
+template<typename ExpressionType> class SwapWrapper;
+template<typename MatrixType> class Minor;
+template<typename MatrixType, int BlockRows=Dynamic, int BlockCols=Dynamic, int PacketAccess=AsRequested,
+         int _DirectAccessStatus = ei_traits<MatrixType>::Flags&DirectAccessBit ? DirectAccessBit
+                                 : ei_traits<MatrixType>::Flags&SparseBit> class Block;
+template<typename MatrixType> class Transpose;
+template<typename MatrixType> class Conjugate;
+template<typename NullaryOp, typename MatrixType>         class CwiseNullaryOp;
+template<typename UnaryOp,   typename MatrixType>         class CwiseUnaryOp;
+template<typename BinaryOp,  typename Lhs, typename Rhs>  class CwiseBinaryOp;
+template<typename Lhs, typename Rhs, int ProductMode> class Product;
+template<typename CoeffsVectorType, typename Derived> class DiagonalMatrixBase;
+template<typename CoeffsVectorType> class DiagonalMatrixWrapper;
+template<typename _Scalar, int _Size> class DiagonalMatrix;
+template<typename MatrixType, int Index> class Diagonal;
+template<typename MatrixType, int PacketAccess = AsRequested> class Map;
+template<typename MatrixType, unsigned int Mode> class Part;
+template<typename MatrixType, unsigned int Mode> class Extract;
+template<typename ExpressionType> class Cwise;
+template<typename ExpressionType> class WithFormat;
+template<typename MatrixType> struct CommaInitializer;
+template<typename Functor, typename EvalType> class ReturnByValue;
+
+
+template<typename Lhs, typename Rhs> struct ei_product_mode;
+template<typename Lhs, typename Rhs, int ProductMode = ei_product_mode<Lhs,Rhs>::value> struct ProductReturnType;
+
+template<typename Scalar> struct ei_scalar_sum_op;
+template<typename Scalar> struct ei_scalar_difference_op;
+template<typename Scalar> struct ei_scalar_product_op;
+template<typename Scalar> struct ei_scalar_quotient_op;
+template<typename Scalar> struct ei_scalar_opposite_op;
+template<typename Scalar> struct ei_scalar_conjugate_op;
+template<typename Scalar> struct ei_scalar_real_op;
+template<typename Scalar> struct ei_scalar_imag_op;
+template<typename Scalar> struct ei_scalar_abs_op;
+template<typename Scalar> struct ei_scalar_abs2_op;
+template<typename Scalar> struct ei_scalar_sqrt_op;
+template<typename Scalar> struct ei_scalar_exp_op;
+template<typename Scalar> struct ei_scalar_log_op;
+template<typename Scalar> struct ei_scalar_cos_op;
+template<typename Scalar> struct ei_scalar_sin_op;
+template<typename Scalar> struct ei_scalar_pow_op;
+template<typename Scalar> struct ei_scalar_inverse_op;
+template<typename Scalar> struct ei_scalar_square_op;
+template<typename Scalar> struct ei_scalar_cube_op;
+template<typename Scalar, typename NewType> struct ei_scalar_cast_op;
+template<typename Scalar> struct ei_scalar_multiple_op;
+template<typename Scalar> struct ei_scalar_quotient1_op;
+template<typename Scalar> struct ei_scalar_min_op;
+template<typename Scalar> struct ei_scalar_max_op;
+template<typename Scalar> struct ei_scalar_random_op;
+template<typename Scalar> struct ei_scalar_add_op;
+template<typename Scalar> struct ei_scalar_constant_op;
+template<typename Scalar> struct ei_scalar_identity_op;
+
+template<typename Scalar1,typename Scalar2> struct ei_scalar_multiple2_op;
+
+struct IOFormat;
+
+template<typename Scalar>
+void ei_cache_friendly_product(
+  int _rows, int _cols, int depth,
+  bool _lhsRowMajor, const Scalar* _lhs, int _lhsStride,
+  bool _rhsRowMajor, const Scalar* _rhs, int _rhsStride,
+  bool resRowMajor, Scalar* res, int resStride);
+
+// Array module
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType> class Select;
+template<typename MatrixType, typename BinaryOp, int Direction> class PartialReduxExpr;
+template<typename ExpressionType, int Direction> class PartialRedux;
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate;
+template<typename MatrixType, int Direction = BothDirections> class Reverse;
+
+template<typename MatrixType> class LU;
+template<typename MatrixType> class PartialLU;
+template<typename MatrixType> class QR;
+template<typename MatrixType> class SVD;
+template<typename MatrixType> class LLT;
+template<typename MatrixType> class LDLT;
+
+// Geometry module:
+template<typename Derived, int _Dim> class RotationBase;
+template<typename Lhs, typename Rhs> class Cross;
+template<typename Scalar> class Quaternion;
+template<typename Scalar> class Rotation2D;
+template<typename Scalar> class AngleAxis;
+template<typename Scalar,int Dim,int Mode=Affine> class Transform;
+template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
+template <typename _Scalar, int _AmbientDim> class Hyperplane;
+template<typename Scalar,int Dim> class Translation;
+template<typename Scalar> class UniformScaling;
+template<typename MatrixType,int Direction> class Homogeneous;
+
+// Sparse module:
+template<typename Lhs, typename Rhs, int ProductMode> class SparseProduct;
+
+#endif // EIGEN_FORWARDDECLARATIONS_H

Eigen/src/Core/util/Macros.h

@@ -0,0 +1,274 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MACROS_H
+#define EIGEN_MACROS_H
+
+#undef minor
+
+#define EIGEN_WORLD_VERSION 2
+#define EIGEN_MAJOR_VERSION 0
+#define EIGEN_MINOR_VERSION 52
+
+#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
+                                      (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
+                                                                 EIGEN_MINOR_VERSION>=z))))
+
+// if the compiler is GNUC, disable 16 byte alignment on exotic archs that probably don't need it, and on which
+// it may be extra trouble to get aligned memory allocation to work (example: on ARM, overloading new[] is a PITA
+// because extra memory must be allocated for bookkeeping).
+// if the compiler is not GNUC, just cross fingers that the architecture isn't too exotic, because we don't want
+// to keep track of all the different preprocessor symbols for all compilers.
+#if (!defined(__GNUC__)) || defined(__i386__) || defined(__x86_64__) || defined(__powerpc__) || defined(__ia64__)
+  #define EIGEN_ARCH_WANTS_ALIGNMENT 1
+#else
+  #define EIGEN_ARCH_WANTS_ALIGNMENT 0
+#endif
+
+// EIGEN_ALIGN is the true test whether we want to align or not. It takes into account both the user choice to explicitly disable
+// alignment (EIGEN_DONT_ALIGN) and the architecture config (EIGEN_ARCH_WANTS_ALIGNMENT). Henceforth, only EIGEN_ALIGN should be used.
+#if EIGEN_ARCH_WANTS_ALIGNMENT && !defined(EIGEN_DONT_ALIGN)
+  #define EIGEN_ALIGN 1
+#else
+  #define EIGEN_ALIGN 0
+  #ifdef EIGEN_VECTORIZE
+    #error Vectorization enabled, but the architecture is not listed among those for which we require 16 byte alignment. If you added vectorization for another architecture, you also need to edit this list.
+  #endif
+  #ifndef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+    #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+  #endif
+#endif
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION RowMajor
+#else
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ColMajor
+#endif
+
+/** Defines the maximal loop size to enable meta unrolling of loops.
+  * Note that the value here is expressed in Eigen's own notion of "number of FLOPS",
+  * it does not correspond to the number of iterations or the number of instructions
+  */
+#ifndef EIGEN_UNROLLING_LIMIT
+#define EIGEN_UNROLLING_LIMIT 100
+#endif
+
+/** Defines the maximal size in Bytes of blocks fitting in CPU cache.
+  * The current value is set to generate blocks of 256x256 for float
+  *
+  * Typically for a single-threaded application you would set that to 25% of the size of your CPU caches in bytes
+  */
+#ifndef EIGEN_TUNE_FOR_CPU_CACHE_SIZE
+#define EIGEN_TUNE_FOR_CPU_CACHE_SIZE (sizeof(float)*256*256)
+#endif
+
+/** Allows to disable some optimizations which might affect the accuracy of the result.
+  * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
+  * They currently include:
+  *   - single precision Cwise::sin() and Cwise::cos() when SSE vectorization is enabled. 
+  */
+#ifndef EIGEN_FAST_MATH
+#define EIGEN_FAST_MATH 1
+#endif
+
+#define USING_PART_OF_NAMESPACE_EIGEN \
+EIGEN_USING_MATRIX_TYPEDEFS \
+using Eigen::Matrix; \
+using Eigen::MatrixBase; \
+using Eigen::ei_random; \
+using Eigen::ei_real; \
+using Eigen::ei_imag; \
+using Eigen::ei_conj; \
+using Eigen::ei_abs; \
+using Eigen::ei_abs2; \
+using Eigen::ei_sqrt; \
+using Eigen::ei_exp; \
+using Eigen::ei_log; \
+using Eigen::ei_sin; \
+using Eigen::ei_cos;
+
+#ifdef NDEBUG
+# ifndef EIGEN_NO_DEBUG
+#  define EIGEN_NO_DEBUG
+# endif
+#endif
+
+#ifndef ei_assert
+#ifdef EIGEN_NO_DEBUG
+#define ei_assert(x)
+#else
+#define ei_assert(x) assert(x)
+#endif
+#endif
+
+#ifdef EIGEN_INTERNAL_DEBUGGING
+#define ei_internal_assert(x) ei_assert(x)
+#else
+#define ei_internal_assert(x)
+#endif
+
+#ifdef EIGEN_NO_DEBUG
+#define EIGEN_ONLY_USED_FOR_DEBUG(x) (void)x
+#else
+#define EIGEN_ONLY_USED_FOR_DEBUG(x)
+#endif
+
+// EIGEN_ALWAYS_INLINE_ATTRIB should be use in the declaration of function
+// which should be inlined even in debug mode.
+// FIXME with the always_inline attribute,
+// gcc 3.4.x reports the following compilation error:
+//   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
+//    : function body not available
+#if EIGEN_GNUC_AT_LEAST(4,0)
+#define EIGEN_ALWAYS_INLINE_ATTRIB __attribute__((always_inline))
+#else
+#define EIGEN_ALWAYS_INLINE_ATTRIB
+#endif
+
+// EIGEN_FORCE_INLINE means "inline as much as possible"
+#if (defined _MSC_VER)
+#define EIGEN_STRONG_INLINE __forceinline
+#else
+#define EIGEN_STRONG_INLINE inline
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_DONT_INLINE __attribute__((noinline))
+#elif (defined _MSC_VER)
+#define EIGEN_DONT_INLINE __declspec(noinline)
+#else
+#define EIGEN_DONT_INLINE
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_DEPRECATED __attribute__((deprecated))
+#elif (defined _MSC_VER)
+#define EIGEN_DEPRECATED __declspec(deprecated)
+#else
+#define EIGEN_DEPRECATED
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_UNUSED __attribute__((unused))
+#else
+#define EIGEN_UNUSED
+#endif
+
+#if (defined __GNUC__)
+#define EIGEN_ASM_COMMENT(X)  asm("#"X)
+#else
+#define EIGEN_ASM_COMMENT(X)
+#endif
+
+/* EIGEN_ALIGN_128 forces data to be 16-byte aligned, EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
+ * so that vectorization doesn't affect binary compatibility.
+ *
+ * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
+ * vectorized and non-vectorized code.
+ */
+#if !EIGEN_ALIGN
+#define EIGEN_ALIGN_128
+#elif (defined __GNUC__)
+#define EIGEN_ALIGN_128 __attribute__((aligned(16)))
+#elif (defined _MSC_VER)
+#define EIGEN_ALIGN_128 __declspec(align(16))
+#else
+#error Please tell me what is the equivalent of __attribute__((aligned(16))) for your compiler
+#endif
+
+#define EIGEN_RESTRICT __restrict
+
+#ifndef EIGEN_STACK_ALLOCATION_LIMIT
+#define EIGEN_STACK_ALLOCATION_LIMIT 1000000
+#endif
+
+#ifndef EIGEN_DEFAULT_IO_FORMAT
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
+#endif
+
+// just an empty macro !
+#define EIGEN_EMPTY
+
+// concatenate two tokens
+#define EIGEN_CAT2(a,b) a ## b
+#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
+
+// convert a token to a string
+#define EIGEN_MAKESTRING2(a) #a
+#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
+
+// format used in Eigen's documentation
+// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
+#define EIGEN_DOCS_IO_FORMAT IOFormat(3, AlignCols, " ", "\n", "", "")
+
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::MatrixBase<OtherDerived>& other) \
+{ \
+  return Base::operator Op(other.derived()); \
+} \
+EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \
+{ \
+  return Base::operator Op(other); \
+}
+
+#define EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename Other> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \
+{ \
+  return Base::operator Op(scalar); \
+}
+
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \
+EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \
+EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \
+EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \
+EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=)
+
+#define _EIGEN_GENERIC_PUBLIC_INTERFACE(Derived, BaseClass) \
+typedef BaseClass Base; \
+typedef typename Eigen::ei_traits<Derived>::Scalar Scalar; \
+typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \
+typedef typename Base::PacketScalar PacketScalar; \
+typedef typename Base::CoeffReturnType CoeffReturnType; \
+typedef typename Eigen::ei_nested<Derived>::type Nested; \
+enum { RowsAtCompileTime = Eigen::ei_traits<Derived>::RowsAtCompileTime, \
+       ColsAtCompileTime = Eigen::ei_traits<Derived>::ColsAtCompileTime, \
+       MaxRowsAtCompileTime = Eigen::ei_traits<Derived>::MaxRowsAtCompileTime, \
+       MaxColsAtCompileTime = Eigen::ei_traits<Derived>::MaxColsAtCompileTime, \
+       Flags = Eigen::ei_traits<Derived>::Flags, \
+       CoeffReadCost = Eigen::ei_traits<Derived>::CoeffReadCost, \
+       SizeAtCompileTime = Base::SizeAtCompileTime, \
+       MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
+       IsVectorAtCompileTime = Base::IsVectorAtCompileTime };
+
+#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+_EIGEN_GENERIC_PUBLIC_INTERFACE(Derived, Eigen::MatrixBase<Derived>)
+
+#define EIGEN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
+#define EIGEN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
+
+#endif // EIGEN_MACROS_H

Eigen/src/Core/util/Memory.h

@@ -0,0 +1,368 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_MEMORY_H
+#define EIGEN_MEMORY_H
+
+#if defined(__APPLE__) || defined(_WIN64)
+  #define EIGEN_MALLOC_ALREADY_ALIGNED 1
+#else
+  #define EIGEN_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+#if ((defined _GNU_SOURCE) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+  #define EIGEN_HAS_POSIX_MEMALIGN 1
+#else
+  #define EIGEN_HAS_POSIX_MEMALIGN 0
+#endif
+
+#ifdef EIGEN_VECTORIZE_SSE
+  #define EIGEN_HAS_MM_MALLOC 1
+#else
+  #define EIGEN_HAS_MM_MALLOC 0
+#endif
+
+/** \internal like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
+  * Fast, but wastes 16 additional bytes of memory.
+  * Does not throw any exception.
+  */
+inline void* ei_handmade_aligned_malloc(size_t size)
+{
+  void *original = malloc(size+16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<size_t>(original) & ~(size_t(15))) + 16);
+  *(reinterpret_cast<void**>(aligned) - 1) = original;
+  return aligned;
+}
+
+/** \internal frees memory allocated with ei_handmade_aligned_malloc */
+inline void ei_handmade_aligned_free(void *ptr)
+{
+  if(ptr)
+    free(*(reinterpret_cast<void**>(ptr) - 1));
+}
+
+/** \internal allocates \a size bytes. The returned pointer is guaranteed to have 16 bytes alignment.
+  * On allocation error, the returned pointer is null, and if exceptions are enabled then a std::bad_alloc is thrown.
+  */
+inline void* ei_aligned_malloc(size_t size)
+{
+  #ifdef EIGEN_NO_MALLOC
+    ei_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
+  #endif
+
+  void *result;  
+  #if !EIGEN_ALIGN
+    result = malloc(size);
+  #elif EIGEN_MALLOC_ALREADY_ALIGNED
+    result = malloc(size);
+  #elif EIGEN_HAS_POSIX_MEMALIGN
+    if(posix_memalign(&result, 16, size)) result = 0;
+  #elif EIGEN_HAS_MM_MALLOC
+    result = _mm_malloc(size, 16);
+  #elif (defined _MSC_VER)
+    result = _aligned_malloc(size, 16);
+  #else
+    result = ei_handmade_aligned_malloc(size);
+  #endif
+    
+  #ifdef EIGEN_EXCEPTIONS
+    if(result == 0)
+      throw std::bad_alloc();
+  #endif
+  return result;
+}
+
+/** allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
+  * On allocation error, the returned pointer is null, and if exceptions are enabled then a std::bad_alloc is thrown.
+  */
+template<bool Align> inline void* ei_conditional_aligned_malloc(size_t size)
+{
+  return ei_aligned_malloc(size);
+}
+
+template<> inline void* ei_conditional_aligned_malloc<false>(size_t size)
+{
+  #ifdef EIGEN_NO_MALLOC
+    ei_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
+  #endif
+
+  void *result = malloc(size);
+  #ifdef EIGEN_EXCEPTIONS
+    if(!result) throw std::bad_alloc();
+  #endif
+  return result;
+}
+
+/** allocates \a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.
+  * On allocation error, the returned pointer is undefined, but if exceptions are enabled then a std::bad_alloc is thrown.
+  * The default constructor of T is called.
+  */
+template<typename T> inline T* ei_aligned_new(size_t size)
+{
+  void *void_result = ei_aligned_malloc(sizeof(T)*size);
+  return ::new(void_result) T[size];
+}
+
+template<typename T, bool Align> inline T* ei_conditional_aligned_new(size_t size)
+{
+  void *void_result = ei_conditional_aligned_malloc<Align>(sizeof(T)*size);
+  return ::new(void_result) T[size];
+}
+
+/** \internal free memory allocated with ei_aligned_malloc
+  */
+inline void ei_aligned_free(void *ptr)
+{
+  #if !EIGEN_ALIGN
+    free(ptr);
+  #elif EIGEN_MALLOC_ALREADY_ALIGNED
+    free(ptr);
+  #elif EIGEN_HAS_POSIX_MEMALIGN
+    free(ptr);
+  #elif EIGEN_HAS_MM_MALLOC
+    _mm_free(ptr);
+  #elif defined(_MSC_VER)
+    _aligned_free(ptr);
+  #else
+    ei_handmade_aligned_free(ptr);
+  #endif
+}
+
+/** \internal free memory allocated with ei_conditional_aligned_malloc
+  */
+template<bool Align> inline void ei_conditional_aligned_free(void *ptr)
+{
+  ei_aligned_free(ptr);
+}
+
+template<> inline void ei_conditional_aligned_free<false>(void *ptr)
+{
+  free(ptr);
+}
+
+/** \internal delete the elements of an array.
+  * The \a size parameters tells on how many objects to call the destructor of T.
+  */
+template<typename T> inline void ei_delete_elements_of_array(T *ptr, size_t size)
+{
+  // always destruct an array starting from the end.
+  while(size) ptr[--size].~T();
+}
+
+/** \internal delete objects constructed with ei_aligned_new
+  * The \a size parameters tells on how many objects to call the destructor of T.
+  */
+template<typename T> inline void ei_aligned_delete(T *ptr, size_t size)
+{
+  ei_delete_elements_of_array<T>(ptr, size);
+  ei_aligned_free(ptr);
+}
+
+/** \internal delete objects constructed with ei_conditional_aligned_new
+  * The \a size parameters tells on how many objects to call the destructor of T.
+  */
+template<typename T, bool Align> inline void ei_conditional_aligned_delete(T *ptr, size_t size)
+{
+  ei_delete_elements_of_array<T>(ptr, size);
+  ei_conditional_aligned_free<Align>(ptr);
+}
+
+/** \internal \returns the number of elements which have to be skipped such that data are 16 bytes aligned */
+template<typename Scalar>
+inline static int ei_alignmentOffset(const Scalar* ptr, int maxOffset)
+{
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  const int PacketSize = ei_packet_traits<Scalar>::size;
+  const int PacketAlignedMask = PacketSize-1;
+  const bool Vectorized = PacketSize>1;
+  return Vectorized
+          ? std::min<int>( (PacketSize - (int((size_t(ptr)/sizeof(Scalar))) & PacketAlignedMask))
+                           & PacketAlignedMask, maxOffset)
+          : 0;
+}
+
+/** \internal
+  * ei_aligned_stack_alloc(SIZE) allocates an aligned buffer of SIZE bytes
+  * on the stack if SIZE is smaller than EIGEN_STACK_ALLOCATION_LIMIT.
+  * Otherwise the memory is allocated on the heap.
+  * Data allocated with ei_aligned_stack_alloc \b must be freed by calling ei_aligned_stack_free(PTR,SIZE).
+  * \code
+  * float * data = ei_aligned_stack_alloc(float,array.size());
+  * // ...
+  * ei_aligned_stack_free(data,float,array.size());
+  * \endcode
+  */
+#ifdef __linux__
+  #define ei_aligned_stack_alloc(SIZE) (SIZE<=EIGEN_STACK_ALLOCATION_LIMIT) \
+                                    ? alloca(SIZE) \
+                                    : ei_aligned_malloc(SIZE)
+  #define ei_aligned_stack_free(PTR,SIZE) if(SIZE>EIGEN_STACK_ALLOCATION_LIMIT) ei_aligned_free(PTR)
+#else
+  #define ei_aligned_stack_alloc(SIZE) ei_aligned_malloc(SIZE)
+  #define ei_aligned_stack_free(PTR,SIZE) ei_aligned_free(PTR)
+#endif
+
+#define ei_aligned_stack_new(TYPE,SIZE) ::new(ei_aligned_stack_alloc(sizeof(TYPE)*SIZE)) TYPE[SIZE]
+#define ei_aligned_stack_delete(TYPE,PTR,SIZE) do {ei_delete_elements_of_array<TYPE>(PTR, SIZE); \
+                                                   ei_aligned_stack_free(PTR,sizeof(TYPE)*SIZE);} while(0)
+
+
+#if EIGEN_ALIGN
+  #ifdef EIGEN_EXCEPTIONS
+    #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+      void* operator new(size_t size, const std::nothrow_t&) throw() { \
+        try { return Eigen::ei_conditional_aligned_malloc<NeedsToAlign>(size); } \
+        catch (...) { return 0; } \
+        return 0; \
+      }
+  #else
+    #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+      void* operator new(size_t size, const std::nothrow_t&) throw() { \
+        return Eigen::ei_conditional_aligned_malloc<NeedsToAlign>(size); \
+      }
+  #endif
+
+  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) \
+      void *operator new(size_t size) { \
+        return Eigen::ei_conditional_aligned_malloc<NeedsToAlign>(size); \
+      } \
+      void *operator new[](size_t size) { \
+        return Eigen::ei_conditional_aligned_malloc<NeedsToAlign>(size); \
+      } \
+      void operator delete(void * ptr) throw() { Eigen::ei_conditional_aligned_free<NeedsToAlign>(ptr); } \
+      void operator delete[](void * ptr) throw() { Eigen::ei_conditional_aligned_free<NeedsToAlign>(ptr); } \
+      /* in-place new and delete. since (at least afaik) there is no actual   */ \
+      /* memory allocated we can safely let the default implementation handle */ \
+      /* this particular case. */ \
+      static void *operator new(size_t size, void *ptr) { return ::operator new(size,ptr); } \
+      void operator delete(void * memory, void *ptr) throw() { return ::operator delete(memory,ptr); } \
+      /* nothrow-new (returns zero instead of std::bad_alloc) */ \
+      EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+      void operator delete(void *ptr, const std::nothrow_t&) throw() { \
+        Eigen::ei_conditional_aligned_free<NeedsToAlign>(ptr); \
+      } \
+      typedef void ei_operator_new_marker_type;
+#else
+  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+#endif
+
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%16==0))
+
+
+/** \class aligned_allocator
+*
+* \brief stl compatible allocator to use with with 16 byte aligned types
+*
+* Example:
+* \code
+* // Matrix4f requires 16 bytes alignment:
+* std::map< int, Matrix4f, std::less<int>, aligned_allocator<Matrix4f> > my_map_mat4;
+* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
+* std::map< int, Vector3f > my_map_vec3;
+* \endcode
+*
+*/
+template<class T>
+class aligned_allocator
+{
+public:
+    typedef size_t    size_type;
+    typedef ptrdiff_t difference_type;
+    typedef T*        pointer;
+    typedef const T*  const_pointer;
+    typedef T&        reference;
+    typedef const T&  const_reference;
+    typedef T         value_type;
+
+    template<class U>
+    struct rebind
+    {
+        typedef aligned_allocator<U> other;
+    };
+
+    pointer address( reference value ) const 
+    {
+        return &value;
+    }
+
+    const_pointer address( const_reference value ) const 
+    {
+        return &value;
+    }
+
+    aligned_allocator() throw() 
+    {
+    }
+
+    aligned_allocator( const aligned_allocator& ) throw() 
+    {
+    }
+
+    template<class U>
+    aligned_allocator( const aligned_allocator<U>& ) throw() 
+    {
+    }
+
+    ~aligned_allocator() throw() 
+    {
+    }
+
+    size_type max_size() const throw() 
+    {
+        return std::numeric_limits<size_type>::max();
+    }
+
+    pointer allocate( size_type num, const_pointer* hint = 0 )
+    {
+        static_cast<void>( hint ); // suppress unused variable warning
+        return static_cast<pointer>( ei_aligned_malloc( num * sizeof(T) ) );
+    }
+
+    void construct( pointer p, const T& value ) 
+    {
+        ::new( p ) T( value );
+    }
+
+    void destroy( pointer p ) 
+    {
+        p->~T();
+    }
+
+    void deallocate( pointer p, size_type /*num*/ ) 
+    {
+        ei_aligned_free( p );
+    }
+    
+    bool operator!=(const aligned_allocator<T>& other) const
+    { return false; }
+    
+    bool operator==(const aligned_allocator<T>& other) const
+    { return true; }
+};
+
+#endif // EIGEN_MEMORY_H

Eigen/src/Core/util/Meta.h

@@ -0,0 +1,191 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_META_H
+#define EIGEN_META_H
+
+/** \internal
+  * \file Meta.h
+  * This file contains generic metaprogramming classes which are not specifically related to Eigen.
+  * \note In case you wonder, yes we're aware that Boost already provides all these features,
+  * we however don't want to add a dependency to Boost.
+  */
+
+struct ei_meta_true {  enum { ret = 1 }; };
+struct ei_meta_false { enum { ret = 0 }; };
+
+template<bool Condition, typename Then, typename Else>
+struct ei_meta_if { typedef Then ret; };
+
+template<typename Then, typename Else>
+struct ei_meta_if <false, Then, Else> { typedef Else ret; };
+
+template<typename T, typename U> struct ei_is_same_type { enum { ret = 0 }; };
+template<typename T> struct ei_is_same_type<T,T> { enum { ret = 1 }; };
+
+template<typename T> struct ei_unref { typedef T type; };
+template<typename T> struct ei_unref<T&> { typedef T type; };
+
+template<typename T> struct ei_unpointer { typedef T type; };
+template<typename T> struct ei_unpointer<T*> { typedef T type; };
+template<typename T> struct ei_unpointer<T*const> { typedef T type; };
+
+template<typename T> struct ei_unconst { typedef T type; };
+template<typename T> struct ei_unconst<const T> { typedef T type; };
+template<typename T> struct ei_unconst<T const &> { typedef T & type; };
+template<typename T> struct ei_unconst<T const *> { typedef T * type; };
+
+template<typename T> struct ei_cleantype { typedef T type; };
+template<typename T> struct ei_cleantype<const T>   { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<const T&>  { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<T&>        { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<const T*>  { typedef typename ei_cleantype<T>::type type; };
+template<typename T> struct ei_cleantype<T*>        { typedef typename ei_cleantype<T>::type type; };
+
+/** \internal Allows to enable/disable an overload
+  * according to a compile time condition.
+  */
+template<bool Condition, typename T> struct ei_enable_if;
+
+template<typename T> struct ei_enable_if<true,T>
+{ typedef T type; };
+
+/** \internal
+  * Convenient struct to get the result type of a unary or binary functor.
+  *
+  * It supports both the current STL mechanism (using the result_type member) as well as
+  * upcoming next STL generation (using a templated result member).
+  * If none of these members is provided, then the type of the first argument is returned. FIXME, that behavior is a pretty bad hack.
+  */
+template<typename T> struct ei_result_of {};
+
+struct ei_has_none {int a[1];};
+struct ei_has_std_result_type {int a[2];};
+struct ei_has_tr1_result {int a[3];};
+
+template<typename Func, typename ArgType, int SizeOf=sizeof(ei_has_none)>
+struct ei_unary_result_of_select {typedef ArgType type;};
+
+template<typename Func, typename ArgType>
+struct ei_unary_result_of_select<Func, ArgType, sizeof(ei_has_std_result_type)> {typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType>
+struct ei_unary_result_of_select<Func, ArgType, sizeof(ei_has_tr1_result)> {typedef typename Func::template result<Func(ArgType)>::type type;};
+
+template<typename Func, typename ArgType>
+struct ei_result_of<Func(ArgType)> {
+    template<typename T>
+    static ei_has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+    template<typename T>
+    static ei_has_tr1_result      testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
+    static ei_has_none            testFunctor(...);
+
+    // note that the following indirection is needed for gcc-3.3
+    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+    typedef typename ei_unary_result_of_select<Func, ArgType, FunctorType>::type type;
+};
+
+template<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(ei_has_none)>
+struct ei_binary_result_of_select {typedef ArgType0 type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct ei_binary_result_of_select<Func, ArgType0, ArgType1, sizeof(ei_has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct ei_binary_result_of_select<Func, ArgType0, ArgType1, sizeof(ei_has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct ei_result_of<Func(ArgType0,ArgType1)> {
+    template<typename T>
+    static ei_has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+    template<typename T>
+    static ei_has_tr1_result      testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
+    static ei_has_none            testFunctor(...);
+
+    // note that the following indirection is needed for gcc-3.3
+    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+    typedef typename ei_binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
+};
+
+/** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
+  * Usage example: \code ei_meta_sqrt<1023>::ret \endcode
+  */
+template<int Y,
+         int InfX = 0,
+         int SupX = ((Y==1) ? 1 : Y/2),
+         bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >
+                                // use ?: instead of || just to shut up a stupid gcc 4.3 warning
+class ei_meta_sqrt
+{
+    enum {
+      MidX = (InfX+SupX)/2,
+      TakeInf = MidX*MidX > Y ? 1 : 0,
+      NewInf = int(TakeInf) ? InfX : int(MidX),
+      NewSup = int(TakeInf) ? int(MidX) : SupX
+    };
+  public:
+    enum { ret = ei_meta_sqrt<Y,NewInf,NewSup>::ret };
+};
+
+template<int Y, int InfX, int SupX>
+class ei_meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
+
+/** \internal determines whether the product of two numeric types is allowed and what the return type is */
+template<typename T, typename U> struct ei_scalar_product_traits
+{
+  // dummy general case where T and U aren't compatible -- not allowed anyway but we catch it elsewhere
+  //enum { Cost = NumTraits<T>::MulCost };
+  typedef T ReturnType;
+};
+
+template<typename T> struct ei_scalar_product_traits<T,T>
+{
+  //enum { Cost = NumTraits<T>::MulCost };
+  typedef T ReturnType;
+};
+
+template<typename T> struct ei_scalar_product_traits<T,std::complex<T> >
+{
+  //enum { Cost = 2*NumTraits<T>::MulCost };
+  typedef std::complex<T> ReturnType;
+};
+
+template<typename T> struct ei_scalar_product_traits<std::complex<T>, T>
+{
+  //enum { Cost = 2*NumTraits<T>::MulCost  };
+  typedef std::complex<T> ReturnType;
+};
+
+// FIXME quick workaround around current limitation of ei_result_of
+template<typename Scalar, typename ArgType0, typename ArgType1>
+struct ei_result_of<ei_scalar_product_op<Scalar>(ArgType0,ArgType1)> {
+typedef typename ei_scalar_product_traits<typename ei_cleantype<ArgType0>::type, typename ei_cleantype<ArgType1>::type>::ReturnType type;
+};
+
+
+
+#endif // EIGEN_META_H

Eigen/src/Core/util/StaticAssert.h

@@ -0,0 +1,148 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_STATIC_ASSERT_H
+#define EIGEN_STATIC_ASSERT_H
+
+/* Some notes on Eigen's static assertion mechanism:
+ *
+ *  - in EIGEN_STATIC_ASSERT(CONDITION,MSG) the parameter CONDITION must be a compile time boolean
+ *    expression, and MSG an enum listed in struct ei_static_assert<true>
+ *
+ *  - define EIGEN_NO_STATIC_ASSERT to disable them (and save compilation time)
+ *    in that case, the static assertion is converted to the following runtime assert:
+ *      ei_assert(CONDITION && "MSG")
+ *
+ *  - currently EIGEN_STATIC_ASSERT can only be used in function scope
+ *
+ */
+
+#ifndef EIGEN_NO_STATIC_ASSERT
+
+  #ifdef __GXX_EXPERIMENTAL_CXX0X__
+
+    // if native static_assert is enabled, let's use it
+    #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);
+
+  #else // CXX0X
+
+    template<bool condition>
+    struct ei_static_assert {};
+
+    template<>
+    struct ei_static_assert<true>
+    {
+      enum {
+        YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX,
+        YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES,
+        YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES,
+        THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE,
+        THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE,
+        YOU_MADE_A_PROGRAMMING_MISTAKE,
+        YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR,
+        UNALIGNED_LOAD_AND_STORE_OPERATIONS_UNIMPLEMENTED_ON_ALTIVEC,
+        NUMERIC_TYPE_MUST_BE_FLOATING_POINT,
+        COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED,
+        WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED,
+        THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE,
+        INVALID_MATRIX_PRODUCT,
+        INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS,
+        INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION,
+        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY,
+        THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES,
+        THIS_METHOD_IS_ONLY_FOR_ROW_MAJOR_MATRICES,
+        INVALID_MATRIX_TEMPLATE_PARAMETERS,
+        BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
+        THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX
+      };
+    };
+
+    // Specialized implementation for MSVC to avoid "conditional
+    // expression is constant" warnings.  This implementation doesn't
+    // appear to work under GCC, hence the multiple implementations.
+    #ifdef _MSC_VER
+
+      #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
+        {Eigen::ei_static_assert<CONDITION ? true : false>::MSG;}
+
+    #else
+
+      #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \
+        if (Eigen::ei_static_assert<CONDITION ? true : false>::MSG) {}
+
+    #endif
+
+  #endif // not CXX0X
+
+#else // EIGEN_NO_STATIC_ASSERT
+
+  #define EIGEN_STATIC_ASSERT(CONDITION,MSG) ei_assert((CONDITION) && #MSG);
+
+#endif // EIGEN_NO_STATIC_ASSERT
+
+
+// static assertion failing if the type \a TYPE is not a vector type
+#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) \
+  EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime, \
+                      YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX)
+
+// static assertion failing if the type \a TYPE is not fixed-size
+#define EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) \
+  EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime!=Eigen::Dynamic, \
+                      YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE) \
+  EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime && TYPE::SizeAtCompileTime==SIZE, \
+                      THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS) \
+  EIGEN_STATIC_ASSERT(TYPE::RowsAtCompileTime==ROWS && TYPE::ColsAtCompileTime==COLS, \
+                      THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the two vector expression types are not compatible (same fixed-size or dynamic size)
+#define EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) \
+  EIGEN_STATIC_ASSERT( \
+      (int(TYPE0::SizeAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE1::SizeAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE0::SizeAtCompileTime)==int(TYPE1::SizeAtCompileTime)),\
+    YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES)
+
+#define EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+      ((int(TYPE0::RowsAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE1::RowsAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE0::RowsAtCompileTime)==int(TYPE1::RowsAtCompileTime)) \
+   && (int(TYPE0::ColsAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE1::ColsAtCompileTime)==Eigen::Dynamic \
+    || int(TYPE0::ColsAtCompileTime)==int(TYPE1::ColsAtCompileTime)))
+
+// static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes
+#define EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+  EIGEN_STATIC_ASSERT( \
+     EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1),\
+    YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)
+
+#endif // EIGEN_STATIC_ASSERT_H

Eigen/src/Core/util/XprHelper.h

@@ -0,0 +1,254 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_XPRHELPER_H
+#define EIGEN_XPRHELPER_H
+
+// just a workaround because GCC seems to not really like empty structs
+#ifdef __GNUG__
+  struct ei_empty_struct{char _ei_dummy_;};
+  #define EIGEN_EMPTY_STRUCT : Eigen::ei_empty_struct
+#else
+  #define EIGEN_EMPTY_STRUCT
+#endif
+
+//classes inheriting ei_no_assignment_operator don't generate a default operator=.
+class ei_no_assignment_operator
+{
+  private:
+    ei_no_assignment_operator& operator=(const ei_no_assignment_operator&);
+};
+
+/** \internal If the template parameter Value is Dynamic, this class is just a wrapper around an int variable that
+  * can be accessed using value() and setValue().
+  * Otherwise, this class is an empty structure and value() just returns the template parameter Value.
+  */
+template<int Value> class ei_int_if_dynamic EIGEN_EMPTY_STRUCT
+{
+  public:
+    ei_int_if_dynamic() {}
+    explicit ei_int_if_dynamic(int) {}
+    static int value() { return Value; }
+    void setValue(int) {}
+};
+
+template<> class ei_int_if_dynamic<Dynamic>
+{
+    int m_value;
+    ei_int_if_dynamic() {}
+  public:
+    explicit ei_int_if_dynamic(int value) : m_value(value) {}
+    int value() const { return m_value; }
+    void setValue(int value) { m_value = value; }
+};
+
+template<typename T> struct ei_functor_traits
+{
+  enum
+  {
+    Cost = 10,
+    PacketAccess = false
+  };
+};
+
+template<typename T> struct ei_packet_traits;
+
+template<typename T> struct ei_unpacket_traits
+{
+  typedef T type;
+  enum {size=1};
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+class ei_compute_matrix_flags
+{
+    enum {
+      row_major_bit = Options&RowMajor ? RowMajorBit : 0,
+      inner_max_size = row_major_bit ? MaxCols : MaxRows,
+      is_big = inner_max_size == Dynamic,
+      is_packet_size_multiple = (Cols*Rows) % ei_packet_traits<Scalar>::size == 0,
+      aligned_bit = (((Options&DontAlign)==0) && (is_big || is_packet_size_multiple)) ? AlignedBit : 0,
+      packet_access_bit = ei_packet_traits<Scalar>::size > 1 && aligned_bit ? PacketAccessBit : 0
+    };
+
+  public:
+    enum { ret = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit | aligned_bit };
+};
+
+template<int _Rows, int _Cols> struct ei_size_at_compile_time
+{
+  enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };
+};
+
+/* ei_eval : the return type of eval(). For matrices, this is just a const reference
+ * in order to avoid a useless copy
+ */
+
+template<typename T, int Sparseness = ei_traits<T>::Flags&SparseBit> class ei_eval;
+
+template<typename T> struct ei_eval<T,IsDense>
+{
+  typedef Matrix<typename ei_traits<T>::Scalar,
+                ei_traits<T>::RowsAtCompileTime,
+                ei_traits<T>::ColsAtCompileTime,
+                AutoAlign | (ei_traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                ei_traits<T>::MaxRowsAtCompileTime,
+                ei_traits<T>::MaxColsAtCompileTime
+          > type;
+};
+
+// for matrices, no need to evaluate, just use a const reference to avoid a useless copy
+template<typename _Scalar, int _Rows, int _Cols, int _StorageOrder, int _MaxRows, int _MaxCols>
+struct ei_eval<Matrix<_Scalar, _Rows, _Cols, _StorageOrder, _MaxRows, _MaxCols>, IsDense>
+{
+  typedef const Matrix<_Scalar, _Rows, _Cols, _StorageOrder, _MaxRows, _MaxCols>& type;
+};
+
+/* ei_plain_matrix_type : the difference from ei_eval is that ei_plain_matrix_type is always a plain matrix type,
+ * whereas ei_eval is a const reference in the case of a matrix
+ */
+template<typename T> struct ei_plain_matrix_type
+{
+  typedef Matrix<typename ei_traits<T>::Scalar,
+                ei_traits<T>::RowsAtCompileTime,
+                ei_traits<T>::ColsAtCompileTime,
+                AutoAlign | (ei_traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+                ei_traits<T>::MaxRowsAtCompileTime,
+                ei_traits<T>::MaxColsAtCompileTime
+          > type;
+};
+
+/* ei_plain_matrix_type_column_major : same as ei_plain_matrix_type but guaranteed to be column-major
+ */
+template<typename T> struct ei_plain_matrix_type_column_major
+{
+  typedef Matrix<typename ei_traits<T>::Scalar,
+                ei_traits<T>::RowsAtCompileTime,
+                ei_traits<T>::ColsAtCompileTime,
+                AutoAlign | ColMajor,
+                ei_traits<T>::MaxRowsAtCompileTime,
+                ei_traits<T>::MaxColsAtCompileTime
+          > type;
+};
+
+template<typename T> struct ei_must_nest_by_value { enum { ret = false }; };
+template<typename T> struct ei_must_nest_by_value<NestByValue<T> > { enum { ret = true }; };
+
+/** \internal Determines how a given expression should be nested into another one.
+  * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
+  * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or
+  * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
+  * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
+  * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
+  *
+  * \param T the type of the expression being nested
+  * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
+  *
+  * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c).
+  * b+c is an expression "sum of matrices", which we will denote by S. In order to determine how to nest it,
+  * the Product expression uses: ei_nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of
+  * ei_nested determined that in this case it was better to evaluate the expression b+c into a temporary. On the other hand,
+  * since a is of type Matrix3d, the Product expression nests it as ei_nested<Matrix3d, 3>::ret, which turns out to be
+  * const Matrix3d&, because the internal logic of ei_nested determined that since a was already a matrix, there was no point
+  * in copying it into another matrix.
+  */
+template<typename T, int n=1, typename PlainMatrixType = typename ei_eval<T>::type> struct ei_nested
+{
+  enum {
+    CostEval   = (n+1) * int(NumTraits<typename ei_traits<T>::Scalar>::ReadCost),
+    CostNoEval = (n-1) * int(ei_traits<T>::CoeffReadCost)
+  };
+  typedef typename ei_meta_if<
+    ei_must_nest_by_value<T>::ret,
+    T,
+    typename ei_meta_if<
+      (int(ei_traits<T>::Flags) & EvalBeforeNestingBit)
+      || ( int(CostEval) <= int(CostNoEval) ),
+      PlainMatrixType,
+      const T&
+    >::ret
+  >::ret type;
+};
+
+template<unsigned int Flags> struct ei_are_flags_consistent
+{
+  enum { ret = !( (Flags&UnitDiagBit && Flags&ZeroDiagBit) )
+  };
+};
+
+/** \internal Helper base class to add a scalar multiple operator
+  * overloads for complex types */
+template<typename Derived,typename Scalar,typename OtherScalar,
+         bool EnableIt = !ei_is_same_type<Scalar,OtherScalar>::ret >
+struct ei_special_scalar_op_base
+{
+  // dummy operator* so that the 
+  // "using ei_special_scalar_op_base::operator*" compiles
+  void operator*() const;
+};
+
+template<typename Derived,typename Scalar,typename OtherScalar>
+struct ei_special_scalar_op_base<Derived,Scalar,OtherScalar,true>
+{
+  const CwiseUnaryOp<ei_scalar_multiple2_op<Scalar,OtherScalar>, Derived>
+  operator*(const OtherScalar& scalar) const
+  {
+    return CwiseUnaryOp<ei_scalar_multiple2_op<Scalar,OtherScalar>, Derived>
+      (*static_cast<const Derived*>(this), ei_scalar_multiple2_op<Scalar,OtherScalar>(scalar));
+  }
+};
+
+/** \internal Gives the type of a sub-matrix or sub-vector of a matrix of type \a ExpressionType and size \a Size
+  * TODO: could be a good idea to define a big ReturnType struct ??
+  */
+template<typename ExpressionType, int RowsOrSize=Dynamic, int Cols=Dynamic> struct BlockReturnType {
+  typedef Block<ExpressionType, (ei_traits<ExpressionType>::RowsAtCompileTime == 1 ? 1 : RowsOrSize),
+                                (ei_traits<ExpressionType>::ColsAtCompileTime == 1 ? 1 : RowsOrSize)> SubVectorType;
+  typedef Block<ExpressionType, RowsOrSize, Cols> Type;
+};
+
+template<typename ExpressionType> struct HNormalizedReturnType {
+
+  enum {
+    SizeAtCompileTime = ExpressionType::SizeAtCompileTime,
+    SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
+  };
+  typedef Block<ExpressionType,
+                ei_traits<ExpressionType>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
+                ei_traits<ExpressionType>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> StartMinusOne;
+  typedef CwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<ExpressionType>::Scalar>, 
+              NestByValue<StartMinusOne> > Type;
+};
+
+template<typename XprType, typename CastType> struct ei_cast_return_type
+{
+  typedef typename XprType::Scalar CurrentScalarType;
+  typedef typename ei_cleantype<CastType>::type _CastType;
+  typedef typename _CastType::Scalar NewScalarType;
+  typedef typename ei_meta_if<ei_is_same_type<CurrentScalarType,NewScalarType>::ret,
+                              const XprType&,CastType>::ret type;
+};
+
+#endif // EIGEN_XPRHELPER_H

Eigen/src/Geometry/AlignedBox.h

@@ -0,0 +1,212 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ALIGNEDBOX_H
+#define EIGEN_ALIGNEDBOX_H
+
+/** \geometry_module \ingroup Geometry_Module
+  * \nonstableyet
+  *
+  * \class AlignedBox
+  *
+  * \brief An axis aligned box
+  *
+  * \param _Scalar the type of the scalar coefficients
+  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  *
+  * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+  */
+template <typename _Scalar, int _AmbientDim>
+class AlignedBox
+{
+public:
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+  enum { AmbientDimAtCompileTime = _AmbientDim };
+  typedef _Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+  /** Default constructor initializing a null box. */
+  inline explicit AlignedBox()
+  { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
+
+  /** Constructs a null box with \a _dim the dimension of the ambient space. */
+  inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim)
+  { setNull(); }
+
+  /** Constructs a box with extremities \a _min and \a _max. */
+  inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {}
+
+  /** Constructs a box containing a single point \a p. */
+  inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {}
+
+  ~AlignedBox() {}
+
+  /** \returns the dimension in which the box holds */
+  inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
+
+  /** \returns true if the box is null, i.e, empty. */
+  inline bool isNull() const { return (m_min.cwise() > m_max).any(); }
+
+  /** Makes \c *this a null/empty box. */
+  inline void setNull()
+  {
+    m_min.setConstant( std::numeric_limits<Scalar>::max());
+    m_max.setConstant(-std::numeric_limits<Scalar>::max());
+  }
+
+  /** \returns the minimal corner */
+  inline const VectorType& min() const { return m_min; }
+  /** \returns a non const reference to the minimal corner */
+  inline VectorType& min() { return m_min; }
+  /** \returns the maximal corner */
+  inline const VectorType& max() const { return m_max; }
+  /** \returns a non const reference to the maximal corner */
+  inline VectorType& max() { return m_max; }
+
+  /** \returns the center of the box */
+  inline VectorType center() const { return (m_min + m_max) / 2; }
+
+  /** \returns true if the point \a p is inside the box \c *this. */
+  inline bool contains(const VectorType& p) const
+  { return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).all(); }
+
+  /** \returns true if the box \a b is entirely inside the box \c *this. */
+  inline bool contains(const AlignedBox& b) const
+  { return (m_min.cwise()<=b.min()).all() && (b.max().cwise()<=m_max).all(); }
+
+  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
+  inline AlignedBox& extend(const VectorType& p)
+  { m_min = m_min.cwise().min(p); m_max = m_max.cwise().max(p); return *this; }
+
+  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
+  inline AlignedBox& extend(const AlignedBox& b)
+  { m_min = m_min.cwise().min(b.m_min); m_max = m_max.cwise().max(b.m_max); return *this; }
+
+  /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
+  inline AlignedBox& clamp(const AlignedBox& b)
+  { m_min = m_min.cwise().max(b.m_min); m_max = m_max.cwise().min(b.m_max); return *this; }
+
+  /** Returns an AlignedBox that is the intersection of \a b and \c *this */
+  inline AlignedBox intersection(const AlignedBox &b) const
+  { return AlignedBox(m_min.cwise().max(b.m_min), m_max.cwise().min(b.m_max)); }
+
+  /** Returns an AlignedBox that is the union of \a b and \c *this */
+  inline AlignedBox merged(const AlignedBox &b) const
+  { return AlignedBox(m_min.cwise().min(b.m_min), m_max.cwise().max(b.m_max)); }
+
+  /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
+  inline AlignedBox& translate(const VectorType& t)
+  { m_min += t; m_max += t; return *this; }
+
+  /** \returns the squared distance between the point \a p and the box \c *this,
+    * and zero if \a p is inside the box.
+    * \sa exteriorDistance()
+    */
+  inline Scalar squaredExteriorDistance(const VectorType& p) const;
+
+  /** \returns the squared distance between the boxes \a b and \c *this,
+    * and zero if the boxes intersect.
+    * \sa exteriorDistance()
+    */
+  inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
+
+  /** \returns the distance between the point \a p and the box \c *this,
+    * and zero if \a p is inside the box.
+    * \sa squaredExteriorDistance()
+    */
+  inline Scalar exteriorDistance(const VectorType& p) const
+  { return ei_sqrt(squaredExteriorDistance(p)); }
+
+  /** \returns the distance between the boxes \a b and \c *this,
+    * and zero if the boxes intersect.
+    * \sa squaredExteriorDistance()
+    */
+  inline Scalar exteriorDistance(const AlignedBox& b) const
+  { return ei_sqrt(squaredExteriorDistance(b)); }
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<AlignedBox,
+           AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+  {
+    return typename ei_cast_return_type<AlignedBox,
+                    AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+  }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+  {
+    m_min = other.min().template cast<Scalar>();
+    m_max = other.max().template cast<Scalar>();
+  }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+  VectorType m_min, m_max;
+};
+
+template<typename Scalar,int AmbiantDim>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
+{
+  Scalar dist2 = 0.;
+  Scalar aux;
+  for (int k=0; k<dim(); ++k)
+  {
+    if ((aux = (p[k]-m_min[k]))<0.)
+      dist2 += aux*aux;
+    else if ( (aux = (m_max[k]-p[k]))<0. )
+      dist2 += aux*aux;
+  }
+  return dist2;
+}
+
+template<typename Scalar,int AmbiantDim>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const AlignedBox& b) const
+{
+  Scalar dist2 = 0.;
+  Scalar aux;
+  for (int k=0; k<dim(); ++k)
+  {
+    if ((aux = (b.m_min[k]-m_max[k]))>0.)
+      dist2 += aux*aux;
+    else if ( (aux = (m_min[k]-b.m_max[k]))>0. )
+      dist2 += aux*aux;
+  }
+  return dist2;
+}
+
+#endif // EIGEN_ALIGNEDBOX_H

Eigen/src/Geometry/AngleAxis.h

@@ -0,0 +1,221 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ANGLEAXIS_H
+#define EIGEN_ANGLEAXIS_H
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class AngleAxis
+  *
+  * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients.
+  *
+  * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
+  *
+  * The following two typedefs are provided for convenience:
+  * \li \c AngleAxisf for \c float
+  * \li \c AngleAxisd for \c double
+  *
+  * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles
+  *
+  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+  * mimic Euler-angles. Here is an example:
+  * \include AngleAxis_mimic_euler.cpp
+  * Output: \verbinclude AngleAxis_mimic_euler.out
+  *
+  * \note This class is not aimed to be used to store a rotation transformation,
+  * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
+  * and transformation objects.
+  *
+  * \sa class Quaternion, class Transform, MatrixBase::UnitX()
+  */
+
+template<typename _Scalar> struct ei_traits<AngleAxis<_Scalar> >
+{
+  typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
+{
+  typedef RotationBase<AngleAxis<_Scalar>,3> Base;
+
+public:
+
+  using Base::operator*;
+
+  enum { Dim = 3 };
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+  Vector3 m_axis;
+  Scalar m_angle;
+
+public:
+
+  /** Default constructor without initialization. */
+  AngleAxis() {}
+  /** Constructs and initialize the angle-axis rotation from an \a angle in radian
+    * and an \a axis which \b must \b be \b normalized.
+    * 
+    * \warning If the \a axis vector is not normalized, then the angle-axis object
+    *          represents an invalid rotation. */
+  template<typename Derived>
+  inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+  /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
+  inline AngleAxis(const QuaternionType& q) { *this = q; }
+  /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
+  template<typename Derived>
+  inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
+
+  Scalar angle() const { return m_angle; }
+  Scalar& angle() { return m_angle; }
+
+  const Vector3& axis() const { return m_axis; }
+  Vector3& axis() { return m_axis; }
+
+  /** Concatenates two rotations */
+  inline QuaternionType operator* (const AngleAxis& other) const
+  { return QuaternionType(*this) * QuaternionType(other); }
+
+  /** Concatenates two rotations */
+  inline QuaternionType operator* (const QuaternionType& other) const
+  { return QuaternionType(*this) * other; }
+
+  /** Concatenates two rotations */
+  friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+  { return a * QuaternionType(b); }
+
+  /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+  AngleAxis inverse() const
+  { return AngleAxis(-m_angle, m_axis); }
+
+  AngleAxis& operator=(const QuaternionType& q);
+  template<typename Derived>
+  AngleAxis& operator=(const MatrixBase<Derived>& m);
+
+  template<typename Derived>
+  AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
+  Matrix3 toRotationMatrix(void) const;
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
+  { return typename ei_cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
+  {
+    m_axis = other.axis().template cast<Scalar>();
+    m_angle = Scalar(other.angle());
+  }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+  * single precision angle-axis type */
+typedef AngleAxis<float> AngleAxisf;
+/** \ingroup Geometry_Module
+  * double precision angle-axis type */
+typedef AngleAxis<double> AngleAxisd;
+
+/** Set \c *this from a quaternion.
+  * The axis is normalized.
+  */
+template<typename Scalar>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q)
+{
+  Scalar n2 = q.vec().squaredNorm();
+  if (n2 < precision<Scalar>()*precision<Scalar>())
+  {
+    m_angle = 0;
+    m_axis << 1, 0, 0;
+  }
+  else
+  {
+    m_angle = 2*std::acos(q.w());
+    m_axis = q.vec() / ei_sqrt(n2);
+  }
+  return *this;
+}
+
+/** Set \c *this from a 3x3 rotation matrix \a mat.
+  */
+template<typename Scalar>
+template<typename Derived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
+{
+  // Since a direct conversion would not be really faster,
+  // let's use the robust Quaternion implementation:
+  return *this = QuaternionType(mat);
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+  */
+template<typename Scalar>
+typename AngleAxis<Scalar>::Matrix3
+AngleAxis<Scalar>::toRotationMatrix(void) const
+{
+  Matrix3 res;
+  Vector3 sin_axis  = ei_sin(m_angle) * m_axis;
+  Scalar c = ei_cos(m_angle);
+  Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
+
+  Scalar tmp;
+  tmp = cos1_axis.x() * m_axis.y();
+  res.coeffRef(0,1) = tmp - sin_axis.z();
+  res.coeffRef(1,0) = tmp + sin_axis.z();
+
+  tmp = cos1_axis.x() * m_axis.z();
+  res.coeffRef(0,2) = tmp + sin_axis.y();
+  res.coeffRef(2,0) = tmp - sin_axis.y();
+
+  tmp = cos1_axis.y() * m_axis.z();
+  res.coeffRef(1,2) = tmp - sin_axis.x();
+  res.coeffRef(2,1) = tmp + sin_axis.x();
+
+  res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c;
+
+  return res;
+}
+
+#endif // EIGEN_ANGLEAXIS_H

Eigen/src/Geometry/CMakeLists.txt

@@ -0,0 +1,8 @@
+FILE(GLOB Eigen_Geometry_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Geometry_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Geometry COMPONENT Devel
+  )
+
+ADD_SUBDIRECTORY(arch)

Eigen/src/Geometry/EulerAngles.h

@@ -0,0 +1,96 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_EULERANGLES_H
+#define EIGEN_EULERANGLES_H
+
+/** \geometry_module \ingroup Geometry_Module
+  * \nonstableyet
+  *
+  * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
+  *
+  * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
+  * For instance, in:
+  * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
+  * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
+  * we have the following equality:
+  * \code
+  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
+  *      * AngleAxisf(ea[1], Vector3f::UnitX())
+  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
+  * This corresponds to the right-multiply conventions (with right hand side frames).
+  */
+template<typename Derived>
+inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
+MatrixBase<Derived>::eulerAngles(int a0, int a1, int a2) const
+{
+  /* Implemented from Graphics Gems IV */
+  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
+
+  Matrix<Scalar,3,1> res;
+  typedef Matrix<typename Derived::Scalar,2,1> Vector2;
+  const Scalar epsilon = precision<Scalar>();
+
+  const int odd = ((a0+1)%3 == a1) ? 0 : 1;
+  const int i = a0;
+  const int j = (a0 + 1 + odd)%3;
+  const int k = (a0 + 2 - odd)%3;
+
+  if (a0==a2)
+  {
+    Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
+    res[1] = std::atan2(s, coeff(i,i));
+    if (s > epsilon)
+    {
+      res[0] = std::atan2(coeff(j,i), coeff(k,i));
+      res[2] = std::atan2(coeff(i,j),-coeff(i,k));
+    }
+    else
+    {
+      res[0] = Scalar(0);
+      res[2] = (coeff(i,i)>0?1:-1)*std::atan2(-coeff(k,j), coeff(j,j));
+    }
+  }
+  else
+  {
+    Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
+    res[1] = std::atan2(-coeff(i,k), c);
+    if (c > epsilon)
+    {
+      res[0] = std::atan2(coeff(j,k), coeff(k,k));
+      res[2] = std::atan2(coeff(i,j), coeff(i,i));
+    }
+    else
+    {
+      res[0] = Scalar(0);
+      res[2] = (coeff(i,k)>0?1:-1)*std::atan2(-coeff(k,j), coeff(j,j));
+    }
+  }
+  if (!odd)
+    res = -res;
+  return res;
+}
+
+
+#endif // EIGEN_EULERANGLES_H

Eigen/src/Geometry/Homogeneous.h

@@ -0,0 +1,260 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_HOMOGENEOUS_H
+#define EIGEN_HOMOGENEOUS_H
+
+/** \geometry_module \ingroup Geometry_Module
+  * \nonstableyet
+  * \class Homogeneous
+  *
+  * \brief Expression of one (or a set of) homogeneous vector(s)
+  *
+  * \param MatrixType the type of the object in which we are making homogeneous
+  *
+  * This class represents an expression of one (or a set of) homogeneous vector(s).
+  * It is the return type of MatrixBase::homogeneous() and most of the time
+  * this is the only way it is used.
+  *
+  * \sa MatrixBase::homogeneous()
+  */
+template<typename MatrixType,int Direction>
+struct ei_traits<Homogeneous<MatrixType,Direction> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
+  typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
+  enum {
+    RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
+                  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
+    ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
+                  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
+    RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = RowsAtCompileTime,
+    MaxColsAtCompileTime = ColsAtCompileTime,
+    Flags = _MatrixTypeNested::Flags & HereditaryBits,
+    CoeffReadCost = _MatrixTypeNested::CoeffReadCost
+  };
+};
+
+template<typename MatrixType,typename Lhs> struct ei_homogeneous_left_product_impl;
+template<typename MatrixType,typename Rhs> struct ei_homogeneous_right_product_impl;
+
+template<typename MatrixType,int Direction> class Homogeneous
+  : public MatrixBase<Homogeneous<MatrixType,Direction> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Homogeneous)
+
+    inline Homogeneous(const MatrixType& matrix)
+      : m_matrix(matrix)
+    {}
+
+    inline int rows() const { return m_matrix.rows() + (Direction==Vertical   ? 1 : 0); }
+    inline int cols() const { return m_matrix.cols() + (Direction==Horizontal ? 1 : 0); }
+
+    inline Scalar coeff(int row, int col) const
+    {
+      if(  (Direction==Vertical   && row==m_matrix.rows())
+        || (Direction==Horizontal && col==m_matrix.cols()))
+        return 1;
+      return m_matrix.coeff(row, col);
+    }
+
+    template<typename Rhs>
+    inline const ei_homogeneous_right_product_impl<Homogeneous,Rhs>
+    operator* (const MatrixBase<Rhs>& rhs) const
+    {
+      ei_assert(Direction==Horizontal);
+      return ei_homogeneous_right_product_impl<Homogeneous,Rhs>(m_matrix,rhs.derived());
+    }
+
+    template<typename Lhs> friend
+    inline const ei_homogeneous_left_product_impl<Homogeneous,Lhs>
+    operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
+    {
+      ei_assert(Direction==Vertical);
+      return ei_homogeneous_left_product_impl<Homogeneous,Lhs>(lhs.derived(),rhs.m_matrix);
+    }
+
+    template<typename Scalar, int Dim, int Mode> friend
+    inline const ei_homogeneous_left_product_impl<Homogeneous,
+      typename Transform<Scalar,Dim,Mode>::AffinePart>
+    operator* (const Transform<Scalar,Dim,Mode>& tr, const Homogeneous& rhs)
+    {
+      ei_assert(Direction==Vertical);
+      return ei_homogeneous_left_product_impl<Homogeneous,typename Transform<Scalar,Dim,Mode>::AffinePart>
+        (tr.affine(),rhs.m_matrix);
+    }
+
+    template<typename Scalar, int Dim> friend
+    inline const ei_homogeneous_left_product_impl<Homogeneous,
+      typename Transform<Scalar,Dim,Projective>::MatrixType>
+    operator* (const Transform<Scalar,Dim,Projective>& tr, const Homogeneous& rhs)
+    {
+      ei_assert(Direction==Vertical);
+      return ei_homogeneous_left_product_impl<Homogeneous,typename Transform<Scalar,Dim,Projective>::MatrixType>
+        (tr.matrix(),rhs.m_matrix);
+    }
+
+  protected:
+    const typename MatrixType::Nested m_matrix;
+};
+
+/** \geometry_module
+  * \nonstableyet
+  * \return an expression of the equivalent homogeneous vector
+  *
+  * \vectoronly
+  *
+  * Example: \include MatrixBase_homogeneous.cpp
+  * Output: \verbinclude MatrixBase_homogeneous.out
+  *
+  * \sa class Homogeneous
+  */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::HomogeneousReturnType
+MatrixBase<Derived>::homogeneous() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+  return derived();
+}
+
+/** \geometry_module
+  * \nonstableyet
+  * \returns a matrix expression of homogeneous column (or row) vectors
+  *
+  * Example: \include PartialRedux_homogeneous.cpp
+  * Output: \verbinclude PartialRedux_homogeneous.out
+  *
+  * \sa MatrixBase::homogeneous() */
+template<typename ExpressionType, int Direction>
+inline const Homogeneous<ExpressionType,Direction>
+PartialRedux<ExpressionType,Direction>::homogeneous() const
+{
+  return _expression();
+}
+
+/** \geometry_module
+  * \nonstableyet
+  * \returns an expression of the homogeneous normalized vector of \c *this
+  *
+  * Example: \include MatrixBase_hnormalized.cpp
+  * Output: \verbinclude MatrixBase_hnormalized.out
+  *
+  * \sa PartialRedux::hnormalized() */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::HNormalizedReturnType
+MatrixBase<Derived>::hnormalized() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+  return StartMinusOne(derived(),0,0,
+    ColsAtCompileTime==1?size()-1:1,
+    ColsAtCompileTime==1?1:size()-1).nestByValue() / coeff(size()-1);
+}
+
+/** \geometry_module
+  * \nonstableyet
+  * \returns an expression of the homogeneous normalized vector of \c *this
+  *
+  * Example: \include DirectionWise_hnormalized.cpp
+  * Output: \verbinclude DirectionWise_hnormalized.out
+  *
+  * \sa MatrixBase::hnormalized() */
+template<typename ExpressionType, int Direction>
+inline const typename PartialRedux<ExpressionType,Direction>::HNormalizedReturnType
+PartialRedux<ExpressionType,Direction>::hnormalized() const
+{
+  return HNormalized_Block(_expression(),0,0,
+      Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
+      Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).nestByValue()
+    .cwise()/
+      Replicate<NestByValue<HNormalized_Factors>,
+                Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
+                Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
+        (HNormalized_Factors(_expression(),
+          Direction==Vertical    ? _expression().rows()-1:0,
+          Direction==Horizontal  ? _expression().cols()-1:0,
+          Direction==Vertical    ? 1 : _expression().rows(),
+          Direction==Horizontal  ? 1 : _expression().cols()).nestByValue(),
+         Direction==Vertical   ? _expression().rows()-1 : 1,
+         Direction==Horizontal ? _expression().cols()-1 : 1).nestByValue();
+}
+
+template<typename MatrixType,typename Lhs>
+struct ei_homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
+  : public ReturnByValue<ei_homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>,
+                         Matrix<typename ei_traits<MatrixType>::Scalar,
+                                Lhs::RowsAtCompileTime,MatrixType::ColsAtCompileTime> >
+{
+  typedef typename ei_cleantype<typename Lhs::Nested>::type LhsNested;
+  ei_homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
+    : m_lhs(lhs), m_rhs(rhs)
+  {}
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    // FIXME investigate how to allow lazy evaluation of this product when possible
+    dst = Block<LhsNested,
+              LhsNested::RowsAtCompileTime,
+              LhsNested::ColsAtCompileTime==Dynamic?Dynamic:LhsNested::ColsAtCompileTime-1>
+            (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
+    dst += m_lhs.col(m_lhs.cols()-1).rowwise()
+            .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
+  }
+
+  const typename Lhs::Nested m_lhs;
+  const typename MatrixType::Nested m_rhs;
+};
+
+template<typename MatrixType,typename Rhs>
+struct ei_homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
+  : public ReturnByValue<ei_homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>,
+                         Matrix<typename ei_traits<MatrixType>::Scalar,
+                                MatrixType::RowsAtCompileTime, Rhs::ColsAtCompileTime> >
+{
+  typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
+  ei_homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
+    : m_lhs(lhs), m_rhs(rhs)
+  {}
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    // FIXME investigate how to allow lazy evaluation of this product when possible
+    dst = m_lhs * Block<RhsNested,
+                        RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
+                        RhsNested::ColsAtCompileTime>
+            (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
+    dst += m_rhs.row(m_rhs.rows()-1).colwise()
+            .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
+  }
+
+  const typename MatrixType::Nested m_lhs;
+  const typename Rhs::Nested m_rhs;
+
+};
+
+#endif // EIGEN_HOMOGENEOUS_H

Eigen/src/Geometry/Hyperplane.h

@@ -0,0 +1,268 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_HYPERPLANE_H
+#define EIGEN_HYPERPLANE_H
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class Hyperplane
+  *
+  * \brief A hyperplane
+  *
+  * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
+  * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  *             Notice that the dimension of the hyperplane is _AmbientDim-1.
+  *
+  * This class represents an hyperplane as the zero set of the implicit equation
+  * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
+  * and \f$ d \f$ is the distance (offset) to the origin.
+  */
+template <typename _Scalar, int _AmbientDim>
+class Hyperplane
+{
+public:
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+  enum { AmbientDimAtCompileTime = _AmbientDim };
+  typedef _Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime==Dynamic
+                        ? Dynamic
+                        : AmbientDimAtCompileTime+1,1> Coefficients;
+  typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
+
+  /** Default constructor without initialization */
+  inline explicit Hyperplane() {}
+
+  /** Constructs a dynamic-size hyperplane with \a _dim the dimension
+    * of the ambient space */
+  inline explicit Hyperplane(int _dim) : m_coeffs(_dim+1) {}
+
+  /** Construct a plane from its normal \a n and a point \a e onto the plane.
+    * \warning the vector normal is assumed to be normalized.
+    */
+  inline Hyperplane(const VectorType& n, const VectorType& e)
+    : m_coeffs(n.size()+1)
+  {
+    normal() = n;
+    offset() = -e.dot(n);
+  }
+
+  /** Constructs a plane from its normal \a n and distance to the origin \a d
+    * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
+    * \warning the vector normal is assumed to be normalized.
+    */
+  inline Hyperplane(const VectorType& n, Scalar d)
+    : m_coeffs(n.size()+1)
+  {
+    normal() = n;
+    offset() = d;
+  }
+
+  /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
+    * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
+    */
+  static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
+  {
+    Hyperplane result(p0.size());
+    result.normal() = (p1 - p0).unitOrthogonal();
+    result.offset() = -result.normal().dot(p0);
+    return result;
+  }
+
+  /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
+    * is required to be exactly 3.
+    */
+  static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+  {
+    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
+    Hyperplane result(p0.size());
+    result.normal() = (p2 - p0).cross(p1 - p0).normalized();
+    result.offset() = -result.normal().dot(p0);
+    return result;
+  }
+
+  /** Constructs a hyperplane passing through the parametrized line \a parametrized.
+    * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
+    * so an arbitrary choice is made.
+    */
+  // FIXME to be consitent with the rest this could be implemented as a static Through function ??
+  explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
+  {
+    normal() = parametrized.direction().unitOrthogonal();
+    offset() = -normal().dot(parametrized.origin());
+  }
+
+  ~Hyperplane() {}
+
+  /** \returns the dimension in which the plane holds */
+  inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : AmbientDimAtCompileTime; }
+
+  /** normalizes \c *this */
+  void normalize(void)
+  {
+    m_coeffs /= normal().norm();
+  }
+
+  /** \returns the signed distance between the plane \c *this and a point \a p.
+    * \sa absDistance()
+    */
+  inline Scalar signedDistance(const VectorType& p) const { return p.dot(normal()) + offset(); }
+
+  /** \returns the absolute distance between the plane \c *this and a point \a p.
+    * \sa signedDistance()
+    */
+  inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); }
+
+  /** \returns the projection of a point \a p onto the plane \c *this.
+    */
+  inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
+
+  /** \returns a constant reference to the unit normal vector of the plane, which corresponds
+    * to the linear part of the implicit equation.
+    */
+  inline const NormalReturnType normal() const { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+  /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
+    * to the linear part of the implicit equation.
+    */
+  inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+  /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
+    * \warning the vector normal is assumed to be normalized.
+    */
+  inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
+
+  /** \returns a non-constant reference to the distance to the origin, which is also the constant part
+    * of the implicit equation */
+  inline Scalar& offset() { return m_coeffs(dim()); }
+
+  /** \returns a constant reference to the coefficients c_i of the plane equation:
+    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+    */
+  inline const Coefficients& coeffs() const { return m_coeffs; }
+
+  /** \returns a non-constant reference to the coefficients c_i of the plane equation:
+    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+    */
+  inline Coefficients& coeffs() { return m_coeffs; }
+
+  /** \returns the intersection of *this with \a other.
+    *
+    * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
+    *
+    * \note If \a other is approximately parallel to *this, this method will return any point on *this.
+    */
+  VectorType intersection(const Hyperplane& other)
+  {
+    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+    Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
+    // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
+    // whether the two lines are approximately parallel.
+    if(ei_isMuchSmallerThan(det, Scalar(1)))
+    {   // special case where the two lines are approximately parallel. Pick any point on the first line.
+        if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0)))
+            return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
+        else
+            return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
+    }
+    else
+    {   // general case
+        Scalar invdet = Scalar(1) / det;
+        return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
+                          invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
+    }
+  }
+
+  /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+    *
+    * \param mat the Dim x Dim transformation matrix
+    * \param traits specifies whether the matrix \a mat represents an Isometry
+    *               or a more generic Affine transformation. The default is Affine.
+    */
+  template<typename XprType>
+  inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+  {
+    if (traits==Affine)
+      normal() = mat.inverse().transpose() * normal();
+    else if (traits==Isometry)
+      normal() = mat * normal();
+    else
+    {
+      ei_assert("invalid traits value in Hyperplane::transform()");
+    }
+    return *this;
+  }
+
+  /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+    *
+    * \param t the transformation of dimension Dim
+    * \param traits specifies whether the transformation \a t represents an Isometry
+    *               or a more generic Affine transformation. The default is Affine.
+    *               Other kind of transformations are not supported.
+    */
+  inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime>& t,
+                                TransformTraits traits = Affine)
+  {
+    transform(t.linear(), traits);
+    offset() -= t.translation().dot(normal());
+    return *this;
+  }
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<Hyperplane,
+           Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+  {
+    return typename ei_cast_return_type<Hyperplane,
+                    Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+  }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime>& other)
+  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+
+  Coefficients m_coeffs;
+};
+
+#endif // EIGEN_HYPERPLANE_H

Eigen/src/Geometry/OrthoMethods.h

@@ -0,0 +1,219 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ORTHOMETHODS_H
+#define EIGEN_ORTHOMETHODS_H
+
+/** \geometry_module
+  *
+  * \returns the cross product of \c *this and \a other
+  *
+  * Here is a very good explanation of cross-product: http://xkcd.com/199/
+  * \sa MatrixBase::cross3()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline typename MatrixBase<Derived>::PlainMatrixType
+MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+
+  // Note that there is no need for an expression here since the compiler
+  // optimize such a small temporary very well (even within a complex expression)
+  const typename ei_nested<Derived,2>::type lhs(derived());
+  const typename ei_nested<OtherDerived,2>::type rhs(other.derived());
+  return typename ei_plain_matrix_type<Derived>::type(
+    lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1),
+    lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2),
+    lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)
+  );
+}
+
+template< int Arch,typename VectorLhs,typename VectorRhs,
+          typename Scalar = typename VectorLhs::Scalar,
+          int Vectorizable = (VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit>
+struct ei_cross3_impl {
+  inline static typename ei_plain_matrix_type<VectorLhs>::type
+  run(const VectorLhs& lhs, const VectorRhs& rhs)
+  {
+    return typename ei_plain_matrix_type<VectorLhs>::type(
+      lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1),
+      lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2),
+      lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0),
+      0
+    );
+  }
+};
+
+/** \geometry_module
+  *
+  * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
+  *
+  * The size of \c *this and \a other must be four. This function is especially useful
+  * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
+  *
+  * \sa MatrixBase::cross()
+  */
+template<typename Derived>
+template<typename OtherDerived>
+inline typename MatrixBase<Derived>::PlainMatrixType
+MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
+
+  typedef typename ei_nested<Derived,2>::type DerivedNested;
+  typedef typename ei_nested<OtherDerived,2>::type OtherDerivedNested;
+  const DerivedNested lhs(derived());
+  const OtherDerivedNested rhs(other.derived());
+
+  return ei_cross3_impl<EiArch,typename ei_cleantype<DerivedNested>::type,
+                               typename ei_cleantype<OtherDerivedNested>::type>::run(lhs,rhs);
+}
+
+/** \returns a matrix expression of the cross product of each column or row
+  * of the referenced expression with the \a other vector.
+  *
+  * The referenced matrix must have one dimension equal to 3.
+  * The result matrix has the same dimensions than the referenced one.
+  *
+  * \geometry_module
+  *
+  * \sa MatrixBase::cross() */
+template<typename ExpressionType, int Direction>
+template<typename OtherDerived>
+const typename PartialRedux<ExpressionType,Direction>::CrossReturnType
+PartialRedux<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+  EIGEN_STATIC_ASSERT((ei_is_same_type<Scalar, typename OtherDerived::Scalar>::ret),
+    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+  CrossReturnType res(_expression().rows(),_expression().cols());
+  if(Direction==Vertical)
+  {
+    ei_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
+    res.row(0) = _expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1);
+    res.row(1) = _expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2);
+    res.row(2) = _expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0);
+  }
+  else
+  {
+    ei_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
+    res.col(0) = _expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1);
+    res.col(1) = _expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2);
+    res.col(2) = _expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0);
+  }
+  return res;
+}
+
+template<typename Derived, int Size = Derived::SizeAtCompileTime>
+struct ei_unitOrthogonal_selector
+{
+  typedef typename ei_plain_matrix_type<Derived>::type VectorType;
+  typedef typename ei_traits<Derived>::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,2,1> Vector2;
+  inline static VectorType run(const Derived& src)
+  {
+    VectorType perp = VectorType::Zero(src.size());
+    int maxi = 0;
+    int sndi = 0;
+    src.cwise().abs().maxCoeff(&maxi);
+    if (maxi==0)
+      sndi = 1;
+    RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
+    perp.coeffRef(maxi) = -ei_conj(src.coeff(sndi)) * invnm;
+    perp.coeffRef(sndi) =  ei_conj(src.coeff(maxi)) * invnm;
+
+    return perp;
+   }
+};
+
+template<typename Derived>
+struct ei_unitOrthogonal_selector<Derived,3>
+{
+  typedef typename ei_plain_matrix_type<Derived>::type VectorType;
+  typedef typename ei_traits<Derived>::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  inline static VectorType run(const Derived& src)
+  {
+    VectorType perp;
+    /* Let us compute the crossed product of *this with a vector
+     * that is not too close to being colinear to *this.
+     */
+
+    /* unless the x and y coords are both close to zero, we can
+     * simply take ( -y, x, 0 ) and normalize it.
+     */
+    if((!ei_isMuchSmallerThan(src.x(), src.z()))
+    || (!ei_isMuchSmallerThan(src.y(), src.z())))
+    {
+      RealScalar invnm = RealScalar(1)/src.template start<2>().norm();
+      perp.coeffRef(0) = -ei_conj(src.y())*invnm;
+      perp.coeffRef(1) = ei_conj(src.x())*invnm;
+      perp.coeffRef(2) = 0;
+    }
+    /* if both x and y are close to zero, then the vector is close
+     * to the z-axis, so it's far from colinear to the x-axis for instance.
+     * So we take the crossed product with (1,0,0) and normalize it.
+     */
+    else
+    {
+      RealScalar invnm = RealScalar(1)/src.template end<2>().norm();
+      perp.coeffRef(0) = 0;
+      perp.coeffRef(1) = -ei_conj(src.z())*invnm;
+      perp.coeffRef(2) = ei_conj(src.y())*invnm;
+    }
+
+    return perp;
+   }
+};
+
+template<typename Derived>
+struct ei_unitOrthogonal_selector<Derived,2>
+{
+  typedef typename ei_plain_matrix_type<Derived>::type VectorType;
+  inline static VectorType run(const Derived& src)
+  { return VectorType(-ei_conj(src.y()), ei_conj(src.x())).normalized(); }
+};
+
+/** \returns a unit vector which is orthogonal to \c *this
+  *
+  * The size of \c *this must be at least 2. If the size is exactly 2,
+  * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
+  *
+  * \sa cross()
+  */
+template<typename Derived>
+typename MatrixBase<Derived>::PlainMatrixType
+MatrixBase<Derived>::unitOrthogonal() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return ei_unitOrthogonal_selector<Derived>::run(derived());
+}
+
+#endif // EIGEN_ORTHOMETHODS_H

Eigen/src/Geometry/ParametrizedLine.h

@@ -0,0 +1,155 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PARAMETRIZEDLINE_H
+#define EIGEN_PARAMETRIZEDLINE_H
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class ParametrizedLine
+  *
+  * \brief A parametrized line
+  *
+  * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
+  * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
+  * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ l \in \mathbf{R} \f$.
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  */
+template <typename _Scalar, int _AmbientDim>
+class ParametrizedLine
+{
+public:
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+  enum { AmbientDimAtCompileTime = _AmbientDim };
+  typedef _Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+  /** Default constructor without initialization */
+  inline explicit ParametrizedLine() {}
+
+  /** Constructs a dynamic-size line with \a _dim the dimension
+    * of the ambient space */
+  inline explicit ParametrizedLine(int _dim) : m_origin(_dim), m_direction(_dim) {}
+
+  /** Initializes a parametrized line of direction \a direction and origin \a origin.
+    * \warning the vector direction is assumed to be normalized.
+    */
+  ParametrizedLine(const VectorType& origin, const VectorType& direction)
+    : m_origin(origin), m_direction(direction) {}
+
+  explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+  /** Constructs a parametrized line going from \a p0 to \a p1. */
+  static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+  { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+  ~ParametrizedLine() {}
+
+  /** \returns the dimension in which the line holds */
+  inline int dim() const { return m_direction.size(); }
+
+  const VectorType& origin() const { return m_origin; }
+  VectorType& origin() { return m_origin; }
+
+  const VectorType& direction() const { return m_direction; }
+  VectorType& direction() { return m_direction; }
+
+  /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+    * \sa distance()
+    */
+  RealScalar squaredDistance(const VectorType& p) const
+  {
+    VectorType diff = p-origin();
+    return (diff - diff.dot(direction())* direction()).squaredNorm();
+  }
+  /** \returns the distance of a point \a p to its projection onto the line \c *this.
+    * \sa squaredDistance()
+    */
+  RealScalar distance(const VectorType& p) const { return ei_sqrt(squaredDistance(p)); }
+
+  /** \returns the projection of a point \a p onto the line \c *this. */
+  VectorType projection(const VectorType& p) const
+  { return origin() + (p-origin()).dot(direction()) * direction(); }
+
+  Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<ParametrizedLine,
+           ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+  {
+    return typename ei_cast_return_type<ParametrizedLine,
+                    ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+  }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime>& other)
+  {
+    m_origin = other.origin().template cast<Scalar>();
+    m_direction = other.direction().template cast<Scalar>();
+  }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
+
+protected:
+
+  VectorType m_origin, m_direction;
+};
+
+/** Constructs a parametrized line from a 2D hyperplane
+  *
+  * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
+  */
+template <typename _Scalar, int _AmbientDim>
+inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+  direction() = hyperplane.normal().unitOrthogonal();
+  origin() = -hyperplane.normal()*hyperplane.offset();
+}
+
+/** \returns the parameter value of the intersection between \c *this and the given hyperplane
+  */
+template <typename _Scalar, int _AmbientDim>
+inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+  return -(hyperplane.offset()+origin().dot(hyperplane.normal()))
+          /(direction().dot(hyperplane.normal()));
+}
+
+#endif // EIGEN_PARAMETRIZEDLINE_H

Eigen/src/Geometry/Quaternion.h

@@ -0,0 +1,499 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_QUATERNION_H
+#define EIGEN_QUATERNION_H
+
+template<typename Other,
+         int OtherRows=Other::RowsAtCompileTime,
+         int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternion_assign_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class Quaternion
+  *
+  * \brief The quaternion class used to represent 3D orientations and rotations
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  *
+  * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
+  * orientations and rotations of objects in three dimensions. Compared to other representations
+  * like Euler angles or 3x3 matrices, quatertions offer the following advantages:
+  * \li \b compact storage (4 scalars)
+  * \li \b efficient to compose (28 flops),
+  * \li \b stable spherical interpolation
+  *
+  * The following two typedefs are provided for convenience:
+  * \li \c Quaternionf for \c float
+  * \li \c Quaterniond for \c double
+  *
+  * \sa  class AngleAxis, class Transform
+  */
+
+template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> >
+{
+  typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Quaternion : public RotationBase<Quaternion<_Scalar>,3>
+{
+  typedef RotationBase<Quaternion<_Scalar>,3> Base;
+
+
+
+public:
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4)
+
+  using Base::operator*;
+
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+
+  /** the type of the Coefficients 4-vector */
+  typedef Matrix<Scalar, 4, 1> Coefficients;
+  /** the type of a 3D vector */
+  typedef Matrix<Scalar,3,1> Vector3;
+  /** the equivalent rotation matrix type */
+  typedef Matrix<Scalar,3,3> Matrix3;
+  /** the equivalent angle-axis type */
+  typedef AngleAxis<Scalar> AngleAxisType;
+
+  /** \returns the \c x coefficient */
+  inline Scalar x() const { return m_coeffs.coeff(0); }
+  /** \returns the \c y coefficient */
+  inline Scalar y() const { return m_coeffs.coeff(1); }
+  /** \returns the \c z coefficient */
+  inline Scalar z() const { return m_coeffs.coeff(2); }
+  /** \returns the \c w coefficient */
+  inline Scalar w() const { return m_coeffs.coeff(3); }
+
+  /** \returns a reference to the \c x coefficient */
+  inline Scalar& x() { return m_coeffs.coeffRef(0); }
+  /** \returns a reference to the \c y coefficient */
+  inline Scalar& y() { return m_coeffs.coeffRef(1); }
+  /** \returns a reference to the \c z coefficient */
+  inline Scalar& z() { return m_coeffs.coeffRef(2); }
+  /** \returns a reference to the \c w coefficient */
+  inline Scalar& w() { return m_coeffs.coeffRef(3); }
+
+  /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+  inline const Block<Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); }
+
+  /** \returns a vector expression of the imaginary part (x,y,z) */
+  inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); }
+
+  /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+  inline const Coefficients& coeffs() const { return m_coeffs; }
+
+  /** \returns a vector expression of the coefficients (x,y,z,w) */
+  inline Coefficients& coeffs() { return m_coeffs; }
+
+  /** Default constructor leaving the quaternion uninitialized. */
+  inline Quaternion() {}
+
+  /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+    * its four coefficients \a w, \a x, \a y and \a z.
+    *
+    * \warning Note the order of the arguments: the real \a w coefficient first,
+    * while internally the coefficients are stored in the following order:
+    * [\c x, \c y, \c z, \c w]
+    */
+  inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
+  { m_coeffs << x, y, z, w; }
+
+  /** Copy constructor */
+  inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
+
+  /** Constructs and initializes a quaternion from the angle-axis \a aa */
+  explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+  /** Constructs and initializes a quaternion from either:
+    *  - a rotation matrix expression,
+    *  - a 4D vector expression representing quaternion coefficients.
+    * \sa operator=(MatrixBase<Derived>)
+    */
+  template<typename Derived>
+  explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+  Quaternion& operator=(const Quaternion& other);
+  Quaternion& operator=(const AngleAxisType& aa);
+  template<typename Derived>
+  Quaternion& operator=(const MatrixBase<Derived>& m);
+
+  /** \returns a quaternion representing an identity rotation
+    * \sa MatrixBase::Identity()
+    */
+  inline static Quaternion Identity() { return Quaternion(1, 0, 0, 0); }
+
+  /** \sa Quaternion::Identity(), MatrixBase::setIdentity()
+    */
+  inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; }
+
+  /** \returns the squared norm of the quaternion's coefficients
+    * \sa Quaternion::norm(), MatrixBase::squaredNorm()
+    */
+  inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); }
+
+  /** \returns the norm of the quaternion's coefficients
+    * \sa Quaternion::squaredNorm(), MatrixBase::norm()
+    */
+  inline Scalar norm() const { return m_coeffs.norm(); }
+
+  /** Normalizes the quaternion \c *this
+    * \sa normalized(), MatrixBase::normalize() */
+  inline void normalize() { m_coeffs.normalize(); }
+  /** \returns a normalized version of \c *this
+    * \sa normalize(), MatrixBase::normalized() */
+  inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); }
+
+  /** \returns the dot product of \c *this and \a other
+    * Geometrically speaking, the dot product of two unit quaternions
+    * corresponds to the cosine of half the angle between the two rotations.
+    * \sa angularDistance()
+    */
+  inline Scalar dot(const Quaternion& other) const { return m_coeffs.dot(other.m_coeffs); }
+
+  inline Scalar angularDistance(const Quaternion& other) const;
+
+  Matrix3 toRotationMatrix(void) const;
+
+  template<typename Derived1, typename Derived2>
+  Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+  inline Quaternion operator* (const Quaternion& q) const;
+  inline Quaternion& operator*= (const Quaternion& q);
+
+  Quaternion inverse(void) const;
+  Quaternion conjugate(void) const;
+
+  Quaternion slerp(Scalar t, const Quaternion& other) const;
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const
+  { return typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit Quaternion(const Quaternion<OtherScalarType>& other)
+  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+  Vector3 _transformVector(Vector3 v) const;
+
+protected:
+  Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+  * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+  * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+// Generic Quaternion * Quaternion product
+template<int Arch,typename Scalar> inline Quaternion<Scalar>
+ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b)
+{
+  return Quaternion<Scalar>
+  (
+    a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+    a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+    a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+    a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+  );
+}
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
+{
+  return ei_quaternion_product<EiArch>(*this,other);
+}
+
+/** \sa operator*(Quaternion) */
+template <typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other)
+{
+  return (*this = *this * other);
+}
+
+/** Rotation of a vector by a quaternion.
+  * \remarks If the quaternion is used to rotate several points (>1)
+  * then it is much more efficient to first convert it to a 3x3 Matrix.
+  * Comparison of the operation cost for n transformations:
+  *   - Quaternion:    30n
+  *   - Via a Matrix3: 24 + 15n
+  */
+template <typename Scalar>
+inline typename Quaternion<Scalar>::Vector3
+Quaternion<Scalar>::_transformVector(Vector3 v) const
+{
+    // Note that this algorithm comes from the optimization by hand
+    // of the conversion to a Matrix followed by a Matrix/Vector product.
+    // It appears to be much faster than the common algorithm found
+    // in the litterature (30 versus 39 flops). It also requires two
+    // Vector3 as temporaries.
+    Vector3 uv = Scalar(2) * this->vec().cross(v);
+    return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other)
+{
+  m_coeffs = other.m_coeffs;
+  return *this;
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+  */
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa)
+{
+  Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+  this->w() = ei_cos(ha);
+  this->vec() = ei_sin(ha) * aa.axis();
+  return *this;
+}
+
+/** Set \c *this from the expression \a xpr:
+  *   - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+  *   - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+  *     and \a xpr is converted to a quaternion
+  */
+template<typename Scalar>
+template<typename Derived>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr)
+{
+  ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived());
+  return *this;
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix */
+template<typename Scalar>
+inline typename Quaternion<Scalar>::Matrix3
+Quaternion<Scalar>::toRotationMatrix(void) const
+{
+  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+  // if not inlined then the cost of the return by value is huge ~ +35%,
+  // however, not inlining this function is an order of magnitude slower, so
+  // it has to be inlined, and so the return by value is not an issue
+  Matrix3 res;
+
+  const Scalar tx  = 2*this->x();
+  const Scalar ty  = 2*this->y();
+  const Scalar tz  = 2*this->z();
+  const Scalar twx = tx*this->w();
+  const Scalar twy = ty*this->w();
+  const Scalar twz = tz*this->w();
+  const Scalar txx = tx*this->x();
+  const Scalar txy = ty*this->x();
+  const Scalar txz = tz*this->x();
+  const Scalar tyy = ty*this->y();
+  const Scalar tyz = tz*this->y();
+  const Scalar tzz = tz*this->z();
+
+  res.coeffRef(0,0) = 1-(tyy+tzz);
+  res.coeffRef(0,1) = txy-twz;
+  res.coeffRef(0,2) = txz+twy;
+  res.coeffRef(1,0) = txy+twz;
+  res.coeffRef(1,1) = 1-(txx+tzz);
+  res.coeffRef(1,2) = tyz-twx;
+  res.coeffRef(2,0) = txz-twy;
+  res.coeffRef(2,1) = tyz+twx;
+  res.coeffRef(2,2) = 1-(txx+tyy);
+
+  return res;
+}
+
+/** Sets *this to be a quaternion representing a rotation sending the vector \a a to the vector \a b.
+  *
+  * \returns a reference to *this.
+  *
+  * Note that the two input vectors do \b not have to be normalized.
+  */
+template<typename Scalar>
+template<typename Derived1, typename Derived2>
+inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+  Vector3 v0 = a.normalized();
+  Vector3 v1 = b.normalized();
+  Scalar c = v0.dot(v1);
+
+  // if dot == 1, vectors are the same
+  if (ei_isApprox(c,Scalar(1)))
+  {
+    // set to identity
+    this->w() = 1; this->vec().setZero();
+    return *this;
+  }
+  // if dot == -1, vectors are opposites
+  if (ei_isApprox(c,Scalar(-1)))
+  {
+    this->vec() = v0.unitOrthogonal();
+    this->w() = 0;
+    return *this;
+  }
+
+  Vector3 axis = v0.cross(v1);
+  Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2));
+  Scalar invs = Scalar(1)/s;
+  this->vec() = axis * invs;
+  this->w() = s * Scalar(0.5);
+
+  return *this;
+}
+
+/** \returns the multiplicative inverse of \c *this
+  * Note that in most cases, i.e., if you simply want the opposite rotation,
+  * and/or the quaternion is normalized, then it is enough to use the conjugate.
+  *
+  * \sa Quaternion::conjugate()
+  */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
+{
+  // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
+  Scalar n2 = this->squaredNorm();
+  if (n2 > 0)
+    return Quaternion(conjugate().coeffs() / n2);
+  else
+  {
+    // return an invalid result to flag the error
+    return Quaternion(Coefficients::Zero());
+  }
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+  * if the quaternion is normalized.
+  * The conjugate of a quaternion represents the opposite rotation.
+  *
+  * \sa Quaternion::inverse()
+  */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
+{
+  return Quaternion(this->w(),-this->x(),-this->y(),-this->z());
+}
+
+/** \returns the angle (in radian) between two rotations
+  * \sa dot()
+  */
+template <typename Scalar>
+inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
+{
+  double d = ei_abs(this->dot(other));
+  if (d>=1.0)
+    return 0;
+  return Scalar(2) * std::acos(d);
+}
+
+/** \returns the spherical linear interpolation between the two quaternions
+  * \c *this and \a other at the parameter \a t
+  */
+template <typename Scalar>
+Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
+{
+  static const Scalar one = Scalar(1) - precision<Scalar>();
+  Scalar d = this->dot(other);
+  Scalar absD = ei_abs(d);
+  if (absD>=one)
+    return *this;
+
+  // theta is the angle between the 2 quaternions
+  Scalar theta = std::acos(absD);
+  Scalar sinTheta = ei_sin(theta);
+
+  Scalar scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta;
+  Scalar scale1 = ei_sin( ( t * theta) ) / sinTheta;
+  if (d<0)
+    scale1 = -scale1;
+
+  return Quaternion(scale0 * m_coeffs + scale1 * other.m_coeffs);
+}
+
+// set from a rotation matrix
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,3,3>
+{
+  typedef typename Other::Scalar Scalar;
+  inline static void run(Quaternion<Scalar>& q, const Other& mat)
+  {
+    // This algorithm comes from  "Quaternion Calculus and Fast Animation",
+    // Ken Shoemake, 1987 SIGGRAPH course notes
+    Scalar t = mat.trace();
+    if (t > 0)
+    {
+      t = ei_sqrt(t + Scalar(1.0));
+      q.w() = Scalar(0.5)*t;
+      t = Scalar(0.5)/t;
+      q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+      q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+      q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+    }
+    else
+    {
+      int i = 0;
+      if (mat.coeff(1,1) > mat.coeff(0,0))
+        i = 1;
+      if (mat.coeff(2,2) > mat.coeff(i,i))
+        i = 2;
+      int j = (i+1)%3;
+      int k = (j+1)%3;
+
+      t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+      q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+      t = Scalar(0.5)/t;
+      q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+      q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+      q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+    }
+  }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,4,1>
+{
+  typedef typename Other::Scalar Scalar;
+  inline static void run(Quaternion<Scalar>& q, const Other& vec)
+  {
+    q.coeffs() = vec;
+  }
+};
+
+#endif // EIGEN_QUATERNION_H

Eigen/src/Geometry/Rotation2D.h

@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ROTATION2D_H
+#define EIGEN_ROTATION2D_H
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class Rotation2D
+  *
+  * \brief Represents a rotation/orientation in a 2 dimensional space.
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  *
+  * This class is equivalent to a single scalar representing a counter clock wise rotation
+  * as a single angle in radian. It provides some additional features such as the automatic
+  * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
+  * interface to Quaternion in order to facilitate the writing of generic algorithms
+  * dealing with rotations.
+  *
+  * \sa class Quaternion, class Transform
+  */
+template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> >
+{
+  typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
+{
+  typedef RotationBase<Rotation2D<_Scalar>,2> Base;
+
+public:
+
+  using Base::operator*;
+
+  enum { Dim = 2 };
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+  typedef Matrix<Scalar,2,1> Vector2;
+  typedef Matrix<Scalar,2,2> Matrix2;
+
+protected:
+
+  Scalar m_angle;
+
+public:
+
+  /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+  inline Rotation2D(Scalar a) : m_angle(a) {}
+
+  /** \returns the rotation angle */
+  inline Scalar angle() const { return m_angle; }
+
+  /** \returns a read-write reference to the rotation angle */
+  inline Scalar& angle() { return m_angle; }
+
+  /** \returns the inverse rotation */
+  inline Rotation2D inverse() const { return -m_angle; }
+
+  /** Concatenates two rotations */
+  inline Rotation2D operator*(const Rotation2D& other) const
+  { return m_angle + other.m_angle; }
+
+  /** Concatenates two rotations */
+  inline Rotation2D& operator*=(const Rotation2D& other)
+  { return m_angle += other.m_angle; }
+
+  /** Applies the rotation to a 2D vector */
+  Vector2 operator* (const Vector2& vec) const
+  { return toRotationMatrix() * vec; }
+
+  template<typename Derived>
+  Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
+  Matrix2 toRotationMatrix(void) const;
+
+  /** \returns the spherical interpolation between \c *this and \a other using
+    * parameter \a t. It is in fact equivalent to a linear interpolation.
+    */
+  inline Rotation2D slerp(Scalar t, const Rotation2D& other) const
+  { return m_angle * (1-t) + other.angle() * t; }
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
+  { return typename ei_cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
+  {
+    m_angle = Scalar(other.angle());
+  }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+  * single precision 2D rotation type */
+typedef Rotation2D<float> Rotation2Df;
+/** \ingroup Geometry_Module
+  * double precision 2D rotation type */
+typedef Rotation2D<double> Rotation2Dd;
+
+/** Set \c *this from a 2x2 rotation matrix \a mat.
+  * In other words, this function extract the rotation angle
+  * from the rotation matrix.
+  */
+template<typename Scalar>
+template<typename Derived>
+Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+  m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0));
+  return *this;
+}
+
+/** Constructs and \returns an equivalent 2x2 rotation matrix.
+  */
+template<typename Scalar>
+typename Rotation2D<Scalar>::Matrix2
+Rotation2D<Scalar>::toRotationMatrix(void) const
+{
+  Scalar sinA = ei_sin(m_angle);
+  Scalar cosA = ei_cos(m_angle);
+  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
+}
+
+#endif // EIGEN_ROTATION2D_H

Eigen/src/Geometry/RotationBase.h

@@ -0,0 +1,178 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ROTATIONBASE_H
+#define EIGEN_ROTATIONBASE_H
+
+// this file aims to contains the various representations of rotation/orientation
+// in 2D and 3D space excepted Matrix and Quaternion.
+
+/** \class RotationBase
+  *
+  * \brief Common base class for compact rotation representations
+  *
+  * \param Derived is the derived type, i.e., a rotation type
+  * \param _Dim the dimension of the space
+  */
+template<typename Derived, int _Dim>
+class RotationBase
+{
+  public:
+    enum { Dim = _Dim };
+    /** the scalar type of the coefficients */
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+
+    /** corresponding linear transformation matrix type */
+    typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
+    typedef Matrix<Scalar,Dim,1> VectorType;
+
+  protected:
+    template<typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
+    struct generic_product_selector
+    {
+      typedef RotationMatrixType ReturnType;
+      inline static RotationMatrixType run(const Derived& r, const MatrixType& m)
+      { return r.toRotationMatrix() * m; }
+    };
+
+    template<typename OtherVectorType>
+    struct generic_product_selector<OtherVectorType,true>
+    {
+      typedef VectorType ReturnType;
+      inline static VectorType run(const Derived& r, const OtherVectorType& v)
+      {
+        return r._transformVector(v);
+      }
+    };
+
+  public:
+    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+    inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+    /** \returns an equivalent rotation matrix */
+    inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
+
+    /** \returns the inverse rotation */
+    inline Derived inverse() const { return derived().inverse(); }
+
+    /** \returns the concatenation of the rotation \c *this with a translation \a t */
+    inline Transform<Scalar,Dim> operator*(const Translation<Scalar,Dim>& t) const
+    { return toRotationMatrix() * t; }
+
+    /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
+    inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
+    { return toRotationMatrix() * s.factor(); }
+
+    /** \returns the concatenation of the rotation \c *this with a generic expression \a e
+      * \a e can be:
+      *  - a DimxDim linear transformation matrix (including an axis aligned scaling)
+      *  - a vector of size Dim
+      */
+    template<typename OtherDerived>
+    inline typename generic_product_selector<OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType
+    operator*(const MatrixBase<OtherDerived>& e) const
+    { return generic_product_selector<OtherDerived>::run(derived(), e.derived()); }
+
+    /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
+    template<typename OtherDerived> friend
+    inline RotationMatrixType operator*(const MatrixBase<OtherDerived>& l, const Derived& r)
+    { return l.derived() * r.toRotationMatrix(); }
+
+    /** \returns the concatenation of the rotation \c *this with a transformation \a t */
+    template<int Mode>
+    inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode>& t) const
+    { return toRotationMatrix() * t; }
+
+    template<typename OtherVectorType>
+    inline VectorType _transformVector(const OtherVectorType& v) const
+    { return toRotationMatrix() * v; }
+};
+
+/** \geometry_module
+  *
+  * Constructs a Dim x Dim rotation matrix from the rotation \a r
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+  *this = r.toRotationMatrix();
+}
+
+/** \geometry_module
+  *
+  * Set a Dim x Dim rotation matrix from the rotation \a r
+  */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+  return *this = r.toRotationMatrix();
+}
+
+/** \internal
+  *
+  * Helper function to return an arbitrary rotation object to a rotation matrix.
+  *
+  * \param Scalar the numeric type of the matrix coefficients
+  * \param Dim the dimension of the current space
+  *
+  * It returns a Dim x Dim fixed size matrix.
+  *
+  * Default specializations are provided for:
+  *   - any scalar type (2D),
+  *   - any matrix expression,
+  *   - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
+  *
+  * Currently ei_toRotationMatrix is only used by Transform.
+  *
+  * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
+  */
+template<typename Scalar, int Dim>
+inline static Matrix<Scalar,2,2> ei_toRotationMatrix(const Scalar& s)
+{
+  EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+  return Rotation2D<Scalar>(s).toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+inline static Matrix<Scalar,Dim,Dim> ei_toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
+{
+  return r.toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+inline static const MatrixBase<OtherDerived>& ei_toRotationMatrix(const MatrixBase<OtherDerived>& mat)
+{
+  EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
+    YOU_MADE_A_PROGRAMMING_MISTAKE)
+  return mat;
+}
+
+#endif // EIGEN_ROTATIONBASE_H

Eigen/src/Geometry/Scaling.h

@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SCALING_H
+#define EIGEN_SCALING_H
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class Scaling
+  *
+  * \brief Represents a generic uniform scaling transformation
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients.
+  *
+  * This class represent a uniform scaling transformation. It is the return
+  * type of Scaling(Scalar), and most of the time this is the only way it
+  * is used. In particular, this class is not aimed to be used to store a scaling transformation,
+  * but rather to make easier the constructions and updates of Transform objects.
+  *
+  * To represent an axis aligned scaling, use the DiagonalMatrix class.
+  *
+  * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
+  */
+template<typename _Scalar>
+class UniformScaling
+{
+public:
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+
+protected:
+
+  Scalar m_factor;
+
+public:
+
+  /** Default constructor without initialization. */
+  UniformScaling() {}
+  /** Constructs and initialize a uniform scaling transformation */
+  explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
+
+  inline const Scalar& factor() const { return m_factor; }
+  inline Scalar& factor() { return m_factor; }
+
+  /** Concatenates two uniform scaling */
+  inline UniformScaling operator* (const UniformScaling& other) const
+  { return UniformScaling(m_factor * other.factor()); }
+
+  /** Concatenates a uniform scaling and a translation */
+  template<int Dim>
+  inline Transform<Scalar,Dim> operator* (const Translation<Scalar,Dim>& t) const;
+
+  /** Concatenates a uniform scaling and an affine transformation */
+  template<int Dim>
+  inline Transform<Scalar,Dim> operator* (const Transform<Scalar,Dim>& t) const;
+
+  /** Concatenates a uniform scaling and a linear transformation matrix */
+  // TODO returns an expression
+  template<typename Derived>
+  inline typename ei_plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const
+  { return other * m_factor; }
+
+  template<typename Derived,int Dim>
+  inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
+  { return r.toRotationMatrix() * m_factor; }
+
+  /** \returns the inverse scaling */
+  inline UniformScaling inverse() const
+  { return UniformScaling(Scalar(1)/m_factor); }
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline UniformScaling<NewScalarType> cast() const
+  { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
+  { m_factor = Scalar(other.factor()); }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const UniformScaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return ei_isApprox(m_factor, other.factor(), prec); }
+
+};
+
+/** Concatenates a linear transformation matrix and a uniform scaling */
+// NOTE this operator is defiend in MatrixBase and not as a friend function
+// of UniformScaling to fix an internal crash of Intel's ICC
+template<typename Derived> const typename MatrixBase<Derived>::ScalarMultipleReturnType
+MatrixBase<Derived>::operator*(const UniformScaling<Scalar>& s) const
+{ return derived() * s.factor(); }
+
+/** Constructs a uniform scaling from scale factor \a s */
+static inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+static inline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+template<typename RealScalar>
+static inline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)
+{ return UniformScaling<std::complex<RealScalar> >(s); }
+
+/** Constructs a 2D axis aligned scaling */
+template<typename Scalar>
+static inline DiagonalMatrix<Scalar,2> Scaling(Scalar sx, Scalar sy)
+{ return DiagonalMatrix<Scalar,2>(sx, sy); }
+/** Constructs a 3D axis aligned scaling */
+template<typename Scalar>
+static inline DiagonalMatrix<Scalar,3> Scaling(Scalar sx, Scalar sy, Scalar sz)
+{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
+
+/** Constructs an axis aligned scaling expression from vector expression \a coeffs
+  * This is an alias for coeffs.asDiagonal()
+  */
+template<typename Derived>
+static inline const DiagonalMatrixWrapper<Derived> Scaling(const MatrixBase<Derived>& coeffs)
+{ return coeffs.asDiagonal(); }
+
+/** \addtogroup Geometry_Module */
+//@{
+/** \deprecated */
+typedef DiagonalMatrix<float, 2> AlignedScaling2f;
+/** \deprecated */
+typedef DiagonalMatrix<double,2> AlignedScaling2d;
+/** \deprecated */
+typedef DiagonalMatrix<float, 3> AlignedScaling3f;
+/** \deprecated */
+typedef DiagonalMatrix<double,3> AlignedScaling3d;
+//@}
+
+#endif // EIGEN_SCALING_H