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COSC-4P80-Assignment-2
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silly files

dev
Brett 2024-10-31 17:12:01 -04:00
parent 1936372611
commit dc258130d4
1789 changed files with 137 additions and 394665 deletions
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4
CMakeLists.txt
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@ -1,5 +1,5 @@
cmake_minimum_required(VERSION 3.25) cmake_minimum_required(VERSION 3.25)
project(COSC-4P80-Assignment-2 VERSION 0.1.1) project(COSC-4P80-Assignment-2 VERSION 0.1.2)
option(ENABLE_ADDRSAN "Enable the address sanitizer" OFF) option(ENABLE_ADDRSAN "Enable the address sanitizer" OFF)
option(ENABLE_UBSAN "Enable the ub sanitizer" OFF) option(ENABLE_UBSAN "Enable the ub sanitizer" OFF)
@ -19,7 +19,7 @@ if (ENABLE_GRAPHICS)
set(EXTRA_SOURCES lib/implot/implot.cpp lib/implot/implot_demo.cpp lib/implot/implot_items.cpp) set(EXTRA_SOURCES lib/implot/implot.cpp lib/implot/implot_demo.cpp lib/implot/implot_items.cpp)
include_directories(lib/implot) include_directories(lib/implot)
else () else ()
add_subdirectory(lib/blt) add_subdirectory(lib/blt-graphics/libraries/BLT)
endif () endif ()
#add_subdirectory(lib/eigen-3.4.0) #add_subdirectory(lib/eigen-3.4.0)

2
include/assign2/common.h
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@ -34,7 +34,7 @@ namespace assign2
{ {
using Scalar = float; using Scalar = float;
// const inline Scalar learn_rate = 0.001; // const inline Scalar learn_rate = 0.001;
inline Scalar learn_rate = 0.001; inline Scalar learn_rate = 0.1;
template<typename T> template<typename T>
decltype(std::cout)& print_vec(const std::vector<T>& vec) decltype(std::cout)& print_vec(const std::vector<T>& vec)

46
include/assign2/file.h
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@ -29,6 +29,7 @@ namespace assign2
std::vector<Scalar> bins; std::vector<Scalar> bins;
[[nodiscard]] data_t normalize() const; [[nodiscard]] data_t normalize() const;
[[nodiscard]] data_t with_padding(blt::size_t desired_size, Scalar padding_value = 0) const; [[nodiscard]] data_t with_padding(blt::size_t desired_size, Scalar padding_value = 0) const;
}; };
@ -38,9 +39,11 @@ namespace assign2
std::vector<data_t> data_points; std::vector<data_t> data_points;
[[nodiscard]] data_file_t normalize() const; [[nodiscard]] data_file_t normalize() const;
[[nodiscard]] data_file_t with_padding(blt::size_t desired_size, Scalar padding_value = 0) const; [[nodiscard]] data_file_t with_padding(blt::size_t desired_size, Scalar padding_value = 0) const;
data_file_t& operator+=(const data_file_t& o); data_file_t& operator+=(const data_file_t& o);
data_file_t friend operator+(const data_file_t& a, const data_file_t& b); data_file_t friend operator+(const data_file_t& a, const data_file_t& b);
static std::vector<data_file_t> load_data_files_from_path(std::string_view path); static std::vector<data_file_t> load_data_files_from_path(std::string_view path);
@ -51,6 +54,49 @@ namespace assign2
static std::vector<data_file_t> load_data_files(const std::vector<std::string>& files); static std::vector<data_file_t> load_data_files(const std::vector<std::string>& files);
}; };
struct partitioned_dataset_t
{
public:
explicit partitioned_dataset_t(std::vector<data_file_t> groups):
groups(std::move(groups)), bins(this->groups.begin()->data_points.begin()->bins.size())
{}
[[nodiscard]] const std::vector<data_file_t>& getGroups() const
{
return groups;
}
[[nodiscard]] blt::size_t bin_size() const
{
return bins;
}
private:
std::vector<data_file_t> groups;
blt::size_t bins;
};
struct dataset_partitioner
{
public:
explicit dataset_partitioner(const data_file_t& file)
{
with(file);
}
dataset_partitioner& with(const data_file_t& data)
{
BLT_ASSERT(data.data_points.begin()->bins.size() == files.begin()->data_points.begin()->bins.size());
files.push_back(data);
return *this;
}
[[nodiscard]] partitioned_dataset_t partition(blt::size_t groups) const;
private:
std::vector<data_file_t> files;
};
void save_as_csv(const std::string& file, const std::vector<std::pair<std::string, std::vector<Scalar>>>& data); void save_as_csv(const std::string& file, const std::vector<std::pair<std::string, std::vector<Scalar>>>& data);
} }

1
lib/blt

@ -1 +0,0 @@
Subproject commit e81f590f5e4f8c79ec99307fcf7d7cbbfcc83217

38
lib/eigen-3.4.0/.gitignore vendored
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@ -1,38 +0,0 @@
qrc_*cxx
*.orig
*.pyc
*.diff
diff
*.save
save
*.old
*.gmo
*.qm
core
core.*
*.bak
*~
*build*
*.moc.*
*.moc
ui_*
CMakeCache.txt
tags
.*.swp
activity.png
*.out
*.php*
*.log
*.orig
*.rej
log
patch
*.patch
a
a.*
lapack/testing
lapack/reference
.*project
.settings
Makefile
!ci/build.gitlab-ci.yml

23
lib/eigen-3.4.0/.gitlab-ci.yml
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@ -1,23 +0,0 @@
# This file is part of Eigen, a lightweight C++ template library
# for linear algebra.
#
# Copyright (C) 2020 Arm Ltd. and Contributors
#
# This Source Code Form is subject to the terms of the Mozilla
# Public License v. 2.0. If a copy of the MPL was not distributed
# with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
stages:
- buildsmoketests
- smoketests
- build
- test
variables:
BUILDDIR: builddir
EIGEN_CI_CMAKE_GENEATOR: "Ninja"
include:
- "/ci/smoketests.gitlab-ci.yml"
- "/ci/build.gitlab-ci.yml"
- "/ci/test.gitlab-ci.yml"

69
lib/eigen-3.4.0/.gitlab/issue_templates/Bug Report.md
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@ -1,69 +0,0 @@
<!--
Please read this!
Before opening a new issue, make sure to search for keywords in the issues
filtered by "bug::confirmed" or "bug::unconfirmed" and "bugzilla" label:
- https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bug%3A%3Aconfirmed
- https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bug%3A%3Aunconfirmed
- https://gitlab.com/libeigen/eigen/-/issues?scope=all&utf8=%E2%9C%93&state=opened&label_name[]=bugzilla
and verify the issue you're about to submit isn't a duplicate. -->
### Summary
<!-- Summarize the bug encountered concisely. -->
### Environment
<!-- Please provide your development environment here -->
- **Operating System** : Windows/Linux
- **Architecture** : x64/Arm64/PowerPC ...
- **Eigen Version** : 3.3.9
- **Compiler Version** : Gcc7.0
- **Compile Flags** : -O3 -march=native
- **Vector Extension** : SSE/AVX/NEON ...
### Minimal Example
<!-- If possible, please create a minimal example here that exhibits the problematic behavior.
You can also link to [godbolt](https://godbolt.org). But please note that you need to click
the "Share" button in the top right-hand corner of the godbolt page where you reproduce the sample
code to get the share link instead of in your browser address bar.
You can read [the guidelines on stackoverflow](https://stackoverflow.com/help/minimal-reproducible-example)
on how to create a good minimal example. -->
```cpp
//show your code here
```
### Steps to reproduce
<!-- Describe how one can reproduce the issue - this is very important. Please use an ordered list. -->
1. first step
2. second step
3. ...
### What is the current *bug* behavior?
<!-- Describe what actually happens. -->
### What is the expected *correct* behavior?
<!-- Describe what you should see instead. -->
### Relevant logs
<!-- Add relevant code snippets or program output within blocks marked by " ``` " -->
<!-- OPTIONAL: remove this section if you are not reporting a compilation warning issue.-->
### Warning Messages
<!-- Show us the warning messages you got! -->
<!-- OPTIONAL: remove this section if you are not reporting a performance issue. -->
### Benchmark scripts and results
<!-- Please share any benchmark scripts - either standalone, or using [Google Benchmark](https://github.com/google/benchmark). -->
### Anything else that might help
<!-- It will be better to provide us more information to help narrow down the cause.
Including but not limited to the following:
- lines of code that might help us diagnose the problem.
- potential ways to address the issue.
- last known working/first broken version (release number or commit hash). -->
- [ ] Have a plan to fix this issue.

7
lib/eigen-3.4.0/.gitlab/issue_templates/Feature Request.md
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@ -1,7 +0,0 @@
### Describe the feature you would like to be implemented.
### Would such a feature be useful for other users? Why?
### Any hints on how to implement the requested feature?
### Additional resources

26
lib/eigen-3.4.0/.gitlab/merge_request_templates/Merge Request Template.md
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@ -1,26 +0,0 @@
<!--
Thanks for contributing a merge request! Please name and fully describe your MR as you would for a commit message.
If the MR fixes an issue, please include "Fixes #issue" in the commit message and the MR description.
In addition, we recommend that first-time contributors read our [contribution guidelines](https://eigen.tuxfamily.org/index.php?title=Contributing_to_Eigen) and [git page](https://eigen.tuxfamily.org/index.php?title=Git), which will help you submit a more standardized MR.
Before submitting the MR, you also need to complete the following checks:
- Make one PR per feature/bugfix (don't mix multiple changes into one PR). Avoid committing unrelated changes.
- Rebase before committing
- For code changes, run the test suite (at least the tests that are likely affected by the change).
See our [test guidelines](https://eigen.tuxfamily.org/index.php?title=Tests).
- If possible, add a test (both for bug-fixes as well as new features)
- Make sure new features are documented
Note that we are a team of volunteers; we appreciate your patience during the review process.
Again, thanks for contributing! -->
### Reference issue
<!-- You can link to a specific issue using the gitlab syntax #<issue number> -->
### What does this implement/fix?
<!--Please explain your changes.-->
### Additional information
<!--Any additional information you think is important.-->

11
lib/eigen-3.4.0/.hgeol
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@ -1,11 +0,0 @@
[patterns]
*.sh = LF
*.MINPACK = CRLF
scripts/*.in = LF
debug/msvc/*.dat = CRLF
debug/msvc/*.natvis = CRLF
unsupported/test/mpreal/*.* = CRLF
** = native
[repository]
native = LF

653
lib/eigen-3.4.0/CMakeLists.txt
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@ -1,653 +0,0 @@
# cmake_minimum_require must be the first command of the file
cmake_minimum_required(VERSION 3.5.0)
project(Eigen3)
# guard against in-source builds
if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR})
message(FATAL_ERROR "In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. ")
endif()
# Alias Eigen_*_DIR to Eigen3_*_DIR:
set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
# guard against bad build-type strings
if (NOT CMAKE_BUILD_TYPE)
set(CMAKE_BUILD_TYPE "Release")
endif()
#############################################################################
# retrieve version information #
#############################################################################
# automatically parse the version number
file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header)
string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})
# if we are not in a git clone
if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.git)
# if the git program is absent or this will leave the EIGEN_GIT_REVNUM string empty,
# but won't stop CMake.
execute_process(COMMAND git ls-remote --refs -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT)
endif()
# extract the git rev number from the git output...
if(EIGEN_GIT_OUTPUT)
string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}")
set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}")
endif()
#...and show it next to the version number
if(EIGEN_GIT_REVNUM)
set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (git rev ${EIGEN_GIT_REVNUM})")
else()
set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
endif()
include(CheckCXXCompilerFlag)
include(GNUInstallDirs)
include(CMakeDependentOption)
set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
option(EIGEN_TEST_CXX11 "Enable testing with C++11 and C++11 features (e.g. Tensor module)." OFF)
macro(ei_add_cxx_compiler_flag FLAG)
string(REGEX REPLACE "-" "" SFLAG1 ${FLAG})
string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1})
check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
if(COMPILER_SUPPORT_${SFLAG})
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
endif()
endmacro()
check_cxx_compiler_flag("-std=c++11" EIGEN_COMPILER_SUPPORT_CPP11)
if(EIGEN_TEST_CXX11)
set(CMAKE_CXX_STANDARD 11)
set(CMAKE_CXX_EXTENSIONS OFF)
if(EIGEN_COMPILER_SUPPORT_CPP11)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
endif()
else()
#set(CMAKE_CXX_STANDARD 03)
#set(CMAKE_CXX_EXTENSIONS OFF)
ei_add_cxx_compiler_flag("-std=c++03")
endif()
# Determine if we should build shared libraries on this platform.
get_cmake_property(EIGEN_BUILD_SHARED_LIBS TARGET_SUPPORTS_SHARED_LIBS)
#############################################################################
# find how to link to the standard libraries #
#############################################################################
find_package(StandardMathLibrary)
set(EIGEN_TEST_CUSTOM_LINKER_FLAGS "" CACHE STRING "Additional linker flags when linking unit tests.")
set(EIGEN_TEST_CUSTOM_CXX_FLAGS "" CACHE STRING "Additional compiler flags when compiling unit tests.")
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
if(NOT STANDARD_MATH_LIBRARY_FOUND)
message(FATAL_ERROR
"Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
else()
if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}")
else()
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}")
endif()
endif()
if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}")
else()
message(STATUS "Standard libraries to link to explicitly: none")
endif()
option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
# Disable pkgconfig only for native Windows builds
if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)
option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON)
endif()
set(CMAKE_INCLUDE_CURRENT_DIR OFF)
option(EIGEN_SPLIT_LARGE_TESTS "Split large tests into smaller executables" ON)
option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF)
if(EIGEN_DEFAULT_TO_ROW_MAJOR)
add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR")
endif()
set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320")
if(NOT MSVC)
# We assume that other compilers are partly compatible with GNUCC
# clang outputs some warnings for unknown flags that are not caught by check_cxx_compiler_flag
# adding -Werror turns such warnings into errors
check_cxx_compiler_flag("-Werror" COMPILER_SUPPORT_WERROR)
if(COMPILER_SUPPORT_WERROR)
set(CMAKE_REQUIRED_FLAGS "-Werror")
endif()
ei_add_cxx_compiler_flag("-pedantic")
ei_add_cxx_compiler_flag("-Wall")
ei_add_cxx_compiler_flag("-Wextra")
#ei_add_cxx_compiler_flag("-Weverything") # clang
ei_add_cxx_compiler_flag("-Wundef")
ei_add_cxx_compiler_flag("-Wcast-align")
ei_add_cxx_compiler_flag("-Wchar-subscripts")
ei_add_cxx_compiler_flag("-Wnon-virtual-dtor")
ei_add_cxx_compiler_flag("-Wunused-local-typedefs")
ei_add_cxx_compiler_flag("-Wpointer-arith")
ei_add_cxx_compiler_flag("-Wwrite-strings")
ei_add_cxx_compiler_flag("-Wformat-security")
ei_add_cxx_compiler_flag("-Wshorten-64-to-32")
ei_add_cxx_compiler_flag("-Wlogical-op")
ei_add_cxx_compiler_flag("-Wenum-conversion")
ei_add_cxx_compiler_flag("-Wc++11-extensions")
ei_add_cxx_compiler_flag("-Wdouble-promotion")
# ei_add_cxx_compiler_flag("-Wconversion")
ei_add_cxx_compiler_flag("-Wshadow")
ei_add_cxx_compiler_flag("-Wno-psabi")
ei_add_cxx_compiler_flag("-Wno-variadic-macros")
ei_add_cxx_compiler_flag("-Wno-long-long")
ei_add_cxx_compiler_flag("-fno-check-new")
ei_add_cxx_compiler_flag("-fno-common")
ei_add_cxx_compiler_flag("-fstrict-aliasing")
ei_add_cxx_compiler_flag("-wd981") # disable ICC's "operands are evaluated in unspecified order" remark
ei_add_cxx_compiler_flag("-wd2304") # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
# The -ansi flag must be added last, otherwise it is also used as a linker flag by check_cxx_compiler_flag making it fails
# Moreover we should not set both -strict-ansi and -ansi
check_cxx_compiler_flag("-strict-ansi" COMPILER_SUPPORT_STRICTANSI)
ei_add_cxx_compiler_flag("-Qunused-arguments") # disable clang warning: argument unused during compilation: '-ansi'
if(COMPILER_SUPPORT_STRICTANSI)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -strict-ansi")
else()
ei_add_cxx_compiler_flag("-ansi")
endif()
if(ANDROID_NDK)
ei_add_cxx_compiler_flag("-pie")
ei_add_cxx_compiler_flag("-fPIE")
endif()
set(CMAKE_REQUIRED_FLAGS "")
option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
if(EIGEN_TEST_SSE2)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2")
message(STATUS "Enabling SSE2 in tests/examples")
endif()
option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF)
if(EIGEN_TEST_SSE3)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3")
message(STATUS "Enabling SSE3 in tests/examples")
endif()
option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF)
if(EIGEN_TEST_SSSE3)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3")
message(STATUS "Enabling SSSE3 in tests/examples")
endif()
option(EIGEN_TEST_SSE4_1 "Enable/Disable SSE4.1 in tests/examples" OFF)
if(EIGEN_TEST_SSE4_1)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.1")
message(STATUS "Enabling SSE4.1 in tests/examples")
endif()
option(EIGEN_TEST_SSE4_2 "Enable/Disable SSE4.2 in tests/examples" OFF)
if(EIGEN_TEST_SSE4_2)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.2")
message(STATUS "Enabling SSE4.2 in tests/examples")
endif()
option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
if(EIGEN_TEST_AVX)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx")
message(STATUS "Enabling AVX in tests/examples")
endif()
option(EIGEN_TEST_FMA "Enable/Disable FMA in tests/examples" OFF)
if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfma")
message(STATUS "Enabling FMA in tests/examples")
endif()
option(EIGEN_TEST_AVX2 "Enable/Disable AVX2 in tests/examples" OFF)
if(EIGEN_TEST_AVX2)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx2 -mfma")
message(STATUS "Enabling AVX2 in tests/examples")
endif()
option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
if(EIGEN_TEST_AVX512)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma")
if (NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fabi-version=6")
endif()
message(STATUS "Enabling AVX512 in tests/examples")
endif()
option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF)
if(EIGEN_TEST_AVX512DQ)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512dq")
if (NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fabi-version=6")
endif()
message(STATUS "Enabling AVX512DQ in tests/examples")
endif()
option(EIGEN_TEST_F16C "Enable/Disable F16C in tests/examples" OFF)
if(EIGEN_TEST_F16C)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mf16c")
message(STATUS "Enabling F16C in tests/examples")
endif()
option(EIGEN_TEST_ALTIVEC "Enable/Disable AltiVec in tests/examples" OFF)
if(EIGEN_TEST_ALTIVEC)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec")
message(STATUS "Enabling AltiVec in tests/examples")
endif()
option(EIGEN_TEST_VSX "Enable/Disable VSX in tests/examples" OFF)
if(EIGEN_TEST_VSX)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m64 -mvsx")
message(STATUS "Enabling VSX in tests/examples")
endif()
option(EIGEN_TEST_MSA "Enable/Disable MSA in tests/examples" OFF)
if(EIGEN_TEST_MSA)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mmsa")
message(STATUS "Enabling MSA in tests/examples")
endif()
option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
if(EIGEN_TEST_NEON)
if(EIGEN_TEST_FMA)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon-vfpv4")
else()
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon")
endif()
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=hard")
message(STATUS "Enabling NEON in tests/examples")
endif()
option(EIGEN_TEST_NEON64 "Enable/Disable Neon in tests/examples" OFF)
if(EIGEN_TEST_NEON64)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
message(STATUS "Enabling NEON in tests/examples")
endif()
option(EIGEN_TEST_Z13 "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
if(EIGEN_TEST_Z13)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector")
message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
endif()
option(EIGEN_TEST_Z14 "Enable/Disable S390X(zEC14) ZVECTOR in tests/examples" OFF)
if(EIGEN_TEST_Z14)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z14 -mzvector")
message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
endif()
check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP)
if(COMPILER_SUPPORT_OPENMP)
option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
if(EIGEN_TEST_OPENMP)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
message(STATUS "Enabling OpenMP in tests/examples")
endif()
endif()
else()
# C4127 - conditional expression is constant
# C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively)
# We can disable this warning in the unit tests since it is clear that it occurs
# because we are oftentimes returning objects that have a destructor or may
# throw exceptions - in particular in the unit tests we are throwing extra many
# exceptions to cover indexing errors.
# C4505 - unreferenced local function has been removed (impossible to deactivate selectively)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714")
# replace all /Wx by /W4
string(REGEX REPLACE "/W[0-9]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
check_cxx_compiler_flag("/openmp" COMPILER_SUPPORT_OPENMP)
if(COMPILER_SUPPORT_OPENMP)
option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
if(EIGEN_TEST_OPENMP)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /openmp")
message(STATUS "Enabling OpenMP in tests/examples")
endif()
endif()
option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
if(EIGEN_TEST_SSE2)
if(NOT CMAKE_CL_64)
# arch is not supported on 64 bit systems, SSE is enabled automatically.
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
endif()
message(STATUS "Enabling SSE2 in tests/examples")
endif()
option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
if(EIGEN_TEST_AVX)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX")
message(STATUS "Enabling AVX in tests/examples")
endif()
option(EIGEN_TEST_FMA "Enable/Disable FMA/AVX2 in tests/examples" OFF)
if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX2")
message(STATUS "Enabling FMA/AVX2 in tests/examples")
endif()
endif()
option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
option(EIGEN_TEST_X87 "Force using X87 instructions. Implies no vectorization." OFF)
option(EIGEN_TEST_32BIT "Force generating 32bit code." OFF)
if(EIGEN_TEST_X87)
set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON)
if(CMAKE_COMPILER_IS_GNUCXX)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpmath=387")
message(STATUS "Forcing use of x87 instructions in tests/examples")
else()
message(STATUS "EIGEN_TEST_X87 ignored on your compiler")
endif()
endif()
if(EIGEN_TEST_32BIT)
if(CMAKE_COMPILER_IS_GNUCXX)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m32")
message(STATUS "Forcing generation of 32-bit code in tests/examples")
else()
message(STATUS "EIGEN_TEST_32BIT ignored on your compiler")
endif()
endif()
if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
add_definitions(-DEIGEN_DONT_VECTORIZE=1)
message(STATUS "Disabling vectorization in tests/examples")
endif()
option(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT "Disable explicit alignment (hence vectorization) in tests/examples" OFF)
if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)
add_definitions(-DEIGEN_DONT_ALIGN=1)
message(STATUS "Disabling alignment in tests/examples")
endif()
option(EIGEN_TEST_NO_EXCEPTIONS "Disables C++ exceptions" OFF)
if(EIGEN_TEST_NO_EXCEPTIONS)
ei_add_cxx_compiler_flag("-fno-exceptions")
message(STATUS "Disabling exceptions in tests/examples")
endif()
set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture level to target when compiling CUDA code")
include_directories(${CMAKE_CURRENT_SOURCE_DIR})
# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR
if(EIGEN_INCLUDE_INSTALL_DIR)
message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.")
endif()
if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)
set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}
CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed")
else()
set(INCLUDE_INSTALL_DIR
"${CMAKE_INSTALL_INCLUDEDIR}/eigen3"
CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed"
)
endif()
set(CMAKEPACKAGE_INSTALL_DIR
"${CMAKE_INSTALL_DATADIR}/eigen3/cmake"
CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen3Config.cmake is installed"
)
set(PKGCONFIG_INSTALL_DIR
"${CMAKE_INSTALL_DATADIR}/pkgconfig"
CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where eigen3.pc is installed"
)
foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR)
# If an absolute path is specified, make it relative to "{CMAKE_INSTALL_PREFIX}".
if(IS_ABSOLUTE "${${var}}")
file(RELATIVE_PATH "${var}" "${CMAKE_INSTALL_PREFIX}" "${${var}}")
endif()
endforeach()
# similar to set_target_properties but append the property instead of overwriting it
macro(ei_add_target_property target prop value)
get_target_property(previous ${target} ${prop})
# if the property wasn't previously set, ${previous} is now "previous-NOTFOUND" which cmake allows catching with plain if()
if(NOT previous)
set(previous "")
endif()
set_target_properties(${target} PROPERTIES ${prop} "${previous} ${value}")
endmacro()
install(FILES
signature_of_eigen3_matrix_library
DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel
)
if(EIGEN_BUILD_PKGCONFIG)
configure_file(eigen3.pc.in eigen3.pc @ONLY)
install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
DESTINATION ${PKGCONFIG_INSTALL_DIR}
)
endif()
install(DIRECTORY Eigen DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel)
option(EIGEN_BUILD_DOC "Enable creation of Eigen documentation" ON)
if(EIGEN_BUILD_DOC)
add_subdirectory(doc EXCLUDE_FROM_ALL)
endif()
option(BUILD_TESTING "Enable creation of Eigen tests." ON)
if(BUILD_TESTING)
include(EigenConfigureTesting)
if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
else()
add_subdirectory(test EXCLUDE_FROM_ALL)
endif()
add_subdirectory(failtest)
endif()
if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
add_subdirectory(blas)
add_subdirectory(lapack)
else()
add_subdirectory(blas EXCLUDE_FROM_ALL)
add_subdirectory(lapack EXCLUDE_FROM_ALL)
endif()
# add SYCL
option(EIGEN_TEST_SYCL "Add Sycl support." OFF)
option(EIGEN_SYCL_TRISYCL "Use the triSYCL Sycl implementation (ComputeCPP by default)." OFF)
if(EIGEN_TEST_SYCL)
set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}")
find_package(Threads REQUIRED)
if(EIGEN_SYCL_TRISYCL)
message(STATUS "Using triSYCL")
include(FindTriSYCL)
else()
message(STATUS "Using ComputeCPP SYCL")
include(FindComputeCpp)
set(COMPUTECPP_DRIVER_DEFAULT_VALUE OFF)
if (NOT MSVC)
set(COMPUTECPP_DRIVER_DEFAULT_VALUE ON)
endif()
option(COMPUTECPP_USE_COMPILER_DRIVER
"Use ComputeCpp driver instead of a 2 steps compilation"
${COMPUTECPP_DRIVER_DEFAULT_VALUE}
)
endif(EIGEN_SYCL_TRISYCL)
option(EIGEN_DONT_VECTORIZE_SYCL "Don't use vectorisation in the SYCL tests." OFF)
if(EIGEN_DONT_VECTORIZE_SYCL)
message(STATUS "Disabling SYCL vectorization in tests/examples")
# When disabling SYCL vectorization, also disable Eigen default vectorization
add_definitions(-DEIGEN_DONT_VECTORIZE=1)
add_definitions(-DEIGEN_DONT_VECTORIZE_SYCL=1)
endif()
endif()
add_subdirectory(unsupported)
add_subdirectory(demos EXCLUDE_FROM_ALL)
# must be after test and unsupported, for configuring buildtests.in
add_subdirectory(scripts EXCLUDE_FROM_ALL)
# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target "make btl"?
if(EIGEN_BUILD_BTL)
add_subdirectory(bench/btl EXCLUDE_FROM_ALL)
endif()
if(NOT WIN32)
add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)
endif()
configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)
if(BUILD_TESTING)
ei_testing_print_summary()
endif()
message(STATUS "")
message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
message(STATUS "")
string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower)
if(cmake_generator_tolower MATCHES "makefile")
message(STATUS "Available targets (use: make TARGET):")
else()
message(STATUS "Available targets (use: cmake --build . --target TARGET):")
endif()
message(STATUS "---------+--------------------------------------------------------------")
message(STATUS "Target | Description")
message(STATUS "---------+--------------------------------------------------------------")
message(STATUS "install | Install Eigen. Headers will be installed to:")
message(STATUS " | <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
message(STATUS " | Using the following values:")
message(STATUS " | CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
message(STATUS " | INCLUDE_INSTALL_DIR: ${INCLUDE_INSTALL_DIR}")
message(STATUS " | Change the install location of Eigen headers using:")
message(STATUS " | cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
message(STATUS " | Or:")
message(STATUS " | cmake . -DINCLUDE_INSTALL_DIR=yourdir")
message(STATUS "doc | Generate the API documentation, requires Doxygen & LaTeX")
if(BUILD_TESTING)
message(STATUS "check | Build and run the unit-tests. Read this page:")
message(STATUS " | http://eigen.tuxfamily.org/index.php?title=Tests")
endif()
message(STATUS "blas | Build BLAS library (not the same thing as Eigen)")
message(STATUS "uninstall| Remove files installed by the install target")
message(STATUS "---------+--------------------------------------------------------------")
message(STATUS "")
set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )
set ( EIGEN_VERSION_MAJOR ${EIGEN_WORLD_VERSION} )
set ( EIGEN_VERSION_MINOR ${EIGEN_MAJOR_VERSION} )
set ( EIGEN_VERSION_PATCH ${EIGEN_MINOR_VERSION} )
set ( EIGEN_DEFINITIONS "")
set ( EIGEN_INCLUDE_DIR "${CMAKE_INSTALL_PREFIX}/${INCLUDE_INSTALL_DIR}" )
set ( EIGEN_ROOT_DIR ${CMAKE_INSTALL_PREFIX} )
include (CMakePackageConfigHelpers)
# Imported target support
add_library (eigen INTERFACE)
add_library (Eigen3::Eigen ALIAS eigen)
target_compile_definitions (eigen INTERFACE ${EIGEN_DEFINITIONS})
target_include_directories (eigen INTERFACE
$<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
$<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
)
# Export as title case Eigen
set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
install (TARGETS eigen EXPORT Eigen3Targets)
configure_package_config_file (
${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR
INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
)
# Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does
# not depend on architecture specific settings or libraries. More
# specifically, an Eigen3Config.cmake generated from a 64 bit target can be
# used for 32 bit targets as well (and vice versa).
set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})
unset (CMAKE_SIZEOF_VOID_P)
write_basic_package_version_file (Eigen3ConfigVersion.cmake
VERSION ${EIGEN_VERSION_NUMBER}
COMPATIBILITY SameMajorVersion)
set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})
# The Eigen target will be located in the Eigen3 namespace. Other CMake
# targets can refer to it using Eigen3::Eigen.
export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)
# Export Eigen3 package to CMake registry such that it can be easily found by
# CMake even if it has not been installed to a standard directory.
export (PACKAGE Eigen3)
install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
install ( FILES ${CMAKE_CURRENT_SOURCE_DIR}/cmake/UseEigen3.cmake
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake
DESTINATION ${CMAKEPACKAGE_INSTALL_DIR} )
# Add uninstall target
add_custom_target ( uninstall
COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
if (EIGEN_SPLIT_TESTSUITE)
ei_split_testsuite("${EIGEN_SPLIT_TESTSUITE}")
endif()

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26
lib/eigen-3.4.0/COPYING.BSD
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@ -1,26 +0,0 @@
/*
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*/

674
lib/eigen-3.4.0/COPYING.GPL
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@ -1,674 +0,0 @@
GNU GENERAL PUBLIC LICENSE
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@ -1,502 +0,0 @@
GNU LESSER GENERAL PUBLIC LICENSE
Version 2.1, February 1999
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Ty Coon, President of Vice
That's all there is to it!

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Minpack Copyright Notice (1999) University of Chicago. All rights reserved
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the
following conditions are met:
1. Redistributions of source code must retain the above
copyright notice, this list of conditions and the following
disclaimer.
2. Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials
provided with the distribution.
3. The end-user documentation included with the
redistribution, if any, must include the following
acknowledgment:
"This product includes software developed by the
University of Chicago, as Operator of Argonne National
Laboratory.
Alternately, this acknowledgment may appear in the software
itself, if and wherever such third-party acknowledgments
normally appear.
4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
BE CORRECTED.
5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
POSSIBILITY OF SUCH LOSS OR DAMAGES.

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Mozilla Public License Version 2.0
==================================
1. Definitions
--------------
1.1. "Contributor"
means each individual or legal entity that creates, contributes to
the creation of, or owns Covered Software.
1.2. "Contributor Version"
means the combination of the Contributions of others (if any) used
by a Contributor and that particular Contributor's Contribution.
1.3. "Contribution"
means Covered Software of a particular Contributor.
1.4. "Covered Software"
means Source Code Form to which the initial Contributor has attached
the notice in Exhibit A, the Executable Form of such Source Code
Form, and Modifications of such Source Code Form, in each case
including portions thereof.
1.5. "Incompatible With Secondary Licenses"
means
(a) that the initial Contributor has attached the notice described
in Exhibit B to the Covered Software; or
(b) that the Covered Software was made available under the terms of
version 1.1 or earlier of the License, but not also under the
terms of a Secondary License.
1.6. "Executable Form"
means any form of the work other than Source Code Form.
1.7. "Larger Work"
means a work that combines Covered Software with other material, in
a separate file or files, that is not Covered Software.
1.8. "License"
means this document.
1.9. "Licensable"
means having the right to grant, to the maximum extent possible,
whether at the time of the initial grant or subsequently, any and
all of the rights conveyed by this License.
1.10. "Modifications"
means any of the following:
(a) any file in Source Code Form that results from an addition to,
deletion from, or modification of the contents of Covered
Software; or
(b) any new file in Source Code Form that contains any Covered
Software.
1.11. "Patent Claims" of a Contributor
means any patent claim(s), including without limitation, method,
process, and apparatus claims, in any patent Licensable by such
Contributor that would be infringed, but for the grant of the
License, by the making, using, selling, offering for sale, having
made, import, or transfer of either its Contributions or its
Contributor Version.
1.12. "Secondary License"
means either the GNU General Public License, Version 2.0, the GNU
Lesser General Public License, Version 2.1, the GNU Affero General
Public License, Version 3.0, or any later versions of those
licenses.
1.13. "Source Code Form"
means the form of the work preferred for making modifications.
1.14. "You" (or "Your")
means an individual or a legal entity exercising rights under this
License. For legal entities, "You" includes any entity that
controls, is controlled by, or is under common control with You. For
purposes of this definition, "control" means (a) the power, direct
or indirect, to cause the direction or management of such entity,
whether by contract or otherwise, or (b) ownership of more than
fifty percent (50%) of the outstanding shares or beneficial
ownership of such entity.
2. License Grants and Conditions
--------------------------------
2.1. Grants
Each Contributor hereby grants You a world-wide, royalty-free,
non-exclusive license:
(a) under intellectual property rights (other than patent or trademark)
Licensable by such Contributor to use, reproduce, make available,
modify, display, perform, distribute, and otherwise exploit its
Contributions, either on an unmodified basis, with Modifications, or
as part of a Larger Work; and
(b) under Patent Claims of such Contributor to make, use, sell, offer
for sale, have made, import, and otherwise transfer either its
Contributions or its Contributor Version.
2.2. Effective Date
The licenses granted in Section 2.1 with respect to any Contribution
become effective for each Contribution on the date the Contributor first
distributes such Contribution.
2.3. Limitations on Grant Scope
The licenses granted in this Section 2 are the only rights granted under
this License. No additional rights or licenses will be implied from the
distribution or licensing of Covered Software under this License.
Notwithstanding Section 2.1(b) above, no patent license is granted by a
Contributor:
(a) for any code that a Contributor has removed from Covered Software;
or
(b) for infringements caused by: (i) Your and any other third party's
modifications of Covered Software, or (ii) the combination of its
Contributions with other software (except as part of its Contributor
Version); or
(c) under Patent Claims infringed by Covered Software in the absence of
its Contributions.
This License does not grant any rights in the trademarks, service marks,
or logos of any Contributor (except as may be necessary to comply with
the notice requirements in Section 3.4).
2.4. Subsequent Licenses
No Contributor makes additional grants as a result of Your choice to
distribute the Covered Software under a subsequent version of this
License (see Section 10.2) or under the terms of a Secondary License (if
permitted under the terms of Section 3.3).
2.5. Representation
Each Contributor represents that the Contributor believes its
Contributions are its original creation(s) or it has sufficient rights
to grant the rights to its Contributions conveyed by this License.
2.6. Fair Use
This License is not intended to limit any rights You have under
applicable copyright doctrines of fair use, fair dealing, or other
equivalents.
2.7. Conditions
Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted
in Section 2.1.
3. Responsibilities
-------------------
3.1. Distribution of Source Form
All distribution of Covered Software in Source Code Form, including any
Modifications that You create or to which You contribute, must be under
the terms of this License. You must inform recipients that the Source
Code Form of the Covered Software is governed by the terms of this
License, and how they can obtain a copy of this License. You may not
attempt to alter or restrict the recipients' rights in the Source Code
Form.
3.2. Distribution of Executable Form
If You distribute Covered Software in Executable Form then:
(a) such Covered Software must also be made available in Source Code
Form, as described in Section 3.1, and You must inform recipients of
the Executable Form how they can obtain a copy of such Source Code
Form by reasonable means in a timely manner, at a charge no more
than the cost of distribution to the recipient; and
(b) You may distribute such Executable Form under the terms of this
License, or sublicense it under different terms, provided that the
license for the Executable Form does not attempt to limit or alter
the recipients' rights in the Source Code Form under this License.
3.3. Distribution of a Larger Work
You may create and distribute a Larger Work under terms of Your choice,
provided that You also comply with the requirements of this License for
the Covered Software. If the Larger Work is a combination of Covered
Software with a work governed by one or more Secondary Licenses, and the
Covered Software is not Incompatible With Secondary Licenses, this
License permits You to additionally distribute such Covered Software
under the terms of such Secondary License(s), so that the recipient of
the Larger Work may, at their option, further distribute the Covered
Software under the terms of either this License or such Secondary
License(s).
3.4. Notices
You may not remove or alter the substance of any license notices
(including copyright notices, patent notices, disclaimers of warranty,
or limitations of liability) contained within the Source Code Form of
the Covered Software, except that You may alter any license notices to
the extent required to remedy known factual inaccuracies.
3.5. Application of Additional Terms
You may choose to offer, and to charge a fee for, warranty, support,
indemnity or liability obligations to one or more recipients of Covered
Software. However, You may do so only on Your own behalf, and not on
behalf of any Contributor. You must make it absolutely clear that any
such warranty, support, indemnity, or liability obligation is offered by
You alone, and You hereby agree to indemnify every Contributor for any
liability incurred by such Contributor as a result of warranty, support,
indemnity or liability terms You offer. You may include additional
disclaimers of warranty and limitations of liability specific to any
jurisdiction.
4. Inability to Comply Due to Statute or Regulation
---------------------------------------------------
If it is impossible for You to comply with any of the terms of this
License with respect to some or all of the Covered Software due to
statute, judicial order, or regulation then You must: (a) comply with
the terms of this License to the maximum extent possible; and (b)
describe the limitations and the code they affect. Such description must
be placed in a text file included with all distributions of the Covered
Software under this License. Except to the extent prohibited by statute
or regulation, such description must be sufficiently detailed for a
recipient of ordinary skill to be able to understand it.
5. Termination
--------------
5.1. The rights granted under this License will terminate automatically
if You fail to comply with any of its terms. However, if You become
compliant, then the rights granted under this License from a particular
Contributor are reinstated (a) provisionally, unless and until such
Contributor explicitly and finally terminates Your grants, and (b) on an
ongoing basis, if such Contributor fails to notify You of the
non-compliance by some reasonable means prior to 60 days after You have
come back into compliance. Moreover, Your grants from a particular
Contributor are reinstated on an ongoing basis if such Contributor
notifies You of the non-compliance by some reasonable means, this is the
first time You have received notice of non-compliance with this License
from such Contributor, and You become compliant prior to 30 days after
Your receipt of the notice.
5.2. If You initiate litigation against any entity by asserting a patent
infringement claim (excluding declaratory judgment actions,
counter-claims, and cross-claims) alleging that a Contributor Version
directly or indirectly infringes any patent, then the rights granted to
You by any and all Contributors for the Covered Software under Section
2.1 of this License shall terminate.
5.3. In the event of termination under Sections 5.1 or 5.2 above, all
end user license agreements (excluding distributors and resellers) which
have been validly granted by You or Your distributors under this License
prior to termination shall survive termination.
************************************************************************
* *
* 6. Disclaimer of Warranty *
* ------------------------- *
* *
* Covered Software is provided under this License on an "as is" *
* basis, without warranty of any kind, either expressed, implied, or *
* statutory, including, without limitation, warranties that the *
* Covered Software is free of defects, merchantable, fit for a *
* particular purpose or non-infringing. The entire risk as to the *
* quality and performance of the Covered Software is with You. *
* Should any Covered Software prove defective in any respect, You *
* (not any Contributor) assume the cost of any necessary servicing, *
* repair, or correction. This disclaimer of warranty constitutes an *
* essential part of this License. No use of any Covered Software is *
* authorized under this License except under this disclaimer. *
* *
************************************************************************
************************************************************************
* *
* 7. Limitation of Liability *
* -------------------------- *
* *
* Under no circumstances and under no legal theory, whether tort *
* (including negligence), contract, or otherwise, shall any *
* Contributor, or anyone who distributes Covered Software as *
* permitted above, be liable to You for any direct, indirect, *
* special, incidental, or consequential damages of any character *
* including, without limitation, damages for lost profits, loss of *
* goodwill, work stoppage, computer failure or malfunction, or any *
* and all other commercial damages or losses, even if such party *
* shall have been informed of the possibility of such damages. This *
* limitation of liability shall not apply to liability for death or *
* personal injury resulting from such party's negligence to the *
* extent applicable law prohibits such limitation. Some *
* jurisdictions do not allow the exclusion or limitation of *
* incidental or consequential damages, so this exclusion and *
* limitation may not apply to You. *
* *
************************************************************************
8. Litigation
-------------
Any litigation relating to this License may be brought only in the
courts of a jurisdiction where the defendant maintains its principal
place of business and such litigation shall be governed by laws of that
jurisdiction, without reference to its conflict-of-law provisions.
Nothing in this Section shall prevent a party's ability to bring
cross-claims or counter-claims.
9. Miscellaneous
----------------
This License represents the complete agreement concerning the subject
matter hereof. If any provision of this License is held to be
unenforceable, such provision shall be reformed only to the extent
necessary to make it enforceable. Any law or regulation which provides
that the language of a contract shall be construed against the drafter
shall not be used to construe this License against a Contributor.
10. Versions of the License
---------------------------
10.1. New Versions
Mozilla Foundation is the license steward. Except as provided in Section
10.3, no one other than the license steward has the right to modify or
publish new versions of this License. Each version will be given a
distinguishing version number.
10.2. Effect of New Versions
You may distribute the Covered Software under the terms of the version
of the License under which You originally received the Covered Software,
or under the terms of any subsequent version published by the license
steward.
10.3. Modified Versions
If you create software not governed by this License, and you want to
create a new license for such software, you may create and use a
modified version of this License if you rename the license and remove
any references to the name of the license steward (except to note that
such modified license differs from this License).
10.4. Distributing Source Code Form that is Incompatible With Secondary
Licenses
If You choose to distribute Source Code Form that is Incompatible With
Secondary Licenses under the terms of this version of the License, the
notice described in Exhibit B of this License must be attached.
Exhibit A - Source Code Form License Notice
-------------------------------------------
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
If it is not possible or desirable to put the notice in a particular
file, then You may include the notice in a location (such as a LICENSE
file in a relevant directory) where a recipient would be likely to look
for such a notice.
You may add additional accurate notices of copyright ownership.
Exhibit B - "Incompatible With Secondary Licenses" Notice
---------------------------------------------------------
This Source Code Form is "Incompatible With Secondary Licenses", as
defined by the Mozilla Public License, v. 2.0.

18
lib/eigen-3.4.0/COPYING.README
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@ -1,18 +0,0 @@
Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:
http://www.mozilla.org/MPL/2.0/
http://www.mozilla.org/MPL/2.0/FAQ.html
Some files contain third-party code under BSD or LGPL licenses, whence the other
COPYING.* files here.
All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later.
For this reason, the COPYING.LGPL file contains the LGPL 2.1 text.
If you want to guarantee that the Eigen code that you are #including is licensed
under the MPL2 and possibly more permissive licenses (like BSD), #define this
preprocessor symbol:
EIGEN_MPL2_ONLY
For example, with most compilers, you could add this to your project CXXFLAGS:
-DEIGEN_MPL2_ONLY
This will cause a compilation error to be generated if you #include any code that is
LGPL licensed.

17
lib/eigen-3.4.0/CTestConfig.cmake
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@ -1,17 +0,0 @@
## This file should be placed in the root directory of your project.
## Then modify the CMakeLists.txt file in the root directory of your
## project to incorporate the testing dashboard.
## # The following are required to uses Dart and the Cdash dashboard
## enable_testing()
## include(CTest)
set(CTEST_PROJECT_NAME "Eigen")
set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC")
set(CTEST_DROP_METHOD "http")
set(CTEST_DROP_SITE "my.cdash.org")
set(CTEST_DROP_LOCATION "/submit.php?project=Eigen")
set(CTEST_DROP_SITE_CDASH TRUE)
#set(CTEST_PROJECT_SUBPROJECTS
#Official
#Unsupported
#)

4
lib/eigen-3.4.0/CTestCustom.cmake.in
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@ -1,4 +0,0 @@
set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "2000")
set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "2000")
list(APPEND CTEST_CUSTOM_ERROR_EXCEPTION @EIGEN_CTEST_ERROR_EXCEPTION@)

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lib/eigen-3.4.0/Eigen/Cholesky
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@ -1,45 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLESKY_MODULE_H
#define EIGEN_CHOLESKY_MODULE_H
#include "Core"
#include "Jacobi"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Cholesky_Module Cholesky module
*
*
*
* This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
* Those decompositions are also accessible via the following methods:
* - MatrixBase::llt()
* - MatrixBase::ldlt()
* - SelfAdjointView::llt()
* - SelfAdjointView::ldlt()
*
* \code
* #include <Eigen/Cholesky>
* \endcode
*/
#include "src/Cholesky/LLT.h"
#include "src/Cholesky/LDLT.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/Cholesky/LLT_LAPACKE.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLESKY_MODULE_H

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lib/eigen-3.4.0/Eigen/CholmodSupport
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@ -1,48 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
#define EIGEN_CHOLMODSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <cholmod.h>
}
/** \ingroup Support_modules
* \defgroup CholmodSupport_Module CholmodSupport module
*
* This module provides an interface to the Cholmod library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
* It provides the two following main factorization classes:
* - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
* - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).
*
* For the sake of completeness, this module also propose the two following classes:
* - class CholmodSimplicialLLT
* - class CholmodSimplicialLDLT
* Note that these classes does not bring any particular advantage compared to the built-in
* SimplicialLLT and SimplicialLDLT factorization classes.
*
* \code
* #include <Eigen/CholmodSupport>
* \endcode
*
* In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.
* The dependencies depend on how cholmod has been compiled.
* For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.
*
*/
#include "src/CholmodSupport/CholmodSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLMODSUPPORT_MODULE_H

384
lib/eigen-3.4.0/Eigen/Core
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@ -1,384 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CORE_H
#define EIGEN_CORE_H
// first thing Eigen does: stop the compiler from reporting useless warnings.
#include "src/Core/util/DisableStupidWarnings.h"
// then include this file where all our macros are defined. It's really important to do it first because
// it's where we do all the compiler/OS/arch detections and define most defaults.
#include "src/Core/util/Macros.h"
// This detects SSE/AVX/NEON/etc. and configure alignment settings
#include "src/Core/util/ConfigureVectorization.h"
// We need cuda_runtime.h/hip_runtime.h to ensure that
// the EIGEN_USING_STD macro works properly on the device side
#if defined(EIGEN_CUDACC)
#include <cuda_runtime.h>
#elif defined(EIGEN_HIPCC)
#include <hip/hip_runtime.h>
#endif
#ifdef EIGEN_EXCEPTIONS
#include <new>
#endif
// Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3)
// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.
#if EIGEN_COMP_MINGW && EIGEN_GNUC_AT_LEAST(4,6) && EIGEN_GNUC_AT_MOST(5,5)
#pragma GCC optimize ("-fno-ipa-cp-clone")
#endif
// Prevent ICC from specializing std::complex operators that silently fail
// on device. This allows us to use our own device-compatible specializations
// instead.
#if defined(EIGEN_COMP_ICC) && defined(EIGEN_GPU_COMPILE_PHASE) \
&& !defined(_OVERRIDE_COMPLEX_SPECIALIZATION_)
#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
#endif
#include <complex>
// this include file manages BLAS and MKL related macros
// and inclusion of their respective header files
#include "src/Core/util/MKL_support.h"
#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
#define EIGEN_HAS_GPU_FP16
#endif
#if defined(EIGEN_HAS_CUDA_BF16) || defined(EIGEN_HAS_HIP_BF16)
#define EIGEN_HAS_GPU_BF16
#endif
#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
#define EIGEN_HAS_OPENMP
#endif
#ifdef EIGEN_HAS_OPENMP
#include <omp.h>
#endif
// MSVC for windows mobile does not have the errno.h file
#if !(EIGEN_COMP_MSVC && EIGEN_OS_WINCE) && !EIGEN_COMP_ARM
#define EIGEN_HAS_ERRNO
#endif
#ifdef EIGEN_HAS_ERRNO
#include <cerrno>
#endif
#include <cstddef>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <functional>
#include <sstream>
#ifndef EIGEN_NO_IO
#include <iosfwd>
#endif
#include <cstring>
#include <string>
#include <limits>
#include <climits> // for CHAR_BIT
// for min/max:
#include <algorithm>
#if EIGEN_HAS_CXX11
#include <array>
#endif
// for std::is_nothrow_move_assignable
#ifdef EIGEN_INCLUDE_TYPE_TRAITS
#include <type_traits>
#endif
// for outputting debug info
#ifdef EIGEN_DEBUG_ASSIGN
#include <iostream>
#endif
// required for __cpuid, needs to be included after cmath
#if EIGEN_COMP_MSVC && EIGEN_ARCH_i386_OR_x86_64 && !EIGEN_OS_WINCE
#include <intrin.h>
#endif
#if defined(EIGEN_USE_SYCL)
#undef min
#undef max
#undef isnan
#undef isinf
#undef isfinite
#include <CL/sycl.hpp>
#include <map>
#include <memory>
#include <utility>
#include <thread>
#ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0
#define EIGEN_SYCL_LOCAL_THREAD_DIM0 16
#endif
#ifndef EIGEN_SYCL_LOCAL_THREAD_DIM1
#define EIGEN_SYCL_LOCAL_THREAD_DIM1 16
#endif
#endif
#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || defined EIGEN2_SUPPORT
// This will generate an error message:
#error Eigen2-support is only available up to version 3.2. Please go to "http://eigen.tuxfamily.org/index.php?title=Eigen2" for further information
#endif
namespace Eigen {
// we use size_t frequently and we'll never remember to prepend it with std:: every time just to
// ensure QNX/QCC support
using std::size_t;
// gcc 4.6.0 wants std:: for ptrdiff_t
using std::ptrdiff_t;
}
/** \defgroup Core_Module Core module
* This is the main module of Eigen providing dense matrix and vector support
* (both fixed and dynamic size) with all the features corresponding to a BLAS library
* and much more...
*
* \code
* #include <Eigen/Core>
* \endcode
*/
#include "src/Core/util/Constants.h"
#include "src/Core/util/Meta.h"
#include "src/Core/util/ForwardDeclarations.h"
#include "src/Core/util/StaticAssert.h"
#include "src/Core/util/XprHelper.h"
#include "src/Core/util/Memory.h"
#include "src/Core/util/IntegralConstant.h"
#include "src/Core/util/SymbolicIndex.h"
#include "src/Core/NumTraits.h"
#include "src/Core/MathFunctions.h"
#include "src/Core/GenericPacketMath.h"
#include "src/Core/MathFunctionsImpl.h"
#include "src/Core/arch/Default/ConjHelper.h"
// Generic half float support
#include "src/Core/arch/Default/Half.h"
#include "src/Core/arch/Default/BFloat16.h"
#include "src/Core/arch/Default/TypeCasting.h"
#include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
#if defined EIGEN_VECTORIZE_AVX512
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/SSE/Complex.h"
#include "src/Core/arch/AVX/PacketMath.h"
#include "src/Core/arch/AVX/TypeCasting.h"
#include "src/Core/arch/AVX/Complex.h"
#include "src/Core/arch/AVX512/PacketMath.h"
#include "src/Core/arch/AVX512/TypeCasting.h"
#include "src/Core/arch/AVX512/Complex.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/AVX/MathFunctions.h"
#include "src/Core/arch/AVX512/MathFunctions.h"
#elif defined EIGEN_VECTORIZE_AVX
// Use AVX for floats and doubles, SSE for integers
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/SSE/Complex.h"
#include "src/Core/arch/AVX/PacketMath.h"
#include "src/Core/arch/AVX/TypeCasting.h"
#include "src/Core/arch/AVX/Complex.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/AVX/MathFunctions.h"
#elif defined EIGEN_VECTORIZE_SSE
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/SSE/Complex.h"
#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
#include "src/Core/arch/AltiVec/PacketMath.h"
#include "src/Core/arch/AltiVec/MathFunctions.h"
#include "src/Core/arch/AltiVec/Complex.h"
#elif defined EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/PacketMath.h"
#include "src/Core/arch/NEON/TypeCasting.h"
#include "src/Core/arch/NEON/MathFunctions.h"
#include "src/Core/arch/NEON/Complex.h"
#elif defined EIGEN_VECTORIZE_SVE
#include "src/Core/arch/SVE/PacketMath.h"
#include "src/Core/arch/SVE/TypeCasting.h"
#include "src/Core/arch/SVE/MathFunctions.h"
#elif defined EIGEN_VECTORIZE_ZVECTOR
#include "src/Core/arch/ZVector/PacketMath.h"
#include "src/Core/arch/ZVector/MathFunctions.h"
#include "src/Core/arch/ZVector/Complex.h"
#elif defined EIGEN_VECTORIZE_MSA
#include "src/Core/arch/MSA/PacketMath.h"
#include "src/Core/arch/MSA/MathFunctions.h"
#include "src/Core/arch/MSA/Complex.h"
#endif
#if defined EIGEN_VECTORIZE_GPU
#include "src/Core/arch/GPU/PacketMath.h"
#include "src/Core/arch/GPU/MathFunctions.h"
#include "src/Core/arch/GPU/TypeCasting.h"
#endif
#if defined(EIGEN_USE_SYCL)
#include "src/Core/arch/SYCL/SyclMemoryModel.h"
#include "src/Core/arch/SYCL/InteropHeaders.h"
#if !defined(EIGEN_DONT_VECTORIZE_SYCL)
#include "src/Core/arch/SYCL/PacketMath.h"
#include "src/Core/arch/SYCL/MathFunctions.h"
#include "src/Core/arch/SYCL/TypeCasting.h"
#endif
#endif
#include "src/Core/arch/Default/Settings.h"
// This file provides generic implementations valid for scalar as well
#include "src/Core/arch/Default/GenericPacketMathFunctions.h"
#include "src/Core/functors/TernaryFunctors.h"
#include "src/Core/functors/BinaryFunctors.h"
#include "src/Core/functors/UnaryFunctors.h"
#include "src/Core/functors/NullaryFunctors.h"
#include "src/Core/functors/StlFunctors.h"
#include "src/Core/functors/AssignmentFunctors.h"
// Specialized functors to enable the processing of complex numbers
// on CUDA devices
#ifdef EIGEN_CUDACC
#include "src/Core/arch/CUDA/Complex.h"
#endif
#include "src/Core/util/IndexedViewHelper.h"
#include "src/Core/util/ReshapedHelper.h"
#include "src/Core/ArithmeticSequence.h"
#ifndef EIGEN_NO_IO
#include "src/Core/IO.h"
#endif
#include "src/Core/DenseCoeffsBase.h"
#include "src/Core/DenseBase.h"
#include "src/Core/MatrixBase.h"
#include "src/Core/EigenBase.h"
#include "src/Core/Product.h"
#include "src/Core/CoreEvaluators.h"
#include "src/Core/AssignEvaluator.h"
#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874
// at least confirmed with Doxygen 1.5.5 and 1.5.6
#include "src/Core/Assign.h"
#endif
#include "src/Core/ArrayBase.h"
#include "src/Core/util/BlasUtil.h"
#include "src/Core/DenseStorage.h"
#include "src/Core/NestByValue.h"
// #include "src/Core/ForceAlignedAccess.h"
#include "src/Core/ReturnByValue.h"
#include "src/Core/NoAlias.h"
#include "src/Core/PlainObjectBase.h"
#include "src/Core/Matrix.h"
#include "src/Core/Array.h"
#include "src/Core/CwiseTernaryOp.h"
#include "src/Core/CwiseBinaryOp.h"
#include "src/Core/CwiseUnaryOp.h"
#include "src/Core/CwiseNullaryOp.h"
#include "src/Core/CwiseUnaryView.h"
#include "src/Core/SelfCwiseBinaryOp.h"
#include "src/Core/Dot.h"
#include "src/Core/StableNorm.h"
#include "src/Core/Stride.h"
#include "src/Core/MapBase.h"
#include "src/Core/Map.h"
#include "src/Core/Ref.h"
#include "src/Core/Block.h"
#include "src/Core/VectorBlock.h"
#include "src/Core/IndexedView.h"
#include "src/Core/Reshaped.h"
#include "src/Core/Transpose.h"
#include "src/Core/DiagonalMatrix.h"
#include "src/Core/Diagonal.h"
#include "src/Core/DiagonalProduct.h"
#include "src/Core/Redux.h"
#include "src/Core/Visitor.h"
#include "src/Core/Fuzzy.h"
#include "src/Core/Swap.h"
#include "src/Core/CommaInitializer.h"
#include "src/Core/GeneralProduct.h"
#include "src/Core/Solve.h"
#include "src/Core/Inverse.h"
#include "src/Core/SolverBase.h"
#include "src/Core/PermutationMatrix.h"
#include "src/Core/Transpositions.h"
#include "src/Core/TriangularMatrix.h"
#include "src/Core/SelfAdjointView.h"
#include "src/Core/products/GeneralBlockPanelKernel.h"
#include "src/Core/products/Parallelizer.h"
#include "src/Core/ProductEvaluators.h"
#include "src/Core/products/GeneralMatrixVector.h"
#include "src/Core/products/GeneralMatrixMatrix.h"
#include "src/Core/SolveTriangular.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular.h"
#include "src/Core/products/SelfadjointMatrixVector.h"
#include "src/Core/products/SelfadjointMatrixMatrix.h"
#include "src/Core/products/SelfadjointProduct.h"
#include "src/Core/products/SelfadjointRank2Update.h"
#include "src/Core/products/TriangularMatrixVector.h"
#include "src/Core/products/TriangularMatrixMatrix.h"
#include "src/Core/products/TriangularSolverMatrix.h"
#include "src/Core/products/TriangularSolverVector.h"
#include "src/Core/BandMatrix.h"
#include "src/Core/CoreIterators.h"
#include "src/Core/ConditionEstimator.h"
#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
#include "src/Core/arch/AltiVec/MatrixProduct.h"
#elif defined EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
#endif
#include "src/Core/BooleanRedux.h"
#include "src/Core/Select.h"
#include "src/Core/VectorwiseOp.h"
#include "src/Core/PartialReduxEvaluator.h"
#include "src/Core/Random.h"
#include "src/Core/Replicate.h"
#include "src/Core/Reverse.h"
#include "src/Core/ArrayWrapper.h"
#include "src/Core/StlIterators.h"
#ifdef EIGEN_USE_BLAS
#include "src/Core/products/GeneralMatrixMatrix_BLAS.h"
#include "src/Core/products/GeneralMatrixVector_BLAS.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h"
#include "src/Core/products/SelfadjointMatrixMatrix_BLAS.h"
#include "src/Core/products/SelfadjointMatrixVector_BLAS.h"
#include "src/Core/products/TriangularMatrixMatrix_BLAS.h"
#include "src/Core/products/TriangularMatrixVector_BLAS.h"
#include "src/Core/products/TriangularSolverMatrix_BLAS.h"
#endif // EIGEN_USE_BLAS
#ifdef EIGEN_USE_MKL_VML
#include "src/Core/Assign_MKL.h"
#endif
#include "src/Core/GlobalFunctions.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CORE_H

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

2
lib/eigen-3.4.0/Eigen/Eigen
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#include "Dense"
#include "Sparse"

60
lib/eigen-3.4.0/Eigen/Eigenvalues
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@ -1,60 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_EIGENVALUES_MODULE_H
#define EIGEN_EIGENVALUES_MODULE_H
#include "Core"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
#include "LU"
#include "Geometry"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Eigenvalues_Module Eigenvalues module
*
*
*
* This module mainly provides various eigenvalue solvers.
* This module also provides some MatrixBase methods, including:
* - MatrixBase::eigenvalues(),
* - MatrixBase::operatorNorm()
*
* \code
* #include <Eigen/Eigenvalues>
* \endcode
*/
#include "src/misc/RealSvd2x2.h"
#include "src/Eigenvalues/Tridiagonalization.h"
#include "src/Eigenvalues/RealSchur.h"
#include "src/Eigenvalues/EigenSolver.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
#include "src/Eigenvalues/HessenbergDecomposition.h"
#include "src/Eigenvalues/ComplexSchur.h"
#include "src/Eigenvalues/ComplexEigenSolver.h"
#include "src/Eigenvalues/RealQZ.h"
#include "src/Eigenvalues/GeneralizedEigenSolver.h"
#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/Eigenvalues/RealSchur_LAPACKE.h"
#include "src/Eigenvalues/ComplexSchur_LAPACKE.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_EIGENVALUES_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GEOMETRY_MODULE_H
#define EIGEN_GEOMETRY_MODULE_H
#include "Core"
#include "SVD"
#include "LU"
#include <limits>
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Geometry_Module Geometry module
*
* This module provides support for:
* - fixed-size homogeneous transformations
* - translation, scaling, 2D and 3D rotations
* - \link Quaternion quaternions \endlink
* - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
* - orthognal vector generation (\ref MatrixBase::unitOrthogonal)
* - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
* - \link AlignedBox axis aligned bounding boxes \endlink
* - \link umeyama least-square transformation fitting \endlink
*
* \code
* #include <Eigen/Geometry>
* \endcode
*/
#include "src/Geometry/OrthoMethods.h"
#include "src/Geometry/EulerAngles.h"
#include "src/Geometry/Homogeneous.h"
#include "src/Geometry/RotationBase.h"
#include "src/Geometry/Rotation2D.h"
#include "src/Geometry/Quaternion.h"
#include "src/Geometry/AngleAxis.h"
#include "src/Geometry/Transform.h"
#include "src/Geometry/Translation.h"
#include "src/Geometry/Scaling.h"
#include "src/Geometry/Hyperplane.h"
#include "src/Geometry/ParametrizedLine.h"
#include "src/Geometry/AlignedBox.h"
#include "src/Geometry/Umeyama.h"
// Use the SSE optimized version whenever possible.
#if (defined EIGEN_VECTORIZE_SSE) || (defined EIGEN_VECTORIZE_NEON)
#include "src/Geometry/arch/Geometry_SIMD.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_GEOMETRY_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_HOUSEHOLDER_MODULE_H
#define EIGEN_HOUSEHOLDER_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Householder_Module Householder module
* This module provides Householder transformations.
*
* \code
* #include <Eigen/Householder>
* \endcode
*/
#include "src/Householder/Householder.h"
#include "src/Householder/HouseholderSequence.h"
#include "src/Householder/BlockHouseholder.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_HOUSEHOLDER_MODULE_H

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lib/eigen-3.4.0/Eigen/IterativeLinearSolvers
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
*
* This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse.
* Those solvers are accessible via the following classes:
* - ConjugateGradient for selfadjoint (hermitian) matrices,
* - LeastSquaresConjugateGradient for rectangular least-square problems,
* - BiCGSTAB for general square matrices.
*
* These iterative solvers are associated with some preconditioners:
* - IdentityPreconditioner - not really useful
* - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
* - IncompleteLUT - incomplete LU factorization with dual thresholding
*
* Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport.
*
\code
#include <Eigen/IterativeLinearSolvers>
\endcode
*/
#include "src/IterativeLinearSolvers/SolveWithGuess.h"
#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
#include "src/IterativeLinearSolvers/ConjugateGradient.h"
#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h"
#include "src/IterativeLinearSolvers/BiCGSTAB.h"
#include "src/IterativeLinearSolvers/IncompleteLUT.h"
#include "src/IterativeLinearSolvers/IncompleteCholesky.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H

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lib/eigen-3.4.0/Eigen/Jacobi
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_JACOBI_MODULE_H
#define EIGEN_JACOBI_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Jacobi_Module Jacobi module
* This module provides Jacobi and Givens rotations.
*
* \code
* #include <Eigen/Jacobi>
* \endcode
*
* In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
* - MatrixBase::applyOnTheLeft()
* - MatrixBase::applyOnTheRight().
*/
#include "src/Jacobi/Jacobi.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_JACOBI_MODULE_H

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lib/eigen-3.4.0/Eigen/KLUSupport
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_KLUSUPPORT_MODULE_H
#define EIGEN_KLUSUPPORT_MODULE_H
#include <Eigen/SparseCore>
#include <Eigen/src/Core/util/DisableStupidWarnings.h>
extern "C" {
#include <btf.h>
#include <klu.h>
}
/** \ingroup Support_modules
* \defgroup KLUSupport_Module KLUSupport module
*
* This module provides an interface to the KLU library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
* It provides the following factorization class:
* - class KLU: a sparse LU factorization, well-suited for circuit simulation.
*
* \code
* #include <Eigen/KLUSupport>
* \endcode
*
* In order to use this module, the klu and btf headers must be accessible from the include paths, and your binary must be linked to the klu library and its dependencies.
* The dependencies depend on how umfpack has been compiled.
* For a cmake based project, you can use our FindKLU.cmake module to help you in this task.
*
*/
#include "src/KLUSupport/KLUSupport.h"
#include <Eigen/src/Core/util/ReenableStupidWarnings.h>
#endif // EIGEN_KLUSUPPORT_MODULE_H

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lib/eigen-3.4.0/Eigen/LU
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LU_MODULE_H
#define EIGEN_LU_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup LU_Module LU module
* This module includes %LU decomposition and related notions such as matrix inversion and determinant.
* This module defines the following MatrixBase methods:
* - MatrixBase::inverse()
* - MatrixBase::determinant()
*
* \code
* #include <Eigen/LU>
* \endcode
*/
#include "src/misc/Kernel.h"
#include "src/misc/Image.h"
#include "src/LU/FullPivLU.h"
#include "src/LU/PartialPivLU.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/LU/PartialPivLU_LAPACKE.h"
#endif
#include "src/LU/Determinant.h"
#include "src/LU/InverseImpl.h"
#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_NEON
#include "src/LU/arch/InverseSize4.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_LU_MODULE_H

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lib/eigen-3.4.0/Eigen/MetisSupport
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_METISSUPPORT_MODULE_H
#define EIGEN_METISSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <metis.h>
}
/** \ingroup Support_modules
* \defgroup MetisSupport_Module MetisSupport module
*
* \code
* #include <Eigen/MetisSupport>
* \endcode
* This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis).
* It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink
*/
#include "src/MetisSupport/MetisSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_METISSUPPORT_MODULE_H

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lib/eigen-3.4.0/Eigen/OrderingMethods
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
#define EIGEN_ORDERINGMETHODS_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup OrderingMethods_Module OrderingMethods module
*
* This module is currently for internal use only
*
* It defines various built-in and external ordering methods for sparse matrices.
* They are typically used to reduce the number of elements during
* the sparse matrix decomposition (LLT, LU, QR).
* Precisely, in a preprocessing step, a permutation matrix P is computed using
* those ordering methods and applied to the columns of the matrix.
* Using for instance the sparse Cholesky decomposition, it is expected that
* the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).
*
*
* Usage :
* \code
* #include <Eigen/OrderingMethods>
* \endcode
*
* A simple usage is as a template parameter in the sparse decomposition classes :
*
* \code
* SparseLU<MatrixType, COLAMDOrdering<int> > solver;
* \endcode
*
* \code
* SparseQR<MatrixType, COLAMDOrdering<int> > solver;
* \endcode
*
* It is possible as well to call directly a particular ordering method for your own purpose,
* \code
* AMDOrdering<int> ordering;
* PermutationMatrix<Dynamic, Dynamic, int> perm;
* SparseMatrix<double> A;
* //Fill the matrix ...
*
* ordering(A, perm); // Call AMD
* \endcode
*
* \note Some of these methods (like AMD or METIS), need the sparsity pattern
* of the input matrix to be symmetric. When the matrix is structurally unsymmetric,
* Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
* If your matrix is already symmetric (at leat in structure), you can avoid that
* by calling the method with a SelfAdjointView type.
*
* \code
* // Call the ordering on the pattern of the lower triangular matrix A
* ordering(A.selfadjointView<Lower>(), perm);
* \endcode
*/
#include "src/OrderingMethods/Amd.h"
#include "src/OrderingMethods/Ordering.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ORDERINGMETHODS_MODULE_H

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lib/eigen-3.4.0/Eigen/PaStiXSupport
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
#define EIGEN_PASTIXSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <pastix_nompi.h>
#include <pastix.h>
}
#ifdef complex
#undef complex
#endif
/** \ingroup Support_modules
* \defgroup PaStiXSupport_Module PaStiXSupport module
*
* This module provides an interface to the <a href="http://pastix.gforge.inria.fr/">PaSTiX</a> library.
* PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver.
* It provides the two following main factorization classes:
* - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.
* - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.
* - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).
*
* \code
* #include <Eigen/PaStiXSupport>
* \endcode
*
* In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.
* This wrapper resuires PaStiX version 5.x compiled without MPI support.
* The dependencies depend on how PaSTiX has been compiled.
* For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.
*
*/
#include "src/PaStiXSupport/PaStiXSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PASTIXSUPPORT_MODULE_H

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lib/eigen-3.4.0/Eigen/PardisoSupport
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
#define EIGEN_PARDISOSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include <mkl_pardiso.h>
/** \ingroup Support_modules
* \defgroup PardisoSupport_Module PardisoSupport module
*
* This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.
*
* \code
* #include <Eigen/PardisoSupport>
* \endcode
*
* In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.
* See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration.
*
*/
#include "src/PardisoSupport/PardisoSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PARDISOSUPPORT_MODULE_H

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lib/eigen-3.4.0/Eigen/QR
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_QR_MODULE_H
#define EIGEN_QR_MODULE_H
#include "Core"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup QR_Module QR module
*
*
*
* This module provides various QR decompositions
* This module also provides some MatrixBase methods, including:
* - MatrixBase::householderQr()
* - MatrixBase::colPivHouseholderQr()
* - MatrixBase::fullPivHouseholderQr()
*
* \code
* #include <Eigen/QR>
* \endcode
*/
#include "src/QR/HouseholderQR.h"
#include "src/QR/FullPivHouseholderQR.h"
#include "src/QR/ColPivHouseholderQR.h"
#include "src/QR/CompleteOrthogonalDecomposition.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/QR/HouseholderQR_LAPACKE.h"
#include "src/QR/ColPivHouseholderQR_LAPACKE.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_QR_MODULE_H

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lib/eigen-3.4.0/Eigen/QtAlignedMalloc
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_QTMALLOC_MODULE_H
#define EIGEN_QTMALLOC_MODULE_H
#include "Core"
#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
#include "src/Core/util/DisableStupidWarnings.h"
void *qMalloc(std::size_t size)
{
return Eigen::internal::aligned_malloc(size);
}
void qFree(void *ptr)
{
Eigen::internal::aligned_free(ptr);
}
void *qRealloc(void *ptr, std::size_t size)
{
void* newPtr = Eigen::internal::aligned_malloc(size);
std::memcpy(newPtr, ptr, size);
Eigen::internal::aligned_free(ptr);
return newPtr;
}
#include "src/Core/util/ReenableStupidWarnings.h"
#endif
#endif // EIGEN_QTMALLOC_MODULE_H

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lib/eigen-3.4.0/Eigen/SPQRSupport
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPQRSUPPORT_MODULE_H
#define EIGEN_SPQRSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include "SuiteSparseQR.hpp"
/** \ingroup Support_modules
* \defgroup SPQRSupport_Module SuiteSparseQR module
*
* This module provides an interface to the SPQR library, which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
*
* \code
* #include <Eigen/SPQRSupport>
* \endcode
*
* In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...).
* For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules
*
*/
#include "src/CholmodSupport/CholmodSupport.h"
#include "src/SPQRSupport/SuiteSparseQRSupport.h"
#endif

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lib/eigen-3.4.0/Eigen/SVD
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@ -1,50 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SVD_MODULE_H
#define EIGEN_SVD_MODULE_H
#include "QR"
#include "Householder"
#include "Jacobi"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup SVD_Module SVD module
*
*
*
* This module provides SVD decomposition for matrices (both real and complex).
* Two decomposition algorithms are provided:
* - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.
* - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.
* These decompositions are accessible via the respective classes and following MatrixBase methods:
* - MatrixBase::jacobiSvd()
* - MatrixBase::bdcSvd()
*
* \code
* #include <Eigen/SVD>
* \endcode
*/
#include "src/misc/RealSvd2x2.h"
#include "src/SVD/UpperBidiagonalization.h"
#include "src/SVD/SVDBase.h"
#include "src/SVD/JacobiSVD.h"
#include "src/SVD/BDCSVD.h"
#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/SVD/JacobiSVD_LAPACKE.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SVD_MODULE_H

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lib/eigen-3.4.0/Eigen/Sparse
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSE_MODULE_H
#define EIGEN_SPARSE_MODULE_H
/** \defgroup Sparse_Module Sparse meta-module
*
* Meta-module including all related modules:
* - \ref SparseCore_Module
* - \ref OrderingMethods_Module
* - \ref SparseCholesky_Module
* - \ref SparseLU_Module
* - \ref SparseQR_Module
* - \ref IterativeLinearSolvers_Module
*
\code
#include <Eigen/Sparse>
\endcode
*/
#include "SparseCore"
#include "OrderingMethods"
#include "SparseCholesky"
#include "SparseLU"
#include "SparseQR"
#include "IterativeLinearSolvers"
#endif // EIGEN_SPARSE_MODULE_H

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lib/eigen-3.4.0/Eigen/SparseCholesky
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
#define EIGEN_SPARSECHOLESKY_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup SparseCholesky_Module SparseCholesky module
*
* This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.
* Those decompositions are accessible via the following classes:
* - SimplicialLLt,
* - SimplicialLDLt
*
* Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.
*
* \code
* #include <Eigen/SparseCholesky>
* \endcode
*/
#include "src/SparseCholesky/SimplicialCholesky.h"
#include "src/SparseCholesky/SimplicialCholesky_impl.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECHOLESKY_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSECORE_MODULE_H
#define EIGEN_SPARSECORE_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include <vector>
#include <map>
#include <cstdlib>
#include <cstring>
#include <algorithm>
/**
* \defgroup SparseCore_Module SparseCore module
*
* This module provides a sparse matrix representation, and basic associated matrix manipulations
* and operations.
*
* See the \ref TutorialSparse "Sparse tutorial"
*
* \code
* #include <Eigen/SparseCore>
* \endcode
*
* This module depends on: Core.
*/
#include "src/SparseCore/SparseUtil.h"
#include "src/SparseCore/SparseMatrixBase.h"
#include "src/SparseCore/SparseAssign.h"
#include "src/SparseCore/CompressedStorage.h"
#include "src/SparseCore/AmbiVector.h"
#include "src/SparseCore/SparseCompressedBase.h"
#include "src/SparseCore/SparseMatrix.h"
#include "src/SparseCore/SparseMap.h"
#include "src/SparseCore/MappedSparseMatrix.h"
#include "src/SparseCore/SparseVector.h"
#include "src/SparseCore/SparseRef.h"
#include "src/SparseCore/SparseCwiseUnaryOp.h"
#include "src/SparseCore/SparseCwiseBinaryOp.h"
#include "src/SparseCore/SparseTranspose.h"
#include "src/SparseCore/SparseBlock.h"
#include "src/SparseCore/SparseDot.h"
#include "src/SparseCore/SparseRedux.h"
#include "src/SparseCore/SparseView.h"
#include "src/SparseCore/SparseDiagonalProduct.h"
#include "src/SparseCore/ConservativeSparseSparseProduct.h"
#include "src/SparseCore/SparseSparseProductWithPruning.h"
#include "src/SparseCore/SparseProduct.h"
#include "src/SparseCore/SparseDenseProduct.h"
#include "src/SparseCore/SparseSelfAdjointView.h"
#include "src/SparseCore/SparseTriangularView.h"
#include "src/SparseCore/TriangularSolver.h"
#include "src/SparseCore/SparsePermutation.h"
#include "src/SparseCore/SparseFuzzy.h"
#include "src/SparseCore/SparseSolverBase.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECORE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSELU_MODULE_H
#define EIGEN_SPARSELU_MODULE_H
#include "SparseCore"
/**
* \defgroup SparseLU_Module SparseLU module
* This module defines a supernodal factorization of general sparse matrices.
* The code is fully optimized for supernode-panel updates with specialized kernels.
* Please, see the documentation of the SparseLU class for more details.
*/
// Ordering interface
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
#include "src/SparseLU/SparseLU_gemm_kernel.h"
#include "src/SparseLU/SparseLU_Structs.h"
#include "src/SparseLU/SparseLU_SupernodalMatrix.h"
#include "src/SparseLU/SparseLUImpl.h"
#include "src/SparseCore/SparseColEtree.h"
#include "src/SparseLU/SparseLU_Memory.h"
#include "src/SparseLU/SparseLU_heap_relax_snode.h"
#include "src/SparseLU/SparseLU_relax_snode.h"
#include "src/SparseLU/SparseLU_pivotL.h"
#include "src/SparseLU/SparseLU_panel_dfs.h"
#include "src/SparseLU/SparseLU_kernel_bmod.h"
#include "src/SparseLU/SparseLU_panel_bmod.h"
#include "src/SparseLU/SparseLU_column_dfs.h"
#include "src/SparseLU/SparseLU_column_bmod.h"
#include "src/SparseLU/SparseLU_copy_to_ucol.h"
#include "src/SparseLU/SparseLU_pruneL.h"
#include "src/SparseLU/SparseLU_Utils.h"
#include "src/SparseLU/SparseLU.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSELU_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSEQR_MODULE_H
#define EIGEN_SPARSEQR_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup SparseQR_Module SparseQR module
* \brief Provides QR decomposition for sparse matrices
*
* This module provides a simplicial version of the left-looking Sparse QR decomposition.
* The columns of the input matrix should be reordered to limit the fill-in during the
* decomposition. Built-in methods (COLAMD, AMD) or external methods (METIS) can be used to this end.
* See the \link OrderingMethods_Module OrderingMethods\endlink module for the list
* of built-in and external ordering methods.
*
* \code
* #include <Eigen/SparseQR>
* \endcode
*
*
*/
#include "src/SparseCore/SparseColEtree.h"
#include "src/SparseQR/SparseQR.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDDEQUE_MODULE_H
#define EIGEN_STDDEQUE_MODULE_H
#include "Core"
#include <deque>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdDeque.h"
#endif
#endif // EIGEN_STDDEQUE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDLIST_MODULE_H
#define EIGEN_STDLIST_MODULE_H
#include "Core"
#include <list>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdList.h"
#endif
#endif // EIGEN_STDLIST_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDVECTOR_MODULE_H
#define EIGEN_STDVECTOR_MODULE_H
#include "Core"
#include <vector>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdVector.h"
#endif
#endif // EIGEN_STDVECTOR_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
#define EIGEN_SUPERLUSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#ifdef EMPTY
#define EIGEN_EMPTY_WAS_ALREADY_DEFINED
#endif
typedef int int_t;
#include <slu_Cnames.h>
#include <supermatrix.h>
#include <slu_util.h>
// slu_util.h defines a preprocessor token named EMPTY which is really polluting,
// so we remove it in favor of a SUPERLU_EMPTY token.
// If EMPTY was already defined then we don't undef it.
#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)
# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED
#elif defined(EMPTY)
# undef EMPTY
#endif
#define SUPERLU_EMPTY (-1)
namespace Eigen { struct SluMatrix; }
/** \ingroup Support_modules
* \defgroup SuperLUSupport_Module SuperLUSupport module
*
* This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
* It provides the following factorization class:
* - class SuperLU: a supernodal sequential LU factorization.
* - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
*
* \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.
*
* \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
*
* \code
* #include <Eigen/SuperLUSupport>
* \endcode
*
* In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.
* The dependencies depend on how superlu has been compiled.
* For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
*
*/
#include "src/SuperLUSupport/SuperLUSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SUPERLUSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
#define EIGEN_UMFPACKSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <umfpack.h>
}
/** \ingroup Support_modules
* \defgroup UmfPackSupport_Module UmfPackSupport module
*
* This module provides an interface to the UmfPack library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
* It provides the following factorization class:
* - class UmfPackLU: a multifrontal sequential LU factorization.
*
* \code
* #include <Eigen/UmfPackSupport>
* \endcode
*
* In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.
* The dependencies depend on how umfpack has been compiled.
* For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
*
*/
#include "src/UmfPackSupport/UmfPackSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_UMFPACKSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LDLT_H
#define EIGEN_LDLT_H
namespace Eigen {
namespace internal {
template<typename _MatrixType, int _UpLo> struct traits<LDLT<_MatrixType, _UpLo> >
: traits<_MatrixType>
{
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template<typename MatrixType, int UpLo> struct LDLT_Traits;
// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
}
/** \ingroup Cholesky_Module
*
* \class LDLT
*
* \brief Robust Cholesky decomposition of a matrix with pivoting
*
* \tparam _MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
* \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
* The other triangular part won't be read.
*
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
* is lower triangular with a unit diagonal and D is a diagonal matrix.
*
* The decomposition uses pivoting to ensure stability, so that D will have
* 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.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
*/
template<typename _MatrixType, int _UpLo> class LDLT
: public SolverBase<LDLT<_MatrixType, _UpLo> >
{
public:
typedef _MatrixType MatrixType;
typedef SolverBase<LDLT> Base;
friend class SolverBase<LDLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
enum {
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = _UpLo
};
typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
/** \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT()
: m_matrix(),
m_transpositions(),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LDLT()
*/
explicit LDLT(Index size)
: m_matrix(size, size),
m_transpositions(size),
m_temporary(size),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{}
/** \brief Constructor with decomposition
*
* This calculates the decomposition for the input \a matrix.
*
* \sa LDLT(Index size)
*/
template<typename InputType>
explicit LDLT(const EigenBase<InputType>& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{
compute(matrix.derived());
}
/** \brief Constructs a LDLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
*
* \sa LDLT(const EigenBase&)
*/
template<typename InputType>
explicit LDLT(EigenBase<InputType>& matrix)
: m_matrix(matrix.derived()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{
compute(matrix.derived());
}
/** Clear any existing decomposition
* \sa rankUpdate(w,sigma)
*/
void setZero()
{
m_isInitialized = false;
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns the permutation matrix P as a transposition sequence.
*/
inline const TranspositionType& transpositionsP() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_transpositions;
}
/** \returns the coefficients of the diagonal matrix D */
inline Diagonal<const MatrixType> vectorD() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix.diagonal();
}
/** \returns true if the matrix is positive (semidefinite) */
inline bool isPositive() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
}
/** \returns true if the matrix is negative (semidefinite) */
inline bool isNegative(void) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
*
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
* computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
*/
template<typename Rhs>
inline const Solve<LDLT, Rhs>
solve(const MatrixBase<Rhs>& b) const;
#endif
template<typename Derived>
bool solveInPlace(MatrixBase<Derived> &bAndX) const;
template<typename InputType>
LDLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the LDLT decomposition.
*/
RealScalar rcond() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
/** \returns the internal LDLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLDLT() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LDLT& adjoint() const { return *this; };
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the factorization failed because of a zero pivot.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_info;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
void _solve_impl(const RhsType &rhs, DstType &dst) const;
template<bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
#endif
protected:
static void check_template_parameters()
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
}
/** \internal
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
* 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;
RealScalar m_l1_norm;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
internal::SignMatrix m_sign;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template<int UpLo> struct ldlt_inplace;
template<> struct ldlt_inplace<Lower>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
{
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename TranspositionType::StorageIndex IndexType;
eigen_assert(mat.rows()==mat.cols());
const Index size = mat.rows();
bool found_zero_pivot = false;
bool ret = true;
if (size <= 1)
{
transpositions.setIdentity();
if(size==0) sign = ZeroSign;
else if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
else sign = ZeroSign;
return true;
}
for (Index k = 0; k < size; ++k)
{
// Find largest diagonal element
Index index_of_biggest_in_corner;
mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
index_of_biggest_in_corner += k;
transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
if(k != index_of_biggest_in_corner)
{
// apply the transposition while taking care to consider only
// the lower triangular part
Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
for(Index i=k+1;i<index_of_biggest_in_corner;++i)
{
Scalar tmp = mat.coeffRef(i,k);
mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
}
if(NumTraits<Scalar>::IsComplex)
mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
}
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index rs = size - k - 1;
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
if(k>0)
{
temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
if(rs>0)
A21.noalias() -= A20 * temp.head(k);
}
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
// was smaller than the cutoff value. However, since LDLT is not rank-revealing
// we should only make sure that we do not introduce INF or NaN values.
// Remark that LAPACK also uses 0 as the cutoff value.
RealScalar realAkk = numext::real(mat.coeffRef(k,k));
bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
if(k==0 && !pivot_is_valid)
{
// The entire diagonal is zero, there is nothing more to do
// except filling the transpositions, and checking whether the matrix is zero.
sign = ZeroSign;
for(Index j = 0; j<size; ++j)
{
transpositions.coeffRef(j) = IndexType(j);
ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();
}
return ret;
}
if((rs>0) && pivot_is_valid)
A21 /= realAkk;
else if(rs>0)
ret = ret && (A21.array()==Scalar(0)).all();
if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed
else if(!pivot_is_valid) found_zero_pivot = true;
if (sign == PositiveSemiDef) {
if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == NegativeSemiDef) {
if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == ZeroSign) {
if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
}
}
return ret;
}
// Reference for the algorithm: Davis and Hager, "Multiple Rank
// Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
// Trivial rearrangements of their computations (Timothy E. Holy)
// allow their algorithm to work for rank-1 updates even if the
// original matrix is not of full rank.
// Here only rank-1 updates are implemented, to reduce the
// requirement for intermediate storage and improve accuracy
template<typename MatrixType, typename WDerived>
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
{
using numext::isfinite;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
const Index size = mat.rows();
eigen_assert(mat.cols() == size && w.size()==size);
RealScalar alpha = 1;
// Apply the update
for (Index j = 0; j < size; j++)
{
// Check for termination due to an original decomposition of low-rank
if (!(isfinite)(alpha))
break;
// Update the diagonal terms
RealScalar dj = numext::real(mat.coeff(j,j));
Scalar wj = w.coeff(j);
RealScalar swj2 = sigma*numext::abs2(wj);
RealScalar gamma = dj*alpha + swj2;
mat.coeffRef(j,j) += swj2/alpha;
alpha += swj2/dj;
// Update the terms of L
Index rs = size-j-1;
w.tail(rs) -= wj * mat.col(j).tail(rs);
if(gamma != 0)
mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
}
return true;
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
{
// Apply the permutation to the input w
tmp = transpositions * w;
return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
}
};
template<> struct ldlt_inplace<Upper>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
{
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
{
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
}
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
{
typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
{
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
};
} // end namespace internal
/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
*/
template<typename MatrixType, int _UpLo>
template<typename InputType>
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
{
check_template_parameters();
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
// TODO move this code to SelfAdjointView
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (_UpLo == Lower)
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm)
m_l1_norm = abs_col_sum;
}
m_transpositions.resize(size);
m_isInitialized = false;
m_temporary.resize(size);
m_sign = internal::ZeroSign;
m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;
m_isInitialized = true;
return *this;
}
/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
* \param w a vector to be incorporated into the decomposition.
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
* \sa setZero()
*/
template<typename MatrixType, int _UpLo>
template<typename Derived>
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma)
{
typedef typename TranspositionType::StorageIndex IndexType;
const Index size = w.rows();
if (m_isInitialized)
{
eigen_assert(m_matrix.rows()==size);
}
else
{
m_matrix.resize(size,size);
m_matrix.setZero();
m_transpositions.resize(size);
for (Index i = 0; i < size; i++)
m_transpositions.coeffRef(i) = IndexType(i);
m_temporary.resize(size);
m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
m_isInitialized = true;
}
internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename _MatrixType, int _UpLo>
template<typename RhsType, typename DstType>
void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
_solve_impl_transposed<true>(rhs, dst);
}
template<typename _MatrixType,int _UpLo>
template<bool Conjugate, typename RhsType, typename DstType>
void LDLT<_MatrixType,_UpLo>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
// dst = P b
dst = m_transpositions * rhs;
// dst = L^-1 (P b)
// dst = L^-*T (P b)
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
// dst = D^-* (L^-1 P b)
// dst = D^-1 (L^-*T P b)
// more precisely, use pseudo-inverse of D (see bug 241)
using std::abs;
const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
// In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
// and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
// However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
// diagonal element is not well justified and leads to numerical issues in some cases.
// Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
// Using numeric_limits::min() gives us more robustness to denormals.
RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
for (Index i = 0; i < vecD.size(); ++i)
{
if(abs(vecD(i)) > tolerance)
dst.row(i) /= vecD(i);
else
dst.row(i).setZero();
}
// dst = L^-* (D^-* L^-1 P b)
// dst = L^-T (D^-1 L^-*T P b)
matrixL().transpose().template conjugateIf<Conjugate>().solveInPlace(dst);
// dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b
// dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b
dst = m_transpositions.transpose() * dst;
}
#endif
/** \internal use x = ldlt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LDLT::solve(), MatrixBase::ldlt()
*/
template<typename MatrixType,int _UpLo>
template<typename Derived>
bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
eigen_assert(m_matrix.rows() == bAndX.rows());
bAndX = this->solve(bAndX);
return true;
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: P^T L D L^* P.
* This function is provided for debug purpose. */
template<typename MatrixType, int _UpLo>
MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
const Index size = m_matrix.rows();
MatrixType res(size,size);
// P
res.setIdentity();
res = transpositionsP() * res;
// L^* P
res = matrixU() * res;
// D(L^*P)
res = vectorD().real().asDiagonal() * res;
// L(DL^*P)
res = matrixL() * res;
// P^T (LDL^*P)
res = transpositionsP().transpose() * res;
return res;
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa MatrixBase::ldlt()
*/
template<typename MatrixType, unsigned int UpLo>
inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::ldlt() const
{
return LDLT<PlainObject,UpLo>(m_matrix);
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa SelfAdjointView::ldlt()
*/
template<typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::ldlt() const
{
return LDLT<PlainObject>(derived());
}
} // end namespace Eigen
#endif // EIGEN_LDLT_H

558
lib/eigen-3.4.0/Eigen/src/Cholesky/LLT.h
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@ -1,558 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LLT_H
#define EIGEN_LLT_H
namespace Eigen {
namespace internal{
template<typename _MatrixType, int _UpLo> struct traits<LLT<_MatrixType, _UpLo> >
: traits<_MatrixType>
{
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template<typename MatrixType, int UpLo> struct LLT_Traits;
}
/** \ingroup Cholesky_Module
*
* \class LLT
*
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
*
* \tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
* \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
* The other triangular part won't be read.
*
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
* 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.
*
* Example: \include LLT_example.cpp
* Output: \verbinclude LLT_example.out
*
* \b Performance: for best performance, it is recommended to use a column-major storage format
* with the Lower triangular part (the default), or, equivalently, a row-major storage format
* with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
* step, and rank-updates can be up to 3 times slower.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* Note that during the decomposition, only the lower (or upper, as defined by _UpLo) triangular part of A is considered.
* Therefore, the strict lower part does not have to store correct values.
*
* \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
*/
template<typename _MatrixType, int _UpLo> class LLT
: public SolverBase<LLT<_MatrixType, _UpLo> >
{
public:
typedef _MatrixType MatrixType;
typedef SolverBase<LLT> Base;
friend class SolverBase<LLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
enum {
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
enum {
PacketSize = internal::packet_traits<Scalar>::size,
AlignmentMask = int(PacketSize)-1,
UpLo = _UpLo
};
typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LLT::compute(const MatrixType&).
*/
LLT() : m_matrix(), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LLT()
*/
explicit LLT(Index size) : m_matrix(size, size),
m_isInitialized(false) {}
template<typename InputType>
explicit LLT(const EigenBase<InputType>& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_isInitialized(false)
{
compute(matrix.derived());
}
/** \brief Constructs a LLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
* \c MatrixType is a Eigen::Ref.
*
* \sa LLT(const EigenBase&)
*/
template<typename InputType>
explicit LLT(EigenBase<InputType>& matrix)
: m_matrix(matrix.derived()),
m_isInitialized(false)
{
compute(matrix.derived());
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getL(m_matrix);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
* theoretically exists and is unique regardless of b.
*
* Example: \include LLT_solve.cpp
* Output: \verbinclude LLT_solve.out
*
* \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
*/
template<typename Rhs>
inline const Solve<LLT, Rhs>
solve(const MatrixBase<Rhs>& b) const;
#endif
template<typename Derived>
void solveInPlace(const MatrixBase<Derived> &bAndX) const;
template<typename InputType>
LLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the Cholesky decomposition.
*/
RealScalar rcond() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
/** \returns the LLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLLT() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears not to be positive definite.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_info;
}
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; };
inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
template<typename VectorType>
LLT & rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
void _solve_impl(const RhsType &rhs, DstType &dst) const;
template<bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
#endif
protected:
static void check_template_parameters()
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
}
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template<typename Scalar, int UpLo> struct llt_inplace;
template<typename MatrixType, typename VectorType>
static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
{
using std::sqrt;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::ColXpr ColXpr;
typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
typedef Matrix<Scalar,Dynamic,1> TempVectorType;
typedef typename TempVectorType::SegmentReturnType TempVecSegment;
Index n = mat.cols();
eigen_assert(mat.rows()==n && vec.size()==n);
TempVectorType temp;
if(sigma>0)
{
// This version is based on Givens rotations.
// It is faster than the other one below, but only works for updates,
// i.e., for sigma > 0
temp = sqrt(sigma) * vec;
for(Index i=0; i<n; ++i)
{
JacobiRotation<Scalar> g;
g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
Index rs = n-i-1;
if(rs>0)
{
ColXprSegment x(mat.col(i).tail(rs));
TempVecSegment y(temp.tail(rs));
apply_rotation_in_the_plane(x, y, g);
}
}
}
else
{
temp = vec;
RealScalar beta = 1;
for(Index j=0; j<n; ++j)
{
RealScalar Ljj = numext::real(mat.coeff(j,j));
RealScalar dj = numext::abs2(Ljj);
Scalar wj = temp.coeff(j);
RealScalar swj2 = sigma*numext::abs2(wj);
RealScalar gamma = dj*beta + swj2;
RealScalar x = dj + swj2/beta;
if (x<=RealScalar(0))
return j;
RealScalar nLjj = sqrt(x);
mat.coeffRef(j,j) = nLjj;
beta += swj2/dj;
// Update the terms of L
Index rs = n-j-1;
if(rs)
{
temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
if(gamma != 0)
mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
}
}
}
return -1;
}
template<typename Scalar> struct llt_inplace<Scalar, Lower>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static Index unblocked(MatrixType& mat)
{
using std::sqrt;
eigen_assert(mat.rows()==mat.cols());
const Index size = mat.rows();
for(Index k = 0; k < size; ++k)
{
Index rs = size-k-1; // remaining size
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
RealScalar x = numext::real(mat.coeff(k,k));
if (k>0) x -= A10.squaredNorm();
if (x<=RealScalar(0))
return k;
mat.coeffRef(k,k) = x = sqrt(x);
if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
if (rs>0) A21 /= x;
}
return -1;
}
template<typename MatrixType>
static Index blocked(MatrixType& m)
{
eigen_assert(m.rows()==m.cols());
Index size = m.rows();
if(size<32)
return unblocked(m);
Index blockSize = size/8;
blockSize = (blockSize/16)*16;
blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
for (Index k=0; k<size; k+=blockSize)
{
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index bs = (std::min)(blockSize, size-k);
Index rs = size - k - bs;
Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
Index ret;
if((ret=unblocked(A11))>=0) return k+ret;
if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
}
return -1;
}
template<typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template<typename Scalar> struct llt_inplace<Scalar, Upper>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::unblocked(matt);
}
template<typename MatrixType>
static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::blocked(matt);
}
template<typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
}
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
{
typedef const TriangularView<const MatrixType, Lower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
{
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
typedef const TriangularView<const MatrixType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
};
} // end namespace internal
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
*
* \returns a reference to *this
*
* Example: \include TutorialLinAlgComputeTwice.cpp
* Output: \verbinclude TutorialLinAlgComputeTwice.out
*/
template<typename MatrixType, int _UpLo>
template<typename InputType>
LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
{
check_template_parameters();
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
m_matrix.resize(size, size);
if (!internal::is_same_dense(m_matrix, a.derived()))
m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
// TODO move this code to SelfAdjointView
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (_UpLo == Lower)
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm)
m_l1_norm = abs_col_sum;
}
m_isInitialized = true;
bool ok = Traits::inplace_decomposition(m_matrix);
m_info = ok ? Success : NumericalIssue;
return *this;
}
/** Performs a rank one update (or dowdate) of the current decomposition.
* If A = LL^* before the rank one update,
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
* of same dimension.
*/
template<typename _MatrixType, int _UpLo>
template<typename VectorType>
LLT<_MatrixType,_UpLo> & LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
eigen_assert(v.size()==m_matrix.cols());
eigen_assert(m_isInitialized);
if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
m_info = NumericalIssue;
else
m_info = Success;
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename _MatrixType,int _UpLo>
template<typename RhsType, typename DstType>
void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
_solve_impl_transposed<true>(rhs, dst);
}
template<typename _MatrixType,int _UpLo>
template<bool Conjugate, typename RhsType, typename DstType>
void LLT<_MatrixType,_UpLo>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
dst = rhs;
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
}
#endif
/** \internal use x = llt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* This version avoids a copy when the right hand side matrix b is not needed anymore.
*
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
* This function will const_cast it, so constness isn't honored here.
*
* \sa LLT::solve(), MatrixBase::llt()
*/
template<typename MatrixType, int _UpLo>
template<typename Derived>
void LLT<MatrixType,_UpLo>::solveInPlace(const MatrixBase<Derived> &bAndX) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_matrix.rows()==bAndX.rows());
matrixL().solveInPlace(bAndX);
matrixU().solveInPlace(bAndX);
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: L L^*.
* This function is provided for debug purpose. */
template<typename MatrixType, int _UpLo>
MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return matrixL() * matrixL().adjoint().toDenseMatrix();
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template<typename Derived>
inline const LLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::llt() const
{
return LLT<PlainObject>(derived());
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template<typename MatrixType, unsigned int UpLo>
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::llt() const
{
return LLT<PlainObject,UpLo>(m_matrix);
}
} // end namespace Eigen
#endif // EIGEN_LLT_H

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lib/eigen-3.4.0/Eigen/src/Cholesky/LLT_LAPACKE.h
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@ -1,99 +0,0 @@
/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to LAPACKe
* LLt decomposition based on LAPACKE_?potrf function.
********************************************************************************
*/
#ifndef EIGEN_LLT_LAPACKE_H
#define EIGEN_LLT_LAPACKE_H
namespace Eigen {
namespace internal {
template<typename Scalar> struct lapacke_llt;
#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \
template<> struct lapacke_llt<EIGTYPE> \
{ \
template<typename MatrixType> \
static inline Index potrf(MatrixType& m, char uplo) \
{ \
lapack_int matrix_order; \
lapack_int size, lda, info, StorageOrder; \
EIGTYPE* a; \
eigen_assert(m.rows()==m.cols()); \
/* Set up parameters for ?potrf */ \
size = convert_index<lapack_int>(m.rows()); \
StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \
matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
a = &(m.coeffRef(0,0)); \
lda = convert_index<lapack_int>(m.outerStride()); \
\
info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \
info = (info==0) ? -1 : info>0 ? info-1 : size; \
return info; \
} \
}; \
template<> struct llt_inplace<EIGTYPE, Lower> \
{ \
template<typename MatrixType> \
static Index blocked(MatrixType& m) \
{ \
return lapacke_llt<EIGTYPE>::potrf(m, 'L'); \
} \
template<typename MatrixType, typename VectorType> \
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
{ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \
}; \
template<> struct llt_inplace<EIGTYPE, Upper> \
{ \
template<typename MatrixType> \
static Index blocked(MatrixType& m) \
{ \
return lapacke_llt<EIGTYPE>::potrf(m, 'U'); \
} \
template<typename MatrixType, typename VectorType> \
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
{ \
Transpose<MatrixType> matt(mat); \
return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \
} \
};
EIGEN_LAPACKE_LLT(double, double, d)
EIGEN_LAPACKE_LLT(float, float, s)
EIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z)
EIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c)
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_LLT_LAPACKE_H

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lib/eigen-3.4.0/Eigen/src/CholmodSupport/CholmodSupport.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_H
#define EIGEN_CHOLMODSUPPORT_H
namespace Eigen {
namespace internal {
template<typename Scalar> struct cholmod_configure_matrix;
template<> struct cholmod_configure_matrix<double> {
template<typename CholmodType>
static void run(CholmodType& mat) {
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_DOUBLE;
}
};
template<> struct cholmod_configure_matrix<std::complex<double> > {
template<typename CholmodType>
static void run(CholmodType& mat) {
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_DOUBLE;
}
};
// Other scalar types are not yet supported by Cholmod
// template<> struct cholmod_configure_matrix<float> {
// template<typename CholmodType>
// static void run(CholmodType& mat) {
// mat.xtype = CHOLMOD_REAL;
// mat.dtype = CHOLMOD_SINGLE;
// }
// };
//
// template<> struct cholmod_configure_matrix<std::complex<float> > {
// template<typename CholmodType>
// static void run(CholmodType& mat) {
// mat.xtype = CHOLMOD_COMPLEX;
// mat.dtype = CHOLMOD_SINGLE;
// }
// };
} // namespace internal
/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
* Note that the data are shared.
*/
template<typename _Scalar, int _Options, typename _StorageIndex>
cholmod_sparse viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_StorageIndex> > mat)
{
cholmod_sparse res;
res.nzmax = mat.nonZeros();
res.nrow = mat.rows();
res.ncol = mat.cols();
res.p = mat.outerIndexPtr();
res.i = mat.innerIndexPtr();
res.x = mat.valuePtr();
res.z = 0;
res.sorted = 1;
if(mat.isCompressed())
{
res.packed = 1;
res.nz = 0;
}
else
{
res.packed = 0;
res.nz = mat.innerNonZeroPtr();
}
res.dtype = 0;
res.stype = -1;
if (internal::is_same<_StorageIndex,int>::value)
{
res.itype = CHOLMOD_INT;
}
else if (internal::is_same<_StorageIndex,SuiteSparse_long>::value)
{
res.itype = CHOLMOD_LONG;
}
else
{
eigen_assert(false && "Index type not supported yet");
}
// setup res.xtype
internal::cholmod_configure_matrix<_Scalar>::run(res);
res.stype = 0;
return res;
}
template<typename _Scalar, int _Options, typename _Index>
const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
{
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
return res;
}
template<typename _Scalar, int _Options, typename _Index>
const cholmod_sparse viewAsCholmod(const SparseVector<_Scalar,_Options,_Index>& mat)
{
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
return res;
}
/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
* The data are not copied but shared. */
template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
{
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.matrix().const_cast_derived()));
if(UpLo==Upper) res.stype = 1;
if(UpLo==Lower) res.stype = -1;
// swap stype for rowmajor matrices (only works for real matrices)
EIGEN_STATIC_ASSERT((_Options & RowMajorBit) == 0 || NumTraits<_Scalar>::IsComplex == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
if(_Options & RowMajorBit) res.stype *=-1;
return res;
}
/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
* The data are not copied but shared. */
template<typename Derived>
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
{
EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
typedef typename Derived::Scalar Scalar;
cholmod_dense res;
res.nrow = mat.rows();
res.ncol = mat.cols();
res.nzmax = res.nrow * res.ncol;
res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
res.x = (void*)(mat.derived().data());
res.z = 0;
internal::cholmod_configure_matrix<Scalar>::run(res);
return res;
}
/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
* The data are not copied but shared. */
template<typename Scalar, int Flags, typename StorageIndex>
MappedSparseMatrix<Scalar,Flags,StorageIndex> viewAsEigen(cholmod_sparse& cm)
{
return MappedSparseMatrix<Scalar,Flags,StorageIndex>
(cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],
static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );
}
namespace internal {
// template specializations for int and long that call the correct cholmod method
#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name) \
template<typename _StorageIndex> inline ret cm_ ## name (cholmod_common &Common) { return cholmod_ ## name (&Common); } \
template<> inline ret cm_ ## name<SuiteSparse_long> (cholmod_common &Common) { return cholmod_l_ ## name (&Common); }
#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1) \
template<typename _StorageIndex> inline ret cm_ ## name (t1& a1, cholmod_common &Common) { return cholmod_ ## name (&a1, &Common); } \
template<> inline ret cm_ ## name<SuiteSparse_long> (t1& a1, cholmod_common &Common) { return cholmod_l_ ## name (&a1, &Common); }
EIGEN_CHOLMOD_SPECIALIZE0(int, start)
EIGEN_CHOLMOD_SPECIALIZE0(int, finish)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)
EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
template<typename _StorageIndex> inline cholmod_dense* cm_solve (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_solve (sys, &L, &B, &Common); }
template<> inline cholmod_dense* cm_solve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_l_solve (sys, &L, &B, &Common); }
template<typename _StorageIndex> inline cholmod_sparse* cm_spsolve (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_spsolve (sys, &L, &B, &Common); }
template<> inline cholmod_sparse* cm_spsolve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_l_spsolve (sys, &L, &B, &Common); }
template<typename _StorageIndex>
inline int cm_factorize_p (cholmod_sparse* A, double beta[2], _StorageIndex* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_factorize_p (A, beta, fset, fsize, L, &Common); }
template<>
inline int cm_factorize_p<SuiteSparse_long> (cholmod_sparse* A, double beta[2], SuiteSparse_long* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_l_factorize_p (A, beta, fset, fsize, L, &Common); }
#undef EIGEN_CHOLMOD_SPECIALIZE0
#undef EIGEN_CHOLMOD_SPECIALIZE1
} // namespace internal
enum CholmodMode {
CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
};
/** \ingroup CholmodSupport_Module
* \class CholmodBase
* \brief The base class for the direct Cholesky factorization of Cholmod
* \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
*/
template<typename _MatrixType, int _UpLo, typename Derived>
class CholmodBase : public SparseSolverBase<Derived>
{
protected:
typedef SparseSolverBase<Derived> Base;
using Base::derived;
using Base::m_isInitialized;
public:
typedef _MatrixType MatrixType;
enum { UpLo = _UpLo };
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef MatrixType CholMatrixType;
typedef typename MatrixType::StorageIndex StorageIndex;
enum {
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
public:
CholmodBase()
: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
{
EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
internal::cm_start<StorageIndex>(m_cholmod);
}
explicit CholmodBase(const MatrixType& matrix)
: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
{
EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
internal::cm_start<StorageIndex>(m_cholmod);
compute(matrix);
}
~CholmodBase()
{
if(m_cholmodFactor)
internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
internal::cm_finish<StorageIndex>(m_cholmod);
}
inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** Computes the sparse Cholesky decomposition of \a matrix */
Derived& compute(const MatrixType& matrix)
{
analyzePattern(matrix);
factorize(matrix);
return derived();
}
/** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
if(m_cholmodFactor)
{
internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
m_cholmodFactor = 0;
}
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
m_cholmodFactor = internal::cm_analyze<StorageIndex>(A, m_cholmod);
this->m_isInitialized = true;
this->m_info = Success;
m_analysisIsOk = true;
m_factorizationIsOk = false;
}
/** Performs a numeric decomposition of \a matrix
*
* The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
*
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix)
{
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
internal::cm_factorize_p<StorageIndex>(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod);
// If the factorization failed, minor is the column at which it did. On success minor == n.
this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
m_factorizationIsOk = true;
}
/** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
* See the Cholmod user guide for details. */
cholmod_common& cholmod() { return m_cholmod; }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal */
template<typename Rhs,typename Dest>
void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size==b.rows());
// Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
cholmod_dense b_cd = viewAsCholmod(b_ref);
cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod);
if(!x_cd)
{
this->m_info = NumericalIssue;
return;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
// NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
}
/** \internal */
template<typename RhsDerived, typename DestDerived>
void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size==b.rows());
// note: cs stands for Cholmod Sparse
Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());
cholmod_sparse b_cs = viewAsCholmod(b_ref);
cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod);
if(!x_cs)
{
this->m_info = NumericalIssue;
return;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
// NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's sparse solver)
dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);
internal::cm_free_sparse<StorageIndex>(x_cs, m_cholmod);
}
#endif // EIGEN_PARSED_BY_DOXYGEN
/** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
*
* During the numerical factorization, an offset term is added to the diagonal coefficients:\n
* \c d_ii = \a offset + \c d_ii
*
* The default is \a offset=0.
*
* \returns a reference to \c *this.
*/
Derived& setShift(const RealScalar& offset)
{
m_shiftOffset[0] = double(offset);
return derived();
}
/** \returns the determinant of the underlying matrix from the current factorization */
Scalar determinant() const
{
using std::exp;
return exp(logDeterminant());
}
/** \returns the log determinant of the underlying matrix from the current factorization */
Scalar logDeterminant() const
{
using std::log;
using numext::real;
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
RealScalar logDet = 0;
Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
if (m_cholmodFactor->is_super)
{
// Supernodal factorization stored as a packed list of dense column-major blocs,
// as described by the following structure:
// super[k] == index of the first column of the j-th super node
StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);
// pi[k] == offset to the description of row indices
StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
// px[k] == offset to the respective dense block
StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
Index nb_super_nodes = m_cholmodFactor->nsuper;
for (Index k=0; k < nb_super_nodes; ++k)
{
StorageIndex ncols = super[k + 1] - super[k];
StorageIndex nrows = pi[k + 1] - pi[k];
Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
logDet += sk.real().log().sum();
}
}
else
{
// Simplicial factorization stored as standard CSC matrix.
StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
Index size = m_cholmodFactor->n;
for (Index k=0; k<size; ++k)
logDet += log(real( x[p[k]] ));
}
if (m_cholmodFactor->is_ll)
logDet *= 2.0;
return logDet;
};
template<typename Stream>
void dumpMemory(Stream& /*s*/)
{}
protected:
mutable cholmod_common m_cholmod;
cholmod_factor* m_cholmodFactor;
double m_shiftOffset[2];
mutable ComputationInfo m_info;
int m_factorizationIsOk;
int m_analysisIsOk;
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLLT
* \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLLT() : Base() { init(); }
CholmodSimplicialLLT(const MatrixType& matrix) : Base()
{
init();
this->compute(matrix);
}
~CholmodSimplicialLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLDLT
* \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLDLT() : Base() { init(); }
CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
{
init();
this->compute(matrix);
}
~CholmodSimplicialLDLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSupernodalLLT
* \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
* using the Cholmod library.
* This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSupernodalLLT() : Base() { init(); }
CholmodSupernodalLLT(const MatrixType& matrix) : Base()
{
init();
this->compute(matrix);
}
~CholmodSupernodalLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodDecomposition
* \brief A general Cholesky factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
* using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* This variant permits to change the underlying Cholesky method at runtime.
* On the other hand, it does not provide access to the result of the factorization.
* The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodDecomposition() : Base() { init(); }
CholmodDecomposition(const MatrixType& matrix) : Base()
{
init();
this->compute(matrix);
}
~CholmodDecomposition() {}
void setMode(CholmodMode mode)
{
switch(mode)
{
case CholmodAuto:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
break;
case CholmodSimplicialLLt:
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
break;
case CholmodSupernodalLLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
break;
case CholmodLDLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
break;
default:
break;
}
}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
}
};
} // end namespace Eigen
#endif // EIGEN_CHOLMODSUPPORT_H

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@ -1,413 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARITHMETIC_SEQUENCE_H
#define EIGEN_ARITHMETIC_SEQUENCE_H
namespace Eigen {
namespace internal {
#if (!EIGEN_HAS_CXX11) || !((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48)
template<typename T> struct aseq_negate {};
template<> struct aseq_negate<Index> {
typedef Index type;
};
template<int N> struct aseq_negate<FixedInt<N> > {
typedef FixedInt<-N> type;
};
// Compilation error in the following case:
template<> struct aseq_negate<FixedInt<DynamicIndex> > {};
template<typename FirstType,typename SizeType,typename IncrType,
bool FirstIsSymbolic=symbolic::is_symbolic<FirstType>::value,
bool SizeIsSymbolic =symbolic::is_symbolic<SizeType>::value>
struct aseq_reverse_first_type {
typedef Index type;
};
template<typename FirstType,typename SizeType,typename IncrType>
struct aseq_reverse_first_type<FirstType,SizeType,IncrType,true,true> {
typedef symbolic::AddExpr<FirstType,
symbolic::ProductExpr<symbolic::AddExpr<SizeType,symbolic::ValueExpr<FixedInt<-1> > >,
symbolic::ValueExpr<IncrType> >
> type;
};
template<typename SizeType,typename IncrType,typename EnableIf = void>
struct aseq_reverse_first_type_aux {
typedef Index type;
};
template<typename SizeType,typename IncrType>
struct aseq_reverse_first_type_aux<SizeType,IncrType,typename internal::enable_if<bool((SizeType::value+IncrType::value)|0x1)>::type> {
typedef FixedInt<(SizeType::value-1)*IncrType::value> type;
};
template<typename FirstType,typename SizeType,typename IncrType>
struct aseq_reverse_first_type<FirstType,SizeType,IncrType,true,false> {
typedef typename aseq_reverse_first_type_aux<SizeType,IncrType>::type Aux;
typedef symbolic::AddExpr<FirstType,symbolic::ValueExpr<Aux> > type;
};
template<typename FirstType,typename SizeType,typename IncrType>
struct aseq_reverse_first_type<FirstType,SizeType,IncrType,false,true> {
typedef symbolic::AddExpr<symbolic::ProductExpr<symbolic::AddExpr<SizeType,symbolic::ValueExpr<FixedInt<-1> > >,
symbolic::ValueExpr<IncrType> >,
symbolic::ValueExpr<> > type;
};
#endif
// Helper to cleanup the type of the increment:
template<typename T> struct cleanup_seq_incr {
typedef typename cleanup_index_type<T,DynamicIndex>::type type;
};
}
//--------------------------------------------------------------------------------
// seq(first,last,incr) and seqN(first,size,incr)
//--------------------------------------------------------------------------------
template<typename FirstType=Index,typename SizeType=Index,typename IncrType=internal::FixedInt<1> >
class ArithmeticSequence;
template<typename FirstType,typename SizeType,typename IncrType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type,
typename internal::cleanup_seq_incr<IncrType>::type >
seqN(FirstType first, SizeType size, IncrType incr);
/** \class ArithmeticSequence
* \ingroup Core_Module
*
* This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by
* its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride)
* that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i.
*
* It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments
* of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the
* only way it is used.
*
* \tparam FirstType type of the first element, usually an Index,
* but internally it can be a symbolic expression
* \tparam SizeType type representing the size of the sequence, usually an Index
* or a compile time integral constant. Internally, it can also be a symbolic expression
* \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is compile-time 1)
*
* \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView
*/
template<typename FirstType,typename SizeType,typename IncrType>
class ArithmeticSequence
{
public:
ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {}
ArithmeticSequence(FirstType first, SizeType size, IncrType incr) : m_first(first), m_size(size), m_incr(incr) {}
enum {
SizeAtCompileTime = internal::get_fixed_value<SizeType>::value,
IncrAtCompileTime = internal::get_fixed_value<IncrType,DynamicIndex>::value
};
/** \returns the size, i.e., number of elements, of the sequence */
Index size() const { return m_size; }
/** \returns the first element \f$ a_0 \f$ in the sequence */
Index first() const { return m_first; }
/** \returns the value \f$ a_i \f$ at index \a i in the sequence. */
Index operator[](Index i) const { return m_first + i * m_incr; }
const FirstType& firstObject() const { return m_first; }
const SizeType& sizeObject() const { return m_size; }
const IncrType& incrObject() const { return m_incr; }
protected:
FirstType m_first;
SizeType m_size;
IncrType m_incr;
public:
#if EIGEN_HAS_CXX11 && ((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48)
auto reverse() const -> decltype(Eigen::seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr)) {
return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr);
}
#else
protected:
typedef typename internal::aseq_negate<IncrType>::type ReverseIncrType;
typedef typename internal::aseq_reverse_first_type<FirstType,SizeType,IncrType>::type ReverseFirstType;
public:
ArithmeticSequence<ReverseFirstType,SizeType,ReverseIncrType>
reverse() const {
return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr);
}
#endif
};
/** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr
*
* \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
template<typename FirstType,typename SizeType,typename IncrType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type >
seqN(FirstType first, SizeType size, IncrType incr) {
return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type>(first,size,incr);
}
/** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment
*
* \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */
template<typename FirstType,typename SizeType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type >
seqN(FirstType first, SizeType size) {
return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type>(first,size);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a incr
*
* It is essentially an alias to:
* \code
* seqN(f, (l-f+incr)/incr, incr);
* \endcode
*
* \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType)
*/
template<typename FirstType,typename LastType, typename IncrType>
auto seq(FirstType f, LastType l, IncrType incr);
/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment
*
* It is essentially an alias to:
* \code
* seqN(f,l-f+1);
* \endcode
*
* \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType)
*/
template<typename FirstType,typename LastType>
auto seq(FirstType f, LastType l);
#else // EIGEN_PARSED_BY_DOXYGEN
#if EIGEN_HAS_CXX11
template<typename FirstType,typename LastType>
auto seq(FirstType f, LastType l) -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
( typename internal::cleanup_index_type<LastType>::type(l)
- typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>())))
{
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(typename internal::cleanup_index_type<LastType>::type(l)
-typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>()));
}
template<typename FirstType,typename LastType, typename IncrType>
auto seq(FirstType f, LastType l, IncrType incr)
-> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
( typename internal::cleanup_index_type<LastType>::type(l)
- typename internal::cleanup_index_type<FirstType>::type(f)+typename internal::cleanup_seq_incr<IncrType>::type(incr)
) / typename internal::cleanup_seq_incr<IncrType>::type(incr),
typename internal::cleanup_seq_incr<IncrType>::type(incr)))
{
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
( typename internal::cleanup_index_type<LastType>::type(l)
-typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr)) / CleanedIncrType(incr),
CleanedIncrType(incr));
}
#else // EIGEN_HAS_CXX11
template<typename FirstType,typename LastType>
typename internal::enable_if<!(symbolic::is_symbolic<FirstType>::value || symbolic::is_symbolic<LastType>::value),
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,Index> >::type
seq(FirstType f, LastType l)
{
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
Index((typename internal::cleanup_index_type<LastType>::type(l)-typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>())));
}
template<typename FirstTypeDerived,typename LastType>
typename internal::enable_if<!symbolic::is_symbolic<LastType>::value,
ArithmeticSequence<FirstTypeDerived, symbolic::AddExpr<symbolic::AddExpr<symbolic::NegateExpr<FirstTypeDerived>,symbolic::ValueExpr<> >,
symbolic::ValueExpr<internal::FixedInt<1> > > > >::type
seq(const symbolic::BaseExpr<FirstTypeDerived> &f, LastType l)
{
return seqN(f.derived(),(typename internal::cleanup_index_type<LastType>::type(l)-f.derived()+fix<1>()));
}
template<typename FirstType,typename LastTypeDerived>
typename internal::enable_if<!symbolic::is_symbolic<FirstType>::value,
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::ValueExpr<> >,
symbolic::ValueExpr<internal::FixedInt<1> > > > >::type
seq(FirstType f, const symbolic::BaseExpr<LastTypeDerived> &l)
{
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),(l.derived()-typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>()));
}
template<typename FirstTypeDerived,typename LastTypeDerived>
ArithmeticSequence<FirstTypeDerived,
symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::NegateExpr<FirstTypeDerived> >,symbolic::ValueExpr<internal::FixedInt<1> > > >
seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<LastTypeDerived> &l)
{
return seqN(f.derived(),(l.derived()-f.derived()+fix<1>()));
}
template<typename FirstType,typename LastType, typename IncrType>
typename internal::enable_if<!(symbolic::is_symbolic<FirstType>::value || symbolic::is_symbolic<LastType>::value),
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,Index,typename internal::cleanup_seq_incr<IncrType>::type> >::type
seq(FirstType f, LastType l, IncrType incr)
{
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
Index((typename internal::cleanup_index_type<LastType>::type(l)-typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr)), incr);
}
template<typename FirstTypeDerived,typename LastType, typename IncrType>
typename internal::enable_if<!symbolic::is_symbolic<LastType>::value,
ArithmeticSequence<FirstTypeDerived,
symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<symbolic::NegateExpr<FirstTypeDerived>,
symbolic::ValueExpr<> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
typename internal::cleanup_seq_incr<IncrType>::type> >::type
seq(const symbolic::BaseExpr<FirstTypeDerived> &f, LastType l, IncrType incr)
{
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(f.derived(),(typename internal::cleanup_index_type<LastType>::type(l)-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr);
}
template<typename FirstType,typename LastTypeDerived, typename IncrType>
typename internal::enable_if<!symbolic::is_symbolic<FirstType>::value,
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::ValueExpr<> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
typename internal::cleanup_seq_incr<IncrType>::type> >::type
seq(FirstType f, const symbolic::BaseExpr<LastTypeDerived> &l, IncrType incr)
{
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(l.derived()-typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr), incr);
}
template<typename FirstTypeDerived,typename LastTypeDerived, typename IncrType>
ArithmeticSequence<FirstTypeDerived,
symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,
symbolic::NegateExpr<FirstTypeDerived> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >,
typename internal::cleanup_seq_incr<IncrType>::type>
seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<LastTypeDerived> &l, IncrType incr)
{
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(f.derived(),(l.derived()-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr);
}
#endif // EIGEN_HAS_CXX11
#endif // EIGEN_PARSED_BY_DOXYGEN
#if EIGEN_HAS_CXX11 || defined(EIGEN_PARSED_BY_DOXYGEN)
/** \cpp11
* \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr.
*
* It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode
*
* \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
template<typename SizeType,typename IncrType>
auto lastN(SizeType size, IncrType incr)
-> decltype(seqN(Eigen::last-(size-fix<1>())*incr, size, incr))
{
return seqN(Eigen::last-(size-fix<1>())*incr, size, incr);
}
/** \cpp11
* \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment.
*
* It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode
*
* \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */
template<typename SizeType>
auto lastN(SizeType size)
-> decltype(seqN(Eigen::last+fix<1>()-size, size))
{
return seqN(Eigen::last+fix<1>()-size, size);
}
#endif
namespace internal {
// Convert a symbolic span into a usable one (i.e., remove last/end "keywords")
template<typename T>
struct make_size_type {
typedef typename internal::conditional<symbolic::is_symbolic<T>::value, Index, T>::type type;
};
template<typename FirstType,typename SizeType,typename IncrType,int XprSize>
struct IndexedViewCompatibleType<ArithmeticSequence<FirstType,SizeType,IncrType>, XprSize> {
typedef ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType> type;
};
template<typename FirstType,typename SizeType,typename IncrType>
ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType>
makeIndexedViewCompatible(const ArithmeticSequence<FirstType,SizeType,IncrType>& ids, Index size,SpecializedType) {
return ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType>(
eval_expr_given_size(ids.firstObject(),size),eval_expr_given_size(ids.sizeObject(),size),ids.incrObject());
}
template<typename FirstType,typename SizeType,typename IncrType>
struct get_compile_time_incr<ArithmeticSequence<FirstType,SizeType,IncrType> > {
enum { value = get_fixed_value<IncrType,DynamicIndex>::value };
};
} // end namespace internal
/** \namespace Eigen::indexing
* \ingroup Core_Module
*
* The sole purpose of this namespace is to be able to import all functions
* and symbols that are expected to be used within operator() for indexing
* and slicing. If you already imported the whole Eigen namespace:
* \code using namespace Eigen; \endcode
* then you are already all set. Otherwise, if you don't want/cannot import
* the whole Eigen namespace, the following line:
* \code using namespace Eigen::indexing; \endcode
* is equivalent to:
* \code
using Eigen::all;
using Eigen::seq;
using Eigen::seqN;
using Eigen::lastN; // c++11 only
using Eigen::last;
using Eigen::lastp1;
using Eigen::fix;
\endcode
*/
namespace indexing {
using Eigen::all;
using Eigen::seq;
using Eigen::seqN;
#if EIGEN_HAS_CXX11
using Eigen::lastN;
#endif
using Eigen::last;
using Eigen::lastp1;
using Eigen::fix;
}
} // end namespace Eigen
#endif // EIGEN_ARITHMETIC_SEQUENCE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAY_H
#define EIGEN_ARRAY_H
namespace Eigen {
namespace internal {
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
typedef ArrayXpr XprKind;
typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
};
}
/** \class Array
* \ingroup Core_Module
*
* \brief General-purpose arrays with easy API for coefficient-wise operations
*
* The %Array class is very similar to the Matrix class. It provides
* general-purpose one- and two-dimensional arrays. The difference between the
* %Array and the %Matrix class is primarily in the API: the API for the
* %Array class provides easy access to coefficient-wise operations, while the
* API for the %Matrix class provides easy access to linear-algebra
* operations.
*
* See documentation of class Matrix for detailed information on the template parameters
* storage layout.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
*
* \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
*/
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Array
: public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
public:
typedef PlainObjectBase<Array> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Array)
enum { Options = _Options };
typedef typename Base::PlainObject PlainObject;
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
public:
using Base::base;
using Base::coeff;
using Base::coeffRef;
/**
* The usage of
* using Base::operator=;
* fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
* the usage of 'using'. This should be done only for operator=.
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
{
return Base::operator=(other);
}
/** Set all the entries to \a value.
* \sa DenseBase::setConstant(), DenseBase::fill()
*/
/* This overload is needed because the usage of
* using Base::operator=;
* fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
* the usage of 'using'. This should be done only for operator=.
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array& operator=(const Scalar &value)
{
Base::setConstant(value);
return *this;
}
/** 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_DEVICE_FUNC
EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other)
{
return Base::_set(other);
}
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array& operator=(const Array& other)
{
return Base::_set(other);
}
/** Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array() : Base()
{
Base::_check_template_params();
EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
// FIXME is it still needed ??
/** \internal */
EIGEN_DEVICE_FUNC
Array(internal::constructor_without_unaligned_array_assert)
: Base(internal::constructor_without_unaligned_array_assert())
{
Base::_check_template_params();
EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
}
#endif
#if EIGEN_HAS_RVALUE_REFERENCES
EIGEN_DEVICE_FUNC
Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
: Base(std::move(other))
{
Base::_check_template_params();
}
EIGEN_DEVICE_FUNC
Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
{
Base::operator=(std::move(other));
return *this;
}
#endif
#if EIGEN_HAS_CXX11
/** \copydoc PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*
* Example: \include Array_variadic_ctor_cxx11.cpp
* Output: \verbinclude Array_variadic_ctor_cxx11.out
*
* \sa Array(const std::initializer_list<std::initializer_list<Scalar>>&)
* \sa Array(const Scalar&), Array(const Scalar&,const Scalar&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
: Base(a0, a1, a2, a3, args...) {}
/** \brief Constructs an array and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11
*
* In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
*
* Example: \include Array_initializer_list_23_cxx11.cpp
* Output: \verbinclude Array_initializer_list_23_cxx11.out
*
* Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered.
*
* In the case of a compile-time column 1D array, implicit transposition from a single row is allowed.
* Therefore <code> Array<int,Dynamic,1>{{1,2,3,4,5}}</code> is legal and the more verbose syntax
* <code>Array<int,Dynamic,1>{{1},{2},{3},{4},{5}}</code> can be avoided:
*
* Example: \include Array_initializer_list_vector_cxx11.cpp
* Output: \verbinclude Array_initializer_list_vector_cxx11.out
*
* In the case of fixed-sized arrays, the initializer list sizes must exactly match the array sizes,
* and implicit transposition is allowed for compile-time 1D arrays only.
*
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const std::initializer_list<std::initializer_list<Scalar>>& list) : Base(list) {}
#endif // end EIGEN_HAS_CXX11
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename T>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE explicit Array(const T& x)
{
Base::_check_template_params();
Base::template _init1<T>(x);
}
template<typename T0, typename T1>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1)
{
Base::_check_template_params();
this->template _init2<T0,T1>(val0, val1);
}
#else
/** \brief Constructs a fixed-sized array initialized with coefficients starting at \a data */
EIGEN_DEVICE_FUNC explicit Array(const Scalar *data);
/** 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 Array() instead.
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE explicit Array(Index dim);
/** constructs an initialized 1x1 Array with the given coefficient
* \sa const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args */
Array(const Scalar& value);
/** constructs an uninitialized array with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size arrays. For fixed-size arrays,
* it is redundant to pass these parameters, so one should use the default constructor
* Array() instead. */
Array(Index rows, Index cols);
/** constructs an initialized 2D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) */
Array(const Scalar& val0, const Scalar& val1);
#endif // end EIGEN_PARSED_BY_DOXYGEN
/** constructs an initialized 3D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
m_storage.data()[0] = val0;
m_storage.data()[1] = val1;
m_storage.data()[2] = val2;
}
/** constructs an initialized 4D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
m_storage.data()[0] = val0;
m_storage.data()[1] = val1;
m_storage.data()[2] = val2;
m_storage.data()[3] = val3;
}
/** Copy constructor */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const Array& other)
: Base(other)
{ }
private:
struct PrivateType {};
public:
/** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other,
typename internal::enable_if<internal::is_convertible<typename OtherDerived::Scalar,Scalar>::value,
PrivateType>::type = PrivateType())
: Base(other.derived())
{ }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT{ return 1; }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
#ifdef EIGEN_ARRAY_PLUGIN
#include EIGEN_ARRAY_PLUGIN
#endif
private:
template<typename MatrixType, typename OtherDerived, bool SwapPointers>
friend struct internal::matrix_swap_impl;
};
/** \defgroup arraytypedefs Global array typedefs
* \ingroup Core_Module
*
* %Eigen defines several typedef shortcuts for most common 1D and 2D array types.
*
* The general patterns are the following:
*
* \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
* and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
* for complex double.
*
* For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
*
* There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
* a fixed-size 1D array of 4 complex floats.
*
* With \cpp11, template alias are also defined for common sizes.
* They follow the same pattern as above except that the scalar type suffix is replaced by a
* template parameter, i.e.:
* - `ArrayRowsCols<Type>` where `Rows` and `Cols` can be \c 2,\c 3,\c 4, or \c X for fixed or dynamic size.
* - `ArraySize<Type>` where `Size` can be \c 2,\c 3,\c 4 or \c X for fixed or dynamic size 1D arrays.
*
* \sa class Array
*/
#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, 1> Array##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_ARRAY_TYPEDEFS
#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
#if EIGEN_HAS_CXX11
#define EIGEN_MAKE_ARRAY_TYPEDEFS(Size, SizeSuffix) \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##SizeSuffix##SizeSuffix = Array<Type, Size, Size>; \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##SizeSuffix = Array<Type, Size, 1>;
#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Size) \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##Size##X = Array<Type, Size, Dynamic>; \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##X##Size = Array<Type, Dynamic, Size>;
EIGEN_MAKE_ARRAY_TYPEDEFS(2, 2)
EIGEN_MAKE_ARRAY_TYPEDEFS(3, 3)
EIGEN_MAKE_ARRAY_TYPEDEFS(4, 4)
EIGEN_MAKE_ARRAY_TYPEDEFS(Dynamic, X)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(2)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(3)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4)
#undef EIGEN_MAKE_ARRAY_TYPEDEFS
#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
#endif // EIGEN_HAS_CXX11
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
using Eigen::Matrix##SizeSuffix##TypeSuffix; \
using Eigen::Vector##SizeSuffix##TypeSuffix; \
using Eigen::RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
#define EIGEN_USING_ARRAY_TYPEDEFS \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
} // end namespace Eigen
#endif // EIGEN_ARRAY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYBASE_H
#define EIGEN_ARRAYBASE_H
namespace Eigen {
template<typename ExpressionType> class MatrixWrapper;
/** \class ArrayBase
* \ingroup Core_Module
*
* \brief Base class for all 1D and 2D array, and related expressions
*
* An array is similar to a dense vector or matrix. While matrices are mathematical
* objects with well defined linear algebra operators, an array is just a collection
* of scalar values arranged in a one or two dimensionnal fashion. As the main consequence,
* all operations applied to an array are performed coefficient wise. Furthermore,
* arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
* constructors allowing to easily write generic code working for both scalar values
* and arrays.
*
* This class is the base that is inherited by all array expression types.
*
* \tparam Derived is the derived type, e.g., an array or an expression type.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
*
* \sa class MatrixBase, \ref TopicClassHierarchy
*/
template<typename Derived> class ArrayBase
: public DenseBase<Derived>
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** The base class for a given storage type. */
typedef ArrayBase StorageBaseType;
typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::operator-;
using Base::operator=;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Base::PlainObject PlainObject;
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
#define EIGEN_DOC_UNARY_ADDONS(X,Y)
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/ArrayCwiseUnaryOps.h"
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# include "../plugins/ArrayCwiseBinaryOps.h"
# ifdef EIGEN_ARRAYBASE_PLUGIN
# include EIGEN_ARRAYBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_UNARY_ADDONS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const ArrayBase& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
/** Set all the entries to \a value.
* \sa DenseBase::setConstant(), DenseBase::fill() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const Scalar &value)
{ Base::setConstant(value); return derived(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator+=(const Scalar& scalar);
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator-=(const Scalar& scalar);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator+=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator-=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator*=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator/=(const ArrayBase<OtherDerived>& other);
public:
EIGEN_DEVICE_FUNC
ArrayBase<Derived>& array() { return *this; }
EIGEN_DEVICE_FUNC
const ArrayBase<Derived>& array() const { return *this; }
/** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array
* \sa MatrixBase::array() */
EIGEN_DEVICE_FUNC
MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }
EIGEN_DEVICE_FUNC
const MatrixWrapper<const Derived> matrix() const { return MatrixWrapper<const Derived>(derived()); }
// template<typename Dest>
// inline void evalTo(Dest& dst) const { dst = matrix(); }
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(ArrayBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(ArrayBase)
private:
explicit ArrayBase(Index);
ArrayBase(Index,Index);
template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
};
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
{
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
{
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this * \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
{
call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this / \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
{
call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_ARRAYBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYWRAPPER_H
#define EIGEN_ARRAYWRAPPER_H
namespace Eigen {
/** \class ArrayWrapper
* \ingroup Core_Module
*
* \brief Expression of a mathematical vector or matrix as an array object
*
* This class is the return type of MatrixBase::array(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::array(), class MatrixWrapper
*/
namespace internal {
template<typename ExpressionType>
struct traits<ArrayWrapper<ExpressionType> >
: public traits<typename remove_all<typename ExpressionType::Nested>::type >
{
typedef ArrayXpr XprKind;
// Let's remove NestByRefBit
enum {
Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
};
};
}
template<typename ExpressionType>
class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
{
public:
typedef ArrayBase<ArrayWrapper> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
typedef typename internal::remove_all<ExpressionType>::type NestedExpression;
typedef typename internal::conditional<
internal::is_lvalue<ExpressionType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
using Base::coeffRef;
EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
EIGEN_DEVICE_FUNC
inline const Scalar* data() const { return m_expression.data(); }
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index rowId, Index colId) const
{
return m_expression.coeffRef(rowId, colId);
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index index) const
{
return m_expression.coeffRef(index);
}
template<typename Dest>
EIGEN_DEVICE_FUNC
inline void evalTo(Dest& dst) const { dst = m_expression; }
EIGEN_DEVICE_FUNC
const typename internal::remove_all<NestedExpressionType>::type&
nestedExpression() const
{
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
EIGEN_DEVICE_FUNC
void resize(Index newSize) { m_expression.resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
EIGEN_DEVICE_FUNC
void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
protected:
NestedExpressionType m_expression;
};
/** \class MatrixWrapper
* \ingroup Core_Module
*
* \brief Expression of an array as a mathematical vector or matrix
*
* This class is the return type of ArrayBase::matrix(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::matrix(), class ArrayWrapper
*/
namespace internal {
template<typename ExpressionType>
struct traits<MatrixWrapper<ExpressionType> >
: public traits<typename remove_all<typename ExpressionType::Nested>::type >
{
typedef MatrixXpr XprKind;
// Let's remove NestByRefBit
enum {
Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
};
};
}
template<typename ExpressionType>
class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
{
public:
typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
typedef typename internal::remove_all<ExpressionType>::type NestedExpression;
typedef typename internal::conditional<
internal::is_lvalue<ExpressionType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
using Base::coeffRef;
EIGEN_DEVICE_FUNC
explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
EIGEN_DEVICE_FUNC
inline const Scalar* data() const { return m_expression.data(); }
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index rowId, Index colId) const
{
return m_expression.derived().coeffRef(rowId, colId);
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index index) const
{
return m_expression.coeffRef(index);
}
EIGEN_DEVICE_FUNC
const typename internal::remove_all<NestedExpressionType>::type&
nestedExpression() const
{
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
EIGEN_DEVICE_FUNC
void resize(Index newSize) { m_expression.resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
EIGEN_DEVICE_FUNC
void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
protected:
NestedExpressionType m_expression;
};
} // end namespace Eigen
#endif // EIGEN_ARRAYWRAPPER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ASSIGN_H
#define EIGEN_ASSIGN_H
namespace Eigen {
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
::lazyAssign(const DenseBase<OtherDerived>& other)
{
enum{
SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
};
EIGEN_STATIC_ASSERT_LVALUE(Derived)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
eigen_assert(rows() == other.rows() && cols() == other.cols());
internal::call_assignment_no_alias(derived(),other.derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
{
internal::call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
{
other.derived().evalTo(derived());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_ASSIGN_H

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/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to Intel(R) MKL
* MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()
********************************************************************************
*/
#ifndef EIGEN_ASSIGN_VML_H
#define EIGEN_ASSIGN_VML_H
namespace Eigen {
namespace internal {
template<typename Dst, typename Src>
class vml_assign_traits
{
private:
enum {
DstHasDirectAccess = Dst::Flags & DirectAccessBit,
SrcHasDirectAccess = Src::Flags & DirectAccessBit,
StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),
InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
: int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime)
: int(Dst::RowsAtCompileTime),
InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
: int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
: int(Dst::MaxRowsAtCompileTime),
MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,
MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD
};
public:
enum {
EnableVml = MightEnableVml && LargeEnough,
Traversal = MightLinearize ? LinearTraversal : DefaultTraversal
};
};
#define EIGEN_PP_EXPAND(ARG) ARG
#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
#define EIGEN_VMLMODE_EXPAND_xLA , VML_HA
#else
#define EIGEN_VMLMODE_EXPAND_xLA , VML_LA
#endif
#define EIGEN_VMLMODE_EXPAND_x_
#define EIGEN_VMLMODE_PREFIX_xLA vm
#define EIGEN_VMLMODE_PREFIX_x_ v
#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_x,VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
template< typename DstXprType, typename SrcXprNested> \
struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE,EIGENTYPE>, \
Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> { \
typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType; \
static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) { \
resize_if_allowed(dst, src, func); \
eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) { \
VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(), \
(VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \
} else { \
const Index outerSize = dst.outerSize(); \
for(Index outer = 0; outer < outerSize; ++outer) { \
const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) : \
&(src.nestedExpression().coeffRef(0, outer)); \
EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \
VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, \
(VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} \
} \
} \
}; \
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),s##VMLOP), float, float, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),d##VMLOP), double, double, VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),c##VMLOP), scomplex, MKL_Complex8, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),z##VMLOP), dcomplex, MKL_Complex16, VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin, Sin, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin, Asin, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh, Sinh, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cos, Cos, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(acos, Acos, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cosh, Cosh, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tan, Tan, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(atan, Atan, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tanh, Tanh, LA)
// EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(exp, Exp, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log, Ln, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log10, Log10, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sqrt, Sqrt, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil, Ceil, _)
#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
template< typename DstXprType, typename SrcXprNested, typename Plain> \
struct Assignment<DstXprType, CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \
const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> >, assign_op<EIGENTYPE,EIGENTYPE>, \
Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> { \
typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \
const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> > SrcXprType; \
static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) { \
resize_if_allowed(dst, src, func); \
eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.rhs().functor().m_other); \
if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) \
{ \
VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent, \
(VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \
} else { \
const Index outerSize = dst.outerSize(); \
for(Index outer = 0; outer < outerSize; ++outer) { \
const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) : \
&(src.lhs().coeffRef(0, outer)); \
EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \
VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent, \
(VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} \
} \
} \
};
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmsPowx, float, float, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdPowx, double, double, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcPowx, scomplex, MKL_Complex8, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzPowx, dcomplex, MKL_Complex16, LA)
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_ASSIGN_VML_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BANDMATRIX_H
#define EIGEN_BANDMATRIX_H
namespace Eigen {
namespace internal {
template<typename Derived>
class BandMatrixBase : public EigenBase<Derived>
{
public:
enum {
Flags = internal::traits<Derived>::Flags,
CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
Supers = internal::traits<Derived>::Supers,
Subs = internal::traits<Derived>::Subs,
Options = internal::traits<Derived>::Options
};
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
typedef typename DenseMatrixType::StorageIndex StorageIndex;
typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
typedef EigenBase<Derived> Base;
protected:
enum {
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
? 1 + Supers + Subs
: Dynamic,
SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
};
public:
using Base::derived;
using Base::rows;
using Base::cols;
/** \returns the number of super diagonals */
inline Index supers() const { return derived().supers(); }
/** \returns the number of sub diagonals */
inline Index subs() const { return derived().subs(); }
/** \returns an expression of the underlying coefficient matrix */
inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
/** \returns an expression of the underlying coefficient matrix */
inline CoefficientsType& coeffs() { return derived().coeffs(); }
/** \returns a vector expression of the \a i -th column,
* only the meaningful part is returned.
* \warning the internal storage must be column major. */
inline Block<CoefficientsType,Dynamic,1> col(Index i)
{
EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
Index start = 0;
Index len = coeffs().rows();
if (i<=supers())
{
start = supers()-i;
len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
}
else if (i>=rows()-subs())
len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
}
/** \returns a vector expression of the main diagonal */
inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
{ return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
/** \returns a vector expression of the main diagonal (const version) */
inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
{ return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
template<int Index> struct DiagonalIntReturnType {
enum {
ReturnOpposite = (int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)),
Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
ActualIndex = ReturnOpposite ? -Index : Index,
DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
? Dynamic
: (ActualIndex<0
? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
: EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
};
typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
typedef typename internal::conditional<Conjugate,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
BuildType>::type Type;
};
/** \returns a vector expression of the \a N -th sub or super diagonal */
template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
{
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a N -th sub or super diagonal */
template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
{
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
{
eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
{
eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
}
template<typename Dest> inline void evalTo(Dest& dst) const
{
dst.resize(rows(),cols());
dst.setZero();
dst.diagonal() = diagonal();
for (Index i=1; i<=supers();++i)
dst.diagonal(i) = diagonal(i);
for (Index i=1; i<=subs();++i)
dst.diagonal(-i) = diagonal(-i);
}
DenseMatrixType toDenseMatrix() const
{
DenseMatrixType res(rows(),cols());
evalTo(res);
return res;
}
protected:
inline Index diagonalLength(Index i) const
{ return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
};
/**
* \class BandMatrix
* \ingroup Core_Module
*
* \brief Represents a rectangular matrix with a banded storage
*
* \tparam _Scalar Numeric type, i.e. float, double, int
* \tparam _Rows Number of rows, or \b Dynamic
* \tparam _Cols Number of columns, or \b Dynamic
* \tparam _Supers Number of super diagonal
* \tparam _Subs Number of sub diagonal
* \tparam _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
* The former controls \ref TopicStorageOrders "storage order", and defaults to
* column-major. The latter controls whether the matrix represents a selfadjoint
* matrix in which case either Supers of Subs have to be null.
*
* \sa class TridiagonalMatrix
*/
template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef Eigen::Index StorageIndex;
enum {
CoeffReadCost = NumTraits<Scalar>::ReadCost,
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _Rows,
MaxColsAtCompileTime = _Cols,
Flags = LvalueBit,
Supers = _Supers,
Subs = _Subs,
Options = _Options,
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef Matrix<Scalar, DataRowsAtCompileTime, ColsAtCompileTime, int(Options) & int(RowMajor) ? RowMajor : ColMajor> CoefficientsType;
};
template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
class BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >
{
public:
typedef typename internal::traits<BandMatrix>::Scalar Scalar;
typedef typename internal::traits<BandMatrix>::StorageIndex StorageIndex;
typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
explicit inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
: m_coeffs(1+supers+subs,cols),
m_rows(rows), m_supers(supers), m_subs(subs)
{
}
/** \returns the number of columns */
inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
inline CoefficientsType& coeffs() { return m_coeffs; }
protected:
CoefficientsType m_coeffs;
internal::variable_if_dynamic<Index, Rows> m_rows;
internal::variable_if_dynamic<Index, Supers> m_supers;
internal::variable_if_dynamic<Index, Subs> m_subs;
};
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
class BandMatrixWrapper;
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef typename _CoefficientsType::Scalar Scalar;
typedef typename _CoefficientsType::StorageKind StorageKind;
typedef typename _CoefficientsType::StorageIndex StorageIndex;
enum {
CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _Rows,
MaxColsAtCompileTime = _Cols,
Flags = LvalueBit,
Supers = _Supers,
Subs = _Subs,
Options = _Options,
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef _CoefficientsType CoefficientsType;
};
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
{
public:
typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
typedef typename internal::traits<BandMatrixWrapper>::StorageIndex StorageIndex;
explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
: m_coeffs(coeffs),
m_rows(rows), m_supers(supers), m_subs(subs)
{
EIGEN_UNUSED_VARIABLE(cols);
//internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
}
/** \returns the number of columns */
inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
protected:
const CoefficientsType& m_coeffs;
internal::variable_if_dynamic<Index, _Rows> m_rows;
internal::variable_if_dynamic<Index, _Supers> m_supers;
internal::variable_if_dynamic<Index, _Subs> m_subs;
};
/**
* \class TridiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a tridiagonal matrix with a compact banded storage
*
* \tparam Scalar Numeric type, i.e. float, double, int
* \tparam Size Number of rows and cols, or \b Dynamic
* \tparam Options Can be 0 or \b SelfAdjoint
*
* \sa class BandMatrix
*/
template<typename Scalar, int Size, int Options>
class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
{
typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
typedef typename Base::StorageIndex StorageIndex;
public:
explicit TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
inline typename Base::template DiagonalIntReturnType<1>::Type super()
{ return Base::template diagonal<1>(); }
inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
{ return Base::template diagonal<1>(); }
inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
{ return Base::template diagonal<-1>(); }
inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
{ return Base::template diagonal<-1>(); }
protected:
};
struct BandShape {};
template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
struct evaluator_traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
: public evaluator_traits_base<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef BandShape Shape;
};
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
struct evaluator_traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
: public evaluator_traits_base<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef BandShape Shape;
};
template<> struct AssignmentKind<DenseShape,BandShape> { typedef EigenBase2EigenBase Kind; };
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BANDMATRIX_H

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@ -1,448 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BLOCK_H
#define EIGEN_BLOCK_H
namespace Eigen {
namespace internal {
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>
{
typedef typename traits<XprType>::Scalar Scalar;
typedef typename traits<XprType>::StorageKind StorageKind;
typedef typename traits<XprType>::XprKind XprKind;
typedef typename ref_selector<XprType>::type XprTypeNested;
typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
enum{
MatrixRows = traits<XprType>::RowsAtCompileTime,
MatrixCols = traits<XprType>::ColsAtCompileTime,
RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
MaxRowsAtCompileTime = BlockRows==0 ? 0
: RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
: int(traits<XprType>::MaxRowsAtCompileTime),
MaxColsAtCompileTime = BlockCols==0 ? 0
: ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
: int(traits<XprType>::MaxColsAtCompileTime),
XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
: (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
: XprTypeIsRowMajor,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(inner_stride_at_compile_time<XprType>::ret)
: int(outer_stride_at_compile_time<XprType>::ret),
OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(outer_stride_at_compile_time<XprType>::ret)
: int(inner_stride_at_compile_time<XprType>::ret),
// FIXME, this traits is rather specialized for dense object and it needs to be cleaned further
FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
Flags = (traits<XprType>::Flags & (DirectAccessBit | (InnerPanel?CompressedAccessBit:0))) | FlagsLvalueBit | FlagsRowMajorBit,
// FIXME DirectAccessBit should not be handled by expressions
//
// Alignment is needed by MapBase's assertions
// We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the respective evaluator
Alignment = 0
};
};
template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false,
bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class BlockImpl_dense;
} // end namespace internal
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;
/** \class Block
* \ingroup Core_Module
*
* \brief Expression of a fixed-size or dynamic-size block
*
* \tparam XprType the type of the expression in which we are taking a block
* \tparam BlockRows the number of rows of the block we are taking at compile time (optional)
* \tparam BlockCols the number of columns of the block we are taking at compile time (optional)
* \tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or
* to set of columns of a column major matrix (optional). The parameter allows to determine
* at compile time whether aligned access is possible on the block expression.
*
* This class represents an expression of either a fixed-size or dynamic-size block. It is the return
* type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
* most of the time this is the only way it is used.
*
* However, if you want to directly maniputate block expressions,
* for instance if you want to write a function returning such an expression, you
* will need to use this class.
*
* Here is an example illustrating the dynamic case:
* \include class_Block.cpp
* Output: \verbinclude class_Block.out
*
* \note Even though this expression has dynamic size, in the case where \a XprType
* has fixed size, this expression inherits a fixed maximal size which means that evaluating
* it does not cause a dynamic memory allocation.
*
* Here is an example illustrating the fixed-size case:
* \include class_FixedBlock.cpp
* Output: \verbinclude class_FixedBlock.out
*
* \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
*/
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block
: public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>
{
typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;
public:
//typedef typename Impl::Base Base;
typedef Impl Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
typedef typename internal::remove_all<XprType>::type NestedExpression;
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Block(XprType& xpr, Index i) : Impl(xpr,i)
{
eigen_assert( (i>=0) && (
((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Block(XprType& xpr, Index startRow, Index startCol)
: Impl(xpr, startRow, startCol)
{
EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows()
&& startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Block(XprType& xpr,
Index startRow, Index startCol,
Index blockRows, Index blockCols)
: Impl(xpr, startRow, startCol, blockRows, blockCols)
{
eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
&& (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
eigen_assert(startRow >= 0 && blockRows >= 0 && startRow <= xpr.rows() - blockRows
&& startCol >= 0 && blockCols >= 0 && startCol <= xpr.cols() - blockCols);
}
};
// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense
// that must be specialized for direct and non-direct access...
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>
: public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel>
{
typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;
typedef typename XprType::StorageIndex StorageIndex;
public:
typedef Impl Base;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol) : Impl(xpr, startRow, startCol) {}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
: Impl(xpr, startRow, startCol, blockRows, blockCols) {}
};
namespace internal {
/** \internal Internal implementation of dense Blocks in the general case. */
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class BlockImpl_dense
: public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type
{
typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
public:
typedef typename internal::dense_xpr_base<BlockType>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
// class InnerIterator; // FIXME apparently never used
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC
inline BlockImpl_dense(XprType& xpr, Index i)
: m_xpr(xpr),
// It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
// and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
// all other cases are invalid.
// The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
m_blockCols(BlockCols==1 ? 1 : xpr.cols())
{}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC
inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
m_blockRows(BlockRows), m_blockCols(BlockCols)
{}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC
inline BlockImpl_dense(XprType& xpr,
Index startRow, Index startCol,
Index blockRows, Index blockCols)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
m_blockRows(blockRows), m_blockCols(blockCols)
{}
EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); }
EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); }
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index rowId, Index colId)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index rowId, Index colId) const
{
return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
{
return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index index) const
{
return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
EIGEN_DEVICE_FUNC
inline const CoeffReturnType coeff(Index index) const
{
return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template<int LoadMode>
inline PacketScalar packet(Index rowId, Index colId) const
{
return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());
}
template<int LoadMode>
inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
{
m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);
}
template<int LoadMode>
inline PacketScalar packet(Index index) const
{
return m_xpr.template packet<Unaligned>
(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& val)
{
m_xpr.template writePacket<Unaligned>
(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \sa MapBase::data() */
EIGEN_DEVICE_FUNC inline const Scalar* data() const;
EIGEN_DEVICE_FUNC inline Index innerStride() const;
EIGEN_DEVICE_FUNC inline Index outerStride() const;
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const
{
return m_xpr;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
XprType& nestedExpression() { return m_xpr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
StorageIndex startRow() const EIGEN_NOEXCEPT
{
return m_startRow.value();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
StorageIndex startCol() const EIGEN_NOEXCEPT
{
return m_startCol.value();
}
protected:
XprTypeNested m_xpr;
const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;
const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;
};
/** \internal Internal implementation of dense Blocks in the direct access case.*/
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
: public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >
{
typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
enum {
XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0
};
public:
typedef MapBase<BlockType> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
BlockImpl_dense(XprType& xpr, Index i)
: Base(xpr.data() + i * ( ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor))
|| ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()),
BlockRows==1 ? 1 : xpr.rows(),
BlockCols==1 ? 1 : xpr.cols()),
m_xpr(xpr),
m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)
{
init();
}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
: Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)),
m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
{
init();
}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
BlockImpl_dense(XprType& xpr,
Index startRow, Index startCol,
Index blockRows, Index blockCols)
: Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols),
m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
{
init();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const EIGEN_NOEXCEPT
{
return m_xpr;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
XprType& nestedExpression() { return m_xpr; }
/** \sa MapBase::innerStride() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index innerStride() const EIGEN_NOEXCEPT
{
return internal::traits<BlockType>::HasSameStorageOrderAsXprType
? m_xpr.innerStride()
: m_xpr.outerStride();
}
/** \sa MapBase::outerStride() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index outerStride() const EIGEN_NOEXCEPT
{
return internal::traits<BlockType>::HasSameStorageOrderAsXprType
? m_xpr.outerStride()
: m_xpr.innerStride();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
StorageIndex startRow() const EIGEN_NOEXCEPT { return m_startRow.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
StorageIndex startCol() const EIGEN_NOEXCEPT { return m_startCol.value(); }
#ifndef __SUNPRO_CC
// FIXME sunstudio is not friendly with the above friend...
// META-FIXME there is no 'friend' keyword around here. Is this obsolete?
protected:
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal used by allowAligned() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
: Base(data, blockRows, blockCols), m_xpr(xpr)
{
init();
}
#endif
protected:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void init()
{
m_outerStride = internal::traits<BlockType>::HasSameStorageOrderAsXprType
? m_xpr.outerStride()
: m_xpr.innerStride();
}
XprTypeNested m_xpr;
const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
Index m_outerStride;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BLOCK_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ALLANDANY_H
#define EIGEN_ALLANDANY_H
namespace Eigen {
namespace internal {
template<typename Derived, int UnrollCount, int Rows>
struct all_unroller
{
enum {
col = (UnrollCount-1) / Rows,
row = (UnrollCount-1) % Rows
};
EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
{
return all_unroller<Derived, UnrollCount-1, Rows>::run(mat) && mat.coeff(row, col);
}
};
template<typename Derived, int Rows>
struct all_unroller<Derived, 0, Rows>
{
EIGEN_DEVICE_FUNC static inline bool run(const Derived &/*mat*/) { return true; }
};
template<typename Derived, int Rows>
struct all_unroller<Derived, Dynamic, Rows>
{
EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; }
};
template<typename Derived, int UnrollCount, int Rows>
struct any_unroller
{
enum {
col = (UnrollCount-1) / Rows,
row = (UnrollCount-1) % Rows
};
EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
{
return any_unroller<Derived, UnrollCount-1, Rows>::run(mat) || mat.coeff(row, col);
}
};
template<typename Derived, int Rows>
struct any_unroller<Derived, 0, Rows>
{
EIGEN_DEVICE_FUNC static inline bool run(const Derived & /*mat*/) { return false; }
};
template<typename Derived, int Rows>
struct any_unroller<Derived, Dynamic, Rows>
{
EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; }
};
} // end namespace internal
/** \returns true if all coefficients are true
*
* Example: \include MatrixBase_all.cpp
* Output: \verbinclude MatrixBase_all.out
*
* \sa any(), Cwise::operator<()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::all() const
{
typedef internal::evaluator<Derived> Evaluator;
enum {
unroll = SizeAtCompileTime != Dynamic
&& SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits<Scalar>::AddCost)) <= EIGEN_UNROLLING_LIMIT
};
Evaluator evaluator(derived());
if(unroll)
return internal::all_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic, internal::traits<Derived>::RowsAtCompileTime>::run(evaluator);
else
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if (!evaluator.coeff(i, j)) return false;
return true;
}
}
/** \returns true if at least one coefficient is true
*
* \sa all()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::any() const
{
typedef internal::evaluator<Derived> Evaluator;
enum {
unroll = SizeAtCompileTime != Dynamic
&& SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits<Scalar>::AddCost)) <= EIGEN_UNROLLING_LIMIT
};
Evaluator evaluator(derived());
if(unroll)
return internal::any_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic, internal::traits<Derived>::RowsAtCompileTime>::run(evaluator);
else
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if (evaluator.coeff(i, j)) return true;
return false;
}
}
/** \returns the number of coefficients which evaluate to true
*
* \sa all(), any()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline Eigen::Index DenseBase<Derived>::count() const
{
return derived().template cast<bool>().template cast<Index>().sum();
}
/** \returns true is \c *this contains at least one Not A Number (NaN).
*
* \sa allFinite()
*/
template<typename Derived>
inline bool DenseBase<Derived>::hasNaN() const
{
#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
return derived().array().isNaN().any();
#else
return !((derived().array()==derived().array()).all());
#endif
}
/** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values.
*
* \sa hasNaN()
*/
template<typename Derived>
inline bool DenseBase<Derived>::allFinite() const
{
#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
return derived().array().isFinite().all();
#else
return !((derived()-derived()).hasNaN());
#endif
}
} // end namespace Eigen
#endif // EIGEN_ALLANDANY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COMMAINITIALIZER_H
#define EIGEN_COMMAINITIALIZER_H
namespace Eigen {
/** \class CommaInitializer
* \ingroup Core_Module
*
* \brief Helper class used by the comma initializer operator
*
* This class is internally used to implement the comma initializer feature. It is
* the return type of MatrixBase::operator<<, and most of the time this is the only
* way it is used.
*
* \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
*/
template<typename XprType>
struct CommaInitializer
{
typedef typename XprType::Scalar Scalar;
EIGEN_DEVICE_FUNC
inline CommaInitializer(XprType& xpr, const Scalar& s)
: m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
{
eigen_assert(m_xpr.rows() > 0 && m_xpr.cols() > 0
&& "Cannot comma-initialize a 0x0 matrix (operator<<)");
m_xpr.coeffRef(0,0) = s;
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
: m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
{
eigen_assert(m_xpr.rows() >= other.rows() && m_xpr.cols() >= other.cols()
&& "Cannot comma-initialize a 0x0 matrix (operator<<)");
m_xpr.block(0, 0, other.rows(), other.cols()) = other;
}
/* Copy/Move constructor which transfers ownership. This is crucial in
* absence of return value optimization to avoid assertions during destruction. */
// FIXME in C++11 mode this could be replaced by a proper RValue constructor
EIGEN_DEVICE_FUNC
inline CommaInitializer(const CommaInitializer& o)
: m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
// Mark original object as finished. In absence of R-value references we need to const_cast:
const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();
const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;
}
/* inserts a scalar value in the target matrix */
EIGEN_DEVICE_FUNC
CommaInitializer& operator,(const Scalar& s)
{
if (m_col==m_xpr.cols())
{
m_row+=m_currentBlockRows;
m_col = 0;
m_currentBlockRows = 1;
eigen_assert(m_row<m_xpr.rows()
&& "Too many rows passed to comma initializer (operator<<)");
}
eigen_assert(m_col<m_xpr.cols()
&& "Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows==1);
m_xpr.coeffRef(m_row, m_col++) = s;
return *this;
}
/* inserts a matrix expression in the target matrix */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
{
if (m_col==m_xpr.cols() && (other.cols()!=0 || other.rows()!=m_currentBlockRows))
{
m_row+=m_currentBlockRows;
m_col = 0;
m_currentBlockRows = other.rows();
eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
&& "Too many rows passed to comma initializer (operator<<)");
}
eigen_assert((m_col + other.cols() <= m_xpr.cols())
&& "Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows==other.rows());
m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>
(m_row, m_col, other.rows(), other.cols()) = other;
m_col += other.cols();
return *this;
}
EIGEN_DEVICE_FUNC
inline ~CommaInitializer()
#if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS
EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception)
#endif
{
finished();
}
/** \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
*/
EIGEN_DEVICE_FUNC
inline XprType& finished() {
eigen_assert(((m_row+m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0)
&& m_col == m_xpr.cols()
&& "Too few coefficients passed to comma initializer (operator<<)");
return m_xpr;
}
XprType& m_xpr; // target expression
Index m_row; // current row id
Index m_col; // current col id
Index m_currentBlockRows; // current block height
};
/** \anchor MatrixBaseCommaInitRef
* Convenient operator to set the coefficients of a matrix.
*
* The coefficients must be provided in a row major order and exactly match
* the size of the matrix. Otherwise an assertion is raised.
*
* Example: \include MatrixBase_set.cpp
* Output: \verbinclude MatrixBase_set.out
*
* \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
*
* \sa CommaInitializer::finished(), class CommaInitializer
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)
{
return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
}
/** \sa operator<<(const Scalar&) */
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline CommaInitializer<Derived>
DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
{
return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
}
} // end namespace Eigen
#endif // EIGEN_COMMAINITIALIZER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CONDITIONESTIMATOR_H
#define EIGEN_CONDITIONESTIMATOR_H
namespace Eigen {
namespace internal {
template <typename Vector, typename RealVector, bool IsComplex>
struct rcond_compute_sign {
static inline Vector run(const Vector& v) {
const RealVector v_abs = v.cwiseAbs();
return (v_abs.array() == static_cast<typename Vector::RealScalar>(0))
.select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs));
}
};
// Partial specialization to avoid elementwise division for real vectors.
template <typename Vector>
struct rcond_compute_sign<Vector, Vector, false> {
static inline Vector run(const Vector& v) {
return (v.array() < static_cast<typename Vector::RealScalar>(0))
.select(-Vector::Ones(v.size()), Vector::Ones(v.size()));
}
};
/**
* \returns an estimate of ||inv(matrix)||_1 given a decomposition of
* \a matrix that implements .solve() and .adjoint().solve() methods.
*
* This function implements Algorithms 4.1 and 5.1 from
* http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf
* which also forms the basis for the condition number estimators in
* LAPACK. Since at most 10 calls to the solve method of dec are
* performed, the total cost is O(dims^2), as opposed to O(dims^3)
* needed to compute the inverse matrix explicitly.
*
* The most common usage is in estimating the condition number
* ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be
* computed directly in O(n^2) operations.
*
* Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and
* LLT.
*
* \sa FullPivLU, PartialPivLU, LDLT, LLT.
*/
template <typename Decomposition>
typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec)
{
typedef typename Decomposition::MatrixType MatrixType;
typedef typename Decomposition::Scalar Scalar;
typedef typename Decomposition::RealScalar RealScalar;
typedef typename internal::plain_col_type<MatrixType>::type Vector;
typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVector;
const bool is_complex = (NumTraits<Scalar>::IsComplex != 0);
eigen_assert(dec.rows() == dec.cols());
const Index n = dec.rows();
if (n == 0)
return 0;
// Disable Index to float conversion warning
#ifdef __INTEL_COMPILER
#pragma warning push
#pragma warning ( disable : 2259 )
#endif
Vector v = dec.solve(Vector::Ones(n) / Scalar(n));
#ifdef __INTEL_COMPILER
#pragma warning pop
#endif
// lower_bound is a lower bound on
// ||inv(matrix)||_1 = sup_v ||inv(matrix) v||_1 / ||v||_1
// and is the objective maximized by the ("super-") gradient ascent
// algorithm below.
RealScalar lower_bound = v.template lpNorm<1>();
if (n == 1)
return lower_bound;
// Gradient ascent algorithm follows: We know that the optimum is achieved at
// one of the simplices v = e_i, so in each iteration we follow a
// super-gradient to move towards the optimal one.
RealScalar old_lower_bound = lower_bound;
Vector sign_vector(n);
Vector old_sign_vector;
Index v_max_abs_index = -1;
Index old_v_max_abs_index = v_max_abs_index;
for (int k = 0; k < 4; ++k)
{
sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);
if (k > 0 && !is_complex && sign_vector == old_sign_vector) {
// Break if the solution stagnated.
break;
}
// v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|
v = dec.adjoint().solve(sign_vector);
v.real().cwiseAbs().maxCoeff(&v_max_abs_index);
if (v_max_abs_index == old_v_max_abs_index) {
// Break if the solution stagnated.
break;
}
// Move to the new simplex e_j, where j = v_max_abs_index.
v = dec.solve(Vector::Unit(n, v_max_abs_index)); // v = inv(matrix) * e_j.
lower_bound = v.template lpNorm<1>();
if (lower_bound <= old_lower_bound) {
// Break if the gradient step did not increase the lower_bound.
break;
}
if (!is_complex) {
old_sign_vector = sign_vector;
}
old_v_max_abs_index = v_max_abs_index;
old_lower_bound = lower_bound;
}
// The following calculates an independent estimate of ||matrix||_1 by
// multiplying matrix by a vector with entries of slowly increasing
// magnitude and alternating sign:
// v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.
// This improvement to Hager's algorithm above is due to Higham. It was
// added to make the algorithm more robust in certain corner cases where
// large elements in the matrix might otherwise escape detection due to
// exact cancellation (especially when op and op_adjoint correspond to a
// sequence of backsubstitutions and permutations), which could cause
// Hager's algorithm to vastly underestimate ||matrix||_1.
Scalar alternating_sign(RealScalar(1));
for (Index i = 0; i < n; ++i) {
// The static_cast is needed when Scalar is a complex and RealScalar implements expression templates
v[i] = alternating_sign * static_cast<RealScalar>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));
alternating_sign = -alternating_sign;
}
v = dec.solve(v);
const RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n));
return numext::maxi(lower_bound, alternate_lower_bound);
}
/** \brief Reciprocal condition number estimator.
*
* Computing a decomposition of a dense matrix takes O(n^3) operations, while
* this method estimates the condition number quickly and reliably in O(n^2)
* operations.
*
* \returns an estimate of the reciprocal condition number
* (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and
* its decomposition. Supports the following decompositions: FullPivLU,
* PartialPivLU, LDLT, and LLT.
*
* \sa FullPivLU, PartialPivLU, LDLT, LLT.
*/
template <typename Decomposition>
typename Decomposition::RealScalar
rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition& dec)
{
typedef typename Decomposition::RealScalar RealScalar;
eigen_assert(dec.rows() == dec.cols());
if (dec.rows() == 0) return NumTraits<RealScalar>::infinity();
if (matrix_norm == RealScalar(0)) return RealScalar(0);
if (dec.rows() == 1) return RealScalar(1);
const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);
return (inverse_matrix_norm == RealScalar(0) ? RealScalar(0)
: (RealScalar(1) / inverse_matrix_norm) / matrix_norm);
}
} // namespace internal
} // namespace Eigen
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COREITERATORS_H
#define EIGEN_COREITERATORS_H
namespace Eigen {
/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core
*/
namespace internal {
template<typename XprType, typename EvaluatorKind>
class inner_iterator_selector;
}
/** \class InnerIterator
* \brief An InnerIterator allows to loop over the element of any matrix expression.
*
* \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is constructed.
*
* TODO: add a usage example
*/
template<typename XprType>
class InnerIterator
{
protected:
typedef internal::inner_iterator_selector<XprType, typename internal::evaluator_traits<XprType>::Kind> IteratorType;
typedef internal::evaluator<XprType> EvaluatorType;
typedef typename internal::traits<XprType>::Scalar Scalar;
public:
/** Construct an iterator over the \a outerId -th row or column of \a xpr */
InnerIterator(const XprType &xpr, const Index &outerId)
: m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize())
{}
/// \returns the value of the current coefficient.
EIGEN_STRONG_INLINE Scalar value() const { return m_iter.value(); }
/** Increment the iterator \c *this to the next non-zero coefficient.
* Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView
*/
EIGEN_STRONG_INLINE InnerIterator& operator++() { m_iter.operator++(); return *this; }
EIGEN_STRONG_INLINE InnerIterator& operator+=(Index i) { m_iter.operator+=(i); return *this; }
EIGEN_STRONG_INLINE InnerIterator operator+(Index i)
{ InnerIterator result(*this); result+=i; return result; }
/// \returns the column or row index of the current coefficient.
EIGEN_STRONG_INLINE Index index() const { return m_iter.index(); }
/// \returns the row index of the current coefficient.
EIGEN_STRONG_INLINE Index row() const { return m_iter.row(); }
/// \returns the column index of the current coefficient.
EIGEN_STRONG_INLINE Index col() const { return m_iter.col(); }
/// \returns \c true if the iterator \c *this still references a valid coefficient.
EIGEN_STRONG_INLINE operator bool() const { return m_iter; }
protected:
EvaluatorType m_eval;
IteratorType m_iter;
private:
// If you get here, then you're not using the right InnerIterator type, e.g.:
// SparseMatrix<double,RowMajor> A;
// SparseMatrix<double>::InnerIterator it(A,0);
template<typename T> InnerIterator(const EigenBase<T>&,Index outer);
};
namespace internal {
// Generic inner iterator implementation for dense objects
template<typename XprType>
class inner_iterator_selector<XprType, IndexBased>
{
protected:
typedef evaluator<XprType> EvaluatorType;
typedef typename traits<XprType>::Scalar Scalar;
enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit };
public:
EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize)
: m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize)
{}
EIGEN_STRONG_INLINE Scalar value() const
{
return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner)
: m_eval.coeff(m_inner, m_outer);
}
EIGEN_STRONG_INLINE inner_iterator_selector& operator++() { m_inner++; return *this; }
EIGEN_STRONG_INLINE Index index() const { return m_inner; }
inline Index row() const { return IsRowMajor ? m_outer : index(); }
inline Index col() const { return IsRowMajor ? index() : m_outer; }
EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }
protected:
const EvaluatorType& m_eval;
Index m_inner;
const Index m_outer;
const Index m_end;
};
// For iterator-based evaluator, inner-iterator is already implemented as
// evaluator<>::InnerIterator
template<typename XprType>
class inner_iterator_selector<XprType, IteratorBased>
: public evaluator<XprType>::InnerIterator
{
protected:
typedef typename evaluator<XprType>::InnerIterator Base;
typedef evaluator<XprType> EvaluatorType;
public:
EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &/*innerSize*/)
: Base(eval, outerId)
{}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_COREITERATORS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_BINARY_OP_H
#define EIGEN_CWISE_BINARY_OP_H
namespace Eigen {
namespace internal {
template<typename BinaryOp, typename Lhs, typename Rhs>
struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
{
// we must not inherit from traits<Lhs> since it has
// the potential to cause problems with MSVC
typedef typename remove_all<Lhs>::type Ancestor;
typedef typename traits<Ancestor>::XprKind XprKind;
enum {
RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
};
// even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
// we still want to handle the case when the result type is different.
typedef typename result_of<
BinaryOp(
const typename Lhs::Scalar&,
const typename Rhs::Scalar&
)
>::type Scalar;
typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,
typename traits<Rhs>::StorageKind,
BinaryOp>::ret StorageKind;
typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,
typename traits<Rhs>::StorageIndex>::type StorageIndex;
typedef typename Lhs::Nested LhsNested;
typedef typename Rhs::Nested RhsNested;
typedef typename remove_reference<LhsNested>::type _LhsNested;
typedef typename remove_reference<RhsNested>::type _RhsNested;
enum {
Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind,typename traits<Rhs>::StorageKind,_LhsNested::Flags & RowMajorBit,_RhsNested::Flags & RowMajorBit>::value
};
};
} // end namespace internal
template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
class CwiseBinaryOpImpl;
/** \class CwiseBinaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
*
* \tparam BinaryOp template functor implementing the operator
* \tparam LhsType the type of the left-hand side
* \tparam RhsType the type of the right-hand side
*
* This class represents an expression where a coefficient-wise binary operator is applied to two expressions.
* It is the return type of binary operators, by which we mean only those binary operators where
* both the left-hand side and the right-hand side are Eigen expressions.
* For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseBinaryOp types explicitly.
*
* \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
*/
template<typename BinaryOp, typename LhsType, typename RhsType>
class CwiseBinaryOp :
public CwiseBinaryOpImpl<
BinaryOp, LhsType, RhsType,
typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
typename internal::traits<RhsType>::StorageKind,
BinaryOp>::ret>,
internal::no_assignment_operator
{
public:
typedef typename internal::remove_all<BinaryOp>::type Functor;
typedef typename internal::remove_all<LhsType>::type Lhs;
typedef typename internal::remove_all<RhsType>::type Rhs;
typedef typename CwiseBinaryOpImpl<
BinaryOp, LhsType, RhsType,
typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
typename internal::traits<Rhs>::StorageKind,
BinaryOp>::ret>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
typedef typename internal::ref_selector<LhsType>::type LhsNested;
typedef typename internal::ref_selector<RhsType>::type RhsNested;
typedef typename internal::remove_reference<LhsNested>::type _LhsNested;
typedef typename internal::remove_reference<RhsNested>::type _RhsNested;
#if EIGEN_COMP_MSVC && EIGEN_HAS_CXX11
//Required for Visual Studio or the Copy constructor will probably not get inlined!
EIGEN_STRONG_INLINE
CwiseBinaryOp(const CwiseBinaryOp<BinaryOp,LhsType,RhsType>&) = default;
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp())
: m_lhs(aLhs), m_rhs(aRhs), m_functor(func)
{
EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);
// require the sizes to match
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT {
// return the fixed size type if available to enable compile time optimizations
return internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic ? m_rhs.rows() : m_lhs.rows();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT {
// return the fixed size type if available to enable compile time optimizations
return internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic ? m_rhs.cols() : m_lhs.cols();
}
/** \returns the left hand side nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const _LhsNested& lhs() const { return m_lhs; }
/** \returns the right hand side nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const _RhsNested& rhs() const { return m_rhs; }
/** \returns the functor representing the binary operation */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const BinaryOp& functor() const { return m_functor; }
protected:
LhsNested m_lhs;
RhsNested m_rhs;
const BinaryOp m_functor;
};
// Generic API dispatcher
template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
class CwiseBinaryOpImpl
: public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
{
public:
typedef typename internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
};
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
{
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
{
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_CWISE_BINARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_TERNARY_OP_H
#define EIGEN_CWISE_TERNARY_OP_H
namespace Eigen {
namespace internal {
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > {
// we must not inherit from traits<Arg1> since it has
// the potential to cause problems with MSVC
typedef typename remove_all<Arg1>::type Ancestor;
typedef typename traits<Ancestor>::XprKind XprKind;
enum {
RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
};
// even though we require Arg1, Arg2, and Arg3 to have the same scalar type
// (see CwiseTernaryOp constructor),
// we still want to handle the case when the result type is different.
typedef typename result_of<TernaryOp(
const typename Arg1::Scalar&, const typename Arg2::Scalar&,
const typename Arg3::Scalar&)>::type Scalar;
typedef typename internal::traits<Arg1>::StorageKind StorageKind;
typedef typename internal::traits<Arg1>::StorageIndex StorageIndex;
typedef typename Arg1::Nested Arg1Nested;
typedef typename Arg2::Nested Arg2Nested;
typedef typename Arg3::Nested Arg3Nested;
typedef typename remove_reference<Arg1Nested>::type _Arg1Nested;
typedef typename remove_reference<Arg2Nested>::type _Arg2Nested;
typedef typename remove_reference<Arg3Nested>::type _Arg3Nested;
enum { Flags = _Arg1Nested::Flags & RowMajorBit };
};
} // end namespace internal
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
typename StorageKind>
class CwiseTernaryOpImpl;
/** \class CwiseTernaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise ternary operator is
* applied to two expressions
*
* \tparam TernaryOp template functor implementing the operator
* \tparam Arg1Type the type of the first argument
* \tparam Arg2Type the type of the second argument
* \tparam Arg3Type the type of the third argument
*
* This class represents an expression where a coefficient-wise ternary
* operator is applied to three expressions.
* It is the return type of ternary operators, by which we mean only those
* ternary operators where
* all three arguments are Eigen expressions.
* For example, the return type of betainc(matrix1, matrix2, matrix3) is a
* CwiseTernaryOp.
*
* Most of the time, this is the only way that it is used, so you typically
* don't have to name
* CwiseTernaryOp types explicitly.
*
* \sa MatrixBase::ternaryExpr(const MatrixBase<Argument2> &, const
* MatrixBase<Argument3> &, const CustomTernaryOp &) const, class CwiseBinaryOp,
* class CwiseUnaryOp, class CwiseNullaryOp
*/
template <typename TernaryOp, typename Arg1Type, typename Arg2Type,
typename Arg3Type>
class CwiseTernaryOp : public CwiseTernaryOpImpl<
TernaryOp, Arg1Type, Arg2Type, Arg3Type,
typename internal::traits<Arg1Type>::StorageKind>,
internal::no_assignment_operator
{
public:
typedef typename internal::remove_all<Arg1Type>::type Arg1;
typedef typename internal::remove_all<Arg2Type>::type Arg2;
typedef typename internal::remove_all<Arg3Type>::type Arg3;
typedef typename CwiseTernaryOpImpl<
TernaryOp, Arg1Type, Arg2Type, Arg3Type,
typename internal::traits<Arg1Type>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp)
typedef typename internal::ref_selector<Arg1Type>::type Arg1Nested;
typedef typename internal::ref_selector<Arg2Type>::type Arg2Nested;
typedef typename internal::ref_selector<Arg3Type>::type Arg3Nested;
typedef typename internal::remove_reference<Arg1Nested>::type _Arg1Nested;
typedef typename internal::remove_reference<Arg2Nested>::type _Arg2Nested;
typedef typename internal::remove_reference<Arg3Nested>::type _Arg3Nested;
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2,
const Arg3& a3,
const TernaryOp& func = TernaryOp())
: m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) {
// require the sizes to match
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
// The index types should match
EIGEN_STATIC_ASSERT((internal::is_same<
typename internal::traits<Arg1Type>::StorageKind,
typename internal::traits<Arg2Type>::StorageKind>::value),
STORAGE_KIND_MUST_MATCH)
EIGEN_STATIC_ASSERT((internal::is_same<
typename internal::traits<Arg1Type>::StorageKind,
typename internal::traits<Arg3Type>::StorageKind>::value),
STORAGE_KIND_MUST_MATCH)
eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() &&
a1.rows() == a3.rows() && a1.cols() == a3.cols());
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Index rows() const {
// return the fixed size type if available to enable compile time
// optimizations
if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
RowsAtCompileTime == Dynamic &&
internal::traits<typename internal::remove_all<Arg2Nested>::type>::
RowsAtCompileTime == Dynamic)
return m_arg3.rows();
else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
RowsAtCompileTime == Dynamic &&
internal::traits<typename internal::remove_all<Arg3Nested>::type>::
RowsAtCompileTime == Dynamic)
return m_arg2.rows();
else
return m_arg1.rows();
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Index cols() const {
// return the fixed size type if available to enable compile time
// optimizations
if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
ColsAtCompileTime == Dynamic &&
internal::traits<typename internal::remove_all<Arg2Nested>::type>::
ColsAtCompileTime == Dynamic)
return m_arg3.cols();
else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::
ColsAtCompileTime == Dynamic &&
internal::traits<typename internal::remove_all<Arg3Nested>::type>::
ColsAtCompileTime == Dynamic)
return m_arg2.cols();
else
return m_arg1.cols();
}
/** \returns the first argument nested expression */
EIGEN_DEVICE_FUNC
const _Arg1Nested& arg1() const { return m_arg1; }
/** \returns the first argument nested expression */
EIGEN_DEVICE_FUNC
const _Arg2Nested& arg2() const { return m_arg2; }
/** \returns the third argument nested expression */
EIGEN_DEVICE_FUNC
const _Arg3Nested& arg3() const { return m_arg3; }
/** \returns the functor representing the ternary operation */
EIGEN_DEVICE_FUNC
const TernaryOp& functor() const { return m_functor; }
protected:
Arg1Nested m_arg1;
Arg2Nested m_arg2;
Arg3Nested m_arg3;
const TernaryOp m_functor;
};
// Generic API dispatcher
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
typename StorageKind>
class CwiseTernaryOpImpl
: public internal::generic_xpr_base<
CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type {
public:
typedef typename internal::generic_xpr_base<
CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type Base;
};
} // end namespace Eigen
#endif // EIGEN_CWISE_TERNARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_OP_H
#define EIGEN_CWISE_UNARY_OP_H
namespace Eigen {
namespace internal {
template<typename UnaryOp, typename XprType>
struct traits<CwiseUnaryOp<UnaryOp, XprType> >
: traits<XprType>
{
typedef typename result_of<
UnaryOp(const typename XprType::Scalar&)
>::type Scalar;
typedef typename XprType::Nested XprTypeNested;
typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
enum {
Flags = _XprTypeNested::Flags & RowMajorBit
};
};
}
template<typename UnaryOp, typename XprType, typename StorageKind>
class CwiseUnaryOpImpl;
/** \class CwiseUnaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise unary operator is applied to an expression
*
* \tparam UnaryOp template functor implementing the operator
* \tparam XprType the type of the expression to which we are applying the unary operator
*
* This class represents an expression where a unary operator is applied to an expression.
* It is the return type of all operations taking exactly 1 input expression, regardless of the
* presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
* is considered unary, because only the right-hand side is an expression, and its
* return type is a specialization of CwiseUnaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseUnaryOp types explicitly.
*
* \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
*/
template<typename UnaryOp, typename XprType>
class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>, internal::no_assignment_operator
{
public:
typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
typedef typename internal::ref_selector<XprType>::type XprTypeNested;
typedef typename internal::remove_all<XprType>::type NestedExpression;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
: m_xpr(xpr), m_functor(func) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
/** \returns the functor representing the unary operation */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const UnaryOp& functor() const { return m_functor; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename internal::remove_all<XprTypeNested>::type&
nestedExpression() const { return m_xpr; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
typename internal::remove_all<XprTypeNested>::type&
nestedExpression() { return m_xpr; }
protected:
XprTypeNested m_xpr;
const UnaryOp m_functor;
};
// Generic API dispatcher
template<typename UnaryOp, typename XprType, typename StorageKind>
class CwiseUnaryOpImpl
: public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
{
public:
typedef typename internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
};
} // end namespace Eigen
#endif // EIGEN_CWISE_UNARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_VIEW_H
#define EIGEN_CWISE_UNARY_VIEW_H
namespace Eigen {
namespace internal {
template<typename ViewOp, typename MatrixType>
struct traits<CwiseUnaryView<ViewOp, MatrixType> >
: traits<MatrixType>
{
typedef typename result_of<
ViewOp(const typename traits<MatrixType>::Scalar&)
>::type Scalar;
typedef typename MatrixType::Nested MatrixTypeNested;
typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
enum {
FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags = traits<_MatrixTypeNested>::Flags & (RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions
MatrixTypeInnerStride = inner_stride_at_compile_time<MatrixType>::ret,
// need to cast the sizeof's from size_t to int explicitly, otherwise:
// "error: no integral type can represent all of the enumerator values
InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic
? int(Dynamic)
: int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),
OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret == Dynamic
? int(Dynamic)
: outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar))
};
};
}
template<typename ViewOp, typename MatrixType, typename StorageKind>
class CwiseUnaryViewImpl;
/** \class CwiseUnaryView
* \ingroup Core_Module
*
* \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
*
* \tparam ViewOp template functor implementing the view
* \tparam MatrixType the type of the matrix we are applying the unary operator
*
* This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
* It is the return type of real() and imag(), and most of the time this is the only way it is used.
*
* \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
*/
template<typename ViewOp, typename MatrixType>
class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
{
public:
typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
typedef typename internal::remove_all<MatrixType>::type NestedExpression;
explicit EIGEN_DEVICE_FUNC inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
: m_matrix(mat), m_functor(func) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
/** \returns the functor representing unary operation */
EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC const typename internal::remove_all<MatrixTypeNested>::type&
nestedExpression() const { return m_matrix; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC typename internal::remove_reference<MatrixTypeNested>::type&
nestedExpression() { return m_matrix; }
protected:
MatrixTypeNested m_matrix;
ViewOp m_functor;
};
// Generic API dispatcher
template<typename ViewOp, typename XprType, typename StorageKind>
class CwiseUnaryViewImpl
: public internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type
{
public:
typedef typename internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type Base;
};
template<typename ViewOp, typename MatrixType>
class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
: public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type
{
public:
typedef CwiseUnaryView<ViewOp, MatrixType> Derived;
typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }
EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeff(0)); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const
{
return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const
{
return derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
}
protected:
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
};
} // end namespace Eigen
#endif // EIGEN_CWISE_UNARY_VIEW_H

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lib/eigen-3.4.0/Eigen/src/Core/DenseBase.h
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@ -1,701 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSEBASE_H
#define EIGEN_DENSEBASE_H
namespace Eigen {
namespace internal {
// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
// This dummy function simply aims at checking that at compile time.
static inline void check_DenseIndex_is_signed() {
EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
}
} // end namespace internal
/** \class DenseBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and arrays
*
* This class is the base that is inherited by all dense objects (matrix, vector, arrays,
* and related expression types). The common Eigen API for dense objects is contained in this class.
*
* \tparam Derived is the derived type, e.g., a matrix type or an expression.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
*
* \sa \blank \ref TopicClassHierarchy
*/
template<typename Derived> class DenseBase
#ifndef EIGEN_PARSED_BY_DOXYGEN
: public DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value>
#else
: public DenseCoeffsBase<Derived,DirectWriteAccessors>
#endif // not EIGEN_PARSED_BY_DOXYGEN
{
public:
/** Inner iterator type to iterate over the coefficients of a row or column.
* \sa class InnerIterator
*/
typedef Eigen::InnerIterator<Derived> InnerIterator;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/**
* \brief The type used to store indices
* \details This typedef is relevant for types that store multiple indices such as
* PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index
* \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.
*/
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
/** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. */
typedef typename internal::traits<Derived>::Scalar Scalar;
/** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.
*
* It is an alias for the Scalar type */
typedef Scalar value_type;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> Base;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::rowIndexByOuterInner;
using Base::colIndexByOuterInner;
using Base::coeff;
using Base::coeffByOuterInner;
using Base::operator();
using Base::operator[];
using Base::x;
using Base::y;
using Base::z;
using Base::w;
using Base::stride;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
typedef typename Base::CoeffReturnType CoeffReturnType;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
/**< The number of rows at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
/**< The number of columns at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime>::ret),
/**< This is equal to the number of coefficients, i.e. the number of
* rows times the number of columns, or to \a Dynamic if this is not
* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
/**< This value is equal to the maximum possible number of rows that this expression
* might have. If this expression might have an arbitrarily high number of rows,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
*/
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
/**< This value is equal to the maximum possible number of columns that this expression
* might have. If this expression might have an arbitrarily high number of columns,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
*/
MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime>::ret),
/**< This value is equal to the maximum possible number of coefficients that this expression
* might have. If this expression might have an arbitrarily high number of coefficients,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
*/
IsVectorAtCompileTime = internal::traits<Derived>::RowsAtCompileTime == 1
|| internal::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). */
NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
/**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
* and 2 for matrices.
*/
Flags = internal::traits<Derived>::Flags,
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
*/
IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
: int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
};
typedef typename internal::find_best_packet<Scalar,SizeAtCompileTime>::type PacketScalar;
enum { IsPlainObjectBase = 0 };
/** The plain matrix type corresponding to this expression.
* \sa PlainObject */
typedef Matrix<typename internal::traits<Derived>::Scalar,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime
> PlainMatrix;
/** The plain array type corresponding to this expression.
* \sa PlainObject */
typedef Array<typename internal::traits<Derived>::Scalar,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime
> PlainArray;
/** \brief The plain matrix or array type corresponding to this expression.
*
* This is not necessarily exactly the return type of eval(). In the case of plain matrices,
* the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
* that the return type of eval() is either PlainObject or const PlainObject&.
*/
typedef typename internal::conditional<internal::is_same<typename internal::traits<Derived>::XprKind,MatrixXpr >::value,
PlainMatrix, PlainArray>::type PlainObject;
/** \returns the number of nonzero coefficients which is in practice the number
* of stored coefficients. */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index nonZeros() const { return size(); }
/** \returns the outer size.
*
* \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
* column-major matrix, and the number of rows for a row-major matrix. */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index outerSize() const
{
return IsVectorAtCompileTime ? 1
: int(IsRowMajor) ? this->rows() : this->cols();
}
/** \returns the inner size.
*
* \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
* column-major matrix, and the number of columns for a row-major matrix. */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index innerSize() const
{
return IsVectorAtCompileTime ? this->size()
: int(IsRowMajor) ? this->cols() : this->rows();
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
EIGEN_DEVICE_FUNC
void resize(Index newSize)
{
EIGEN_ONLY_USED_FOR_DEBUG(newSize);
eigen_assert(newSize == this->size()
&& "DenseBase::resize() does not actually allow to resize.");
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
EIGEN_DEVICE_FUNC
void resize(Index rows, Index cols)
{
EIGEN_ONLY_USED_FOR_DEBUG(rows);
EIGEN_ONLY_USED_FOR_DEBUG(cols);
eigen_assert(rows == this->rows() && cols == this->cols()
&& "DenseBase::resize() does not actually allow to resize.");
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
/** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */
EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>,PlainObject> SequentialLinSpacedReturnType;
/** \internal Represents a vector with linearly spaced coefficients that allows random access. */
typedef CwiseNullaryOp<internal::linspaced_op<Scalar>,PlainObject> RandomAccessLinSpacedReturnType;
/** \internal the return type of MatrixBase::eigenvalues() */
typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** Copies \a other into *this. \returns a reference to *this. */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const DenseBase<OtherDerived>& other);
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const DenseBase& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator+=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator-=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator=(const ReturnByValue<OtherDerived>& func);
/** \internal
* Copies \a other into *this without evaluating other. \returns a reference to *this. */
template<typename OtherDerived>
/** \deprecated */
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
Derived& lazyAssign(const DenseBase<OtherDerived>& other);
EIGEN_DEVICE_FUNC
CommaInitializer<Derived> operator<< (const Scalar& s);
template<unsigned int Added,unsigned int Removed>
/** \deprecated it now returns \c *this */
EIGEN_DEPRECATED
const Derived& flagged() const
{ return derived(); }
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
typedef Transpose<Derived> TransposeReturnType;
EIGEN_DEVICE_FUNC
TransposeReturnType transpose();
typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;
EIGEN_DEVICE_FUNC
ConstTransposeReturnType transpose() const;
EIGEN_DEVICE_FUNC
void transposeInPlace();
EIGEN_DEVICE_FUNC static const ConstantReturnType
Constant(Index rows, Index cols, const Scalar& value);
EIGEN_DEVICE_FUNC static const ConstantReturnType
Constant(Index size, const Scalar& value);
EIGEN_DEVICE_FUNC static const ConstantReturnType
Constant(const Scalar& value);
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
LinSpaced(Index size, const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
LinSpaced(const Scalar& low, const Scalar& high);
template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
NullaryExpr(Index size, const CustomNullaryOp& func);
template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
NullaryExpr(const CustomNullaryOp& func);
EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size);
EIGEN_DEVICE_FUNC static const ConstantReturnType Zero();
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();
EIGEN_DEVICE_FUNC void fill(const Scalar& value);
EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value);
EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC Derived& setZero();
EIGEN_DEVICE_FUNC Derived& setOnes();
EIGEN_DEVICE_FUNC Derived& setRandom();
template<typename OtherDerived> EIGEN_DEVICE_FUNC
bool isApprox(const DenseBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC
bool isMuchSmallerThan(const RealScalar& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived> EIGEN_DEVICE_FUNC
bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
inline bool hasNaN() const;
inline bool allFinite() const;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator*=(const Scalar& other);
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator/=(const Scalar& other);
typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;
/** \returns the matrix or vector obtained by evaluating this expression.
*
* Notice that in the case of a plain matrix or vector (not an expression) this function just returns
* a const reference, in order to avoid a useless copy.
*
* \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page \endlink.
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE EvalReturnType eval() const
{
// Even though MSVC does not honor strong inlining when the return type
// is a dynamic matrix, we desperately need strong inlining for fixed
// size types on MSVC.
return typename internal::eval<Derived>::type(derived());
}
/** swaps *this with the expression \a other.
*
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void swap(const DenseBase<OtherDerived>& other)
{
EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
eigen_assert(rows()==other.rows() && cols()==other.cols());
call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
}
/** swaps *this with the matrix or array \a other.
*
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void swap(PlainObjectBase<OtherDerived>& other)
{
eigen_assert(rows()==other.rows() && cols()==other.cols());
call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());
}
EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const;
EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess();
template<bool Enable> EIGEN_DEVICE_FUNC
inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;
template<bool Enable> EIGEN_DEVICE_FUNC
inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
EIGEN_DEVICE_FUNC Scalar sum() const;
EIGEN_DEVICE_FUNC Scalar mean() const;
EIGEN_DEVICE_FUNC Scalar trace() const;
EIGEN_DEVICE_FUNC Scalar prod() const;
template<int NaNPropagation>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const;
template<int NaNPropagation>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const;
// By default, the fastest version with undefined NaN propagation semantics is
// used.
// TODO(rmlarsen): Replace with default template argument when we move to
// c++11 or beyond.
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff() const {
return minCoeff<PropagateFast>();
}
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff() const {
return maxCoeff<PropagateFast>();
}
template<int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC
typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
template<int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
template<int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC
typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
template<int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
// TODO(rmlarsen): Replace these methods with a default template argument.
template<typename IndexType>
EIGEN_DEVICE_FUNC inline
typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const {
return minCoeff<PropagateFast>(row, col);
}
template<typename IndexType>
EIGEN_DEVICE_FUNC inline
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const {
return maxCoeff<PropagateFast>(row, col);
}
template<typename IndexType>
EIGEN_DEVICE_FUNC inline
typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const {
return minCoeff<PropagateFast>(index);
}
template<typename IndexType>
EIGEN_DEVICE_FUNC inline
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const {
return maxCoeff<PropagateFast>(index);
}
template<typename BinaryOp>
EIGEN_DEVICE_FUNC
Scalar redux(const BinaryOp& func) const;
template<typename Visitor>
EIGEN_DEVICE_FUNC
void visit(Visitor& func) const;
/** \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
*/
inline const WithFormat<Derived> format(const IOFormat& fmt) const
{
return WithFormat<Derived>(derived(), fmt);
}
/** \returns the unique coefficient of a 1x1 expression */
EIGEN_DEVICE_FUNC
CoeffReturnType value() const
{
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
return derived().coeff(0,0);
}
EIGEN_DEVICE_FUNC bool all() const;
EIGEN_DEVICE_FUNC bool any() const;
EIGEN_DEVICE_FUNC Index count() const;
typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
/** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions
*
* Example: \include MatrixBase_rowwise.cpp
* Output: \verbinclude MatrixBase_rowwise.out
*
* \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
*/
//Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const {
return ConstRowwiseReturnType(derived());
}
EIGEN_DEVICE_FUNC RowwiseReturnType rowwise();
/** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions
*
* Example: \include MatrixBase_colwise.cpp
* Output: \verbinclude MatrixBase_colwise.out
*
* \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
*/
EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const {
return ConstColwiseReturnType(derived());
}
EIGEN_DEVICE_FUNC ColwiseReturnType colwise();
typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>,PlainObject> RandomReturnType;
static const RandomReturnType Random(Index rows, Index cols);
static const RandomReturnType Random(Index size);
static const RandomReturnType Random();
template<typename ThenDerived,typename ElseDerived>
inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived,ElseDerived>
select(const DenseBase<ThenDerived>& thenMatrix,
const DenseBase<ElseDerived>& elseMatrix) const;
template<typename ThenDerived>
inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;
template<typename ElseDerived>
inline EIGEN_DEVICE_FUNC const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
template<int p> RealScalar lpNorm() const;
template<int RowFactor, int ColFactor>
EIGEN_DEVICE_FUNC
const Replicate<Derived,RowFactor,ColFactor> replicate() const;
/**
* \return an expression of the replication of \c *this
*
* Example: \include MatrixBase_replicate_int_int.cpp
* Output: \verbinclude MatrixBase_replicate_int_int.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
*/
//Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC
const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const
{
return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);
}
typedef Reverse<Derived, BothDirections> ReverseReturnType;
typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
EIGEN_DEVICE_FUNC ReverseReturnType reverse();
/** This is the const version of reverse(). */
//Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const
{
return ConstReverseReturnType(derived());
}
EIGEN_DEVICE_FUNC void reverseInPlace();
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
* iterator type as returned by the begin() and end() methods.
*/
typedef random_access_iterator_type iterator;
/** This is the const version of iterator (aka read-only) */
typedef random_access_iterator_type const_iterator;
#else
typedef typename internal::conditional< (Flags&DirectAccessBit)==DirectAccessBit,
internal::pointer_based_stl_iterator<Derived>,
internal::generic_randaccess_stl_iterator<Derived>
>::type iterator_type;
typedef typename internal::conditional< (Flags&DirectAccessBit)==DirectAccessBit,
internal::pointer_based_stl_iterator<const Derived>,
internal::generic_randaccess_stl_iterator<const Derived>
>::type const_iterator_type;
// Stl-style iterators are supported only for vectors.
typedef typename internal::conditional< IsVectorAtCompileTime,
iterator_type,
void
>::type iterator;
typedef typename internal::conditional< IsVectorAtCompileTime,
const_iterator_type,
void
>::type const_iterator;
#endif
inline iterator begin();
inline const_iterator begin() const;
inline const_iterator cbegin() const;
inline iterator end();
inline const_iterator end() const;
inline const_iterator cend() const;
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
#define EIGEN_DOC_UNARY_ADDONS(X,Y)
# include "../plugins/CommonCwiseUnaryOps.h"
# include "../plugins/BlockMethods.h"
# include "../plugins/IndexedViewMethods.h"
# include "../plugins/ReshapedMethods.h"
# ifdef EIGEN_DENSEBASE_PLUGIN
# include EIGEN_DENSEBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
#undef EIGEN_DOC_UNARY_ADDONS
// disable the use of evalTo for dense objects with a nice compilation error
template<typename Dest>
EIGEN_DEVICE_FUNC
inline void evalTo(Dest& ) const
{
EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
}
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase)
/** Default constructor. Do nothing. */
EIGEN_DEVICE_FUNC DenseBase()
{
/* Just checks for self-consistency of the flags.
* Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down
*/
#ifdef EIGEN_INTERNAL_DEBUGGING
EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
&& EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
#endif
}
private:
EIGEN_DEVICE_FUNC explicit DenseBase(int);
EIGEN_DEVICE_FUNC DenseBase(int,int);
template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
};
} // end namespace Eigen
#endif // EIGEN_DENSEBASE_H

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lib/eigen-3.4.0/Eigen/src/Core/DenseCoeffsBase.h
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@ -1,685 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSECOEFFSBASE_H
#define EIGEN_DENSECOEFFSBASE_H
namespace Eigen {
namespace internal {
template<typename T> struct add_const_on_value_type_if_arithmetic
{
typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
};
}
/** \brief Base class providing read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #ReadOnlyAccessors Constant indicating read-only access
*
* This class defines the \c operator() \c const function and friends, which can be used to read specific
* entries of a matrix or array.
*
* \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
* \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
{
public:
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
// Explanation for this CoeffReturnType typedef.
// - This is the return type of the coeff() method.
// - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
// to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
// - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
// while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
// not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
const Scalar&,
typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type
>::type CoeffReturnType;
typedef typename internal::add_const_on_value_type_if_arithmetic<
typename internal::packet_traits<Scalar>::type
>::type PacketReturnType;
typedef EigenBase<Derived> Base;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
{
return int(Derived::RowsAtCompileTime) == 1 ? 0
: int(Derived::ColsAtCompileTime) == 1 ? inner
: int(Derived::Flags)&RowMajorBit ? outer
: inner;
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
{
return int(Derived::ColsAtCompileTime) == 1 ? 0
: int(Derived::RowsAtCompileTime) == 1 ? inner
: int(Derived::Flags)&RowMajorBit ? inner
: outer;
}
/** Short version: don't use this function, use
* \link operator()(Index,Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) const \endlink.
*
* \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).coeff(row,col);
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
{
return coeff(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \returns the coefficient at given the given row and column.
*
* \sa operator()(Index,Index), operator[](Index)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
{
eigen_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return coeff(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameter \a index is in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) const \endlink.
*
* \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
coeff(Index index) const
{
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).coeff(index);
}
/** \returns the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
operator[](Index index) const
{
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
eigen_assert(index >= 0 && index < size());
return coeff(index);
}
/** \returns the coefficient at given index.
*
* This is synonymous to operator[](Index) const.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
operator()(Index index) const
{
eigen_assert(index >= 0 && index < size());
return coeff(index);
}
/** equivalent to operator[](0). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
x() const { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
y() const
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
return (*this)[1];
}
/** equivalent to operator[](2). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
z() const
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
return (*this)[2];
}
/** equivalent to operator[](3). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType
w() const
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
return (*this)[3];
}
/** \internal
* \returns the packet of coefficients starting at the given row and column. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
{
typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(row,col);
}
/** \internal */
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
{
return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \internal
* \returns the packet of coefficients starting at the given index. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit and the LinearAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
{
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(index);
}
protected:
// explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
// But some methods are only available in the DirectAccess case.
// So we add dummy methods here with these names, so that "using... " doesn't fail.
// It's not private so that the child class DenseBase can access them, and it's not public
// either since it's an implementation detail, so has to be protected.
void coeffRef();
void coeffRefByOuterInner();
void writePacket();
void writePacketByOuterInner();
void copyCoeff();
void copyCoeffByOuterInner();
void copyPacket();
void copyPacketByOuterInner();
void stride();
void innerStride();
void outerStride();
void rowStride();
void colStride();
};
/** \brief Base class providing read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #WriteAccessors Constant indicating read/write access
*
* This class defines the non-const \c operator() function and friends, which can be used to write specific
* entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
* defines the const variant for reading specific entries.
*
* \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
{
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::coeff;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
using Base::rowIndexByOuterInner;
using Base::colIndexByOuterInner;
using Base::operator[];
using Base::operator();
using Base::x;
using Base::y;
using Base::z;
using Base::w;
/** Short version: don't use this function, use
* \link operator()(Index,Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) \endlink.
*
* \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).coeffRef(row,col);
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
coeffRefByOuterInner(Index outer, Index inner)
{
return coeffRef(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \returns a reference to the coefficient at given the given row and column.
*
* \sa operator[](Index)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
operator()(Index row, Index col)
{
eigen_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return coeffRef(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) \endlink.
*
* \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
coeffRef(Index index)
{
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
operator[](Index index)
{
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
eigen_assert(index >= 0 && index < size());
return coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This is synonymous to operator[](Index).
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
operator()(Index index)
{
eigen_assert(index >= 0 && index < size());
return coeffRef(index);
}
/** equivalent to operator[](0). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
x() { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
y()
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
return (*this)[1];
}
/** equivalent to operator[](2). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
z()
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
return (*this)[2];
}
/** equivalent to operator[](3). */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Scalar&
w()
{
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
return (*this)[3];
}
};
/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #DirectAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
* \c operator() .
*
* \sa \blank \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
{
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const
{
return derived().innerStride();
}
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const
{
return derived().outerStride();
}
// FIXME shall we remove it ?
EIGEN_CONSTEXPR inline Index stride() const
{
return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
}
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rowStride() const
{
return Derived::IsRowMajor ? outerStride() : innerStride();
}
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index colStride() const
{
return Derived::IsRowMajor ? innerStride() : outerStride();
}
};
/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #DirectWriteAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
* \c operator().
*
* \sa \blank \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, DirectWriteAccessors>
: public DenseCoeffsBase<Derived, WriteAccessors>
{
public:
typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT
{
return derived().innerStride();
}
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT
{
return derived().outerStride();
}
// FIXME shall we remove it ?
EIGEN_CONSTEXPR inline Index stride() const EIGEN_NOEXCEPT
{
return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
}
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rowStride() const EIGEN_NOEXCEPT
{
return Derived::IsRowMajor ? outerStride() : innerStride();
}
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index colStride() const EIGEN_NOEXCEPT
{
return Derived::IsRowMajor ? innerStride() : outerStride();
}
};
namespace internal {
template<int Alignment, typename Derived, bool JustReturnZero>
struct first_aligned_impl
{
static EIGEN_CONSTEXPR inline Index run(const Derived&) EIGEN_NOEXCEPT
{ return 0; }
};
template<int Alignment, typename Derived>
struct first_aligned_impl<Alignment, Derived, false>
{
static inline Index run(const Derived& m)
{
return internal::first_aligned<Alignment>(m.data(), m.size());
}
};
/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization.
*
* \tparam Alignment requested alignment in Bytes.
*
* There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
* documentation.
*/
template<int Alignment, typename Derived>
static inline Index first_aligned(const DenseBase<Derived>& m)
{
enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };
return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());
}
template<typename Derived>
static inline Index first_default_aligned(const DenseBase<Derived>& m)
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type DefaultPacketType;
return internal::first_aligned<int(unpacket_traits<DefaultPacketType>::alignment),Derived>(m);
}
template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct inner_stride_at_compile_time
{
enum { ret = traits<Derived>::InnerStrideAtCompileTime };
};
template<typename Derived>
struct inner_stride_at_compile_time<Derived, false>
{
enum { ret = 0 };
};
template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct outer_stride_at_compile_time
{
enum { ret = traits<Derived>::OuterStrideAtCompileTime };
};
template<typename Derived>
struct outer_stride_at_compile_time<Derived, false>
{
enum { ret = 0 };
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_DENSECOEFFSBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2010-2013 Hauke Heibel <hauke.heibel@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXSTORAGE_H
#define EIGEN_MATRIXSTORAGE_H
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) X; EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
#else
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X)
#endif
namespace Eigen {
namespace internal {
struct constructor_without_unaligned_array_assert {};
template<typename T, int Size>
EIGEN_DEVICE_FUNC
void check_static_allocation_size()
{
// if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit
#if EIGEN_STACK_ALLOCATION_LIMIT
EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
#endif
}
/** \internal
* Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
* to 16 bytes boundary if the total size is a multiple of 16 bytes.
*/
template <typename T, int Size, int MatrixOrArrayOptions,
int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0
: compute_default_alignment<T,Size>::value >
struct plain_array
{
T array[Size];
EIGEN_DEVICE_FUNC
plain_array()
{
check_static_allocation_size<T,Size>();
}
EIGEN_DEVICE_FUNC
plain_array(constructor_without_unaligned_array_assert)
{
check_static_allocation_size<T,Size>();
}
};
#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)
#elif EIGEN_GNUC_AT_LEAST(4,7)
// GCC 4.7 is too aggressive in its optimizations and remove the alignment test based on the fact the array is declared to be aligned.
// See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900
// Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined:
template<typename PtrType>
EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; }
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
eigen_assert((internal::UIntPtr(eigen_unaligned_array_assert_workaround_gcc47(array)) & (sizemask)) == 0 \
&& "this assertion is explained here: " \
"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
" **** READ THIS WEB PAGE !!! ****");
#else
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
eigen_assert((internal::UIntPtr(array) & (sizemask)) == 0 \
&& "this assertion is explained here: " \
"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
" **** READ THIS WEB PAGE !!! ****");
#endif
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 8>
{
EIGEN_ALIGN_TO_BOUNDARY(8) T array[Size];
EIGEN_DEVICE_FUNC
plain_array()
{
EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(7);
check_static_allocation_size<T,Size>();
}
EIGEN_DEVICE_FUNC
plain_array(constructor_without_unaligned_array_assert)
{
check_static_allocation_size<T,Size>();
}
};
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 16>
{
EIGEN_ALIGN_TO_BOUNDARY(16) T array[Size];
EIGEN_DEVICE_FUNC
plain_array()
{
EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(15);
check_static_allocation_size<T,Size>();
}
EIGEN_DEVICE_FUNC
plain_array(constructor_without_unaligned_array_assert)
{
check_static_allocation_size<T,Size>();
}
};
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 32>
{
EIGEN_ALIGN_TO_BOUNDARY(32) T array[Size];
EIGEN_DEVICE_FUNC
plain_array()
{
EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(31);
check_static_allocation_size<T,Size>();
}
EIGEN_DEVICE_FUNC
plain_array(constructor_without_unaligned_array_assert)
{
check_static_allocation_size<T,Size>();
}
};
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 64>
{
EIGEN_ALIGN_TO_BOUNDARY(64) T array[Size];
EIGEN_DEVICE_FUNC
plain_array()
{
EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(63);
check_static_allocation_size<T,Size>();
}
EIGEN_DEVICE_FUNC
plain_array(constructor_without_unaligned_array_assert)
{
check_static_allocation_size<T,Size>();
}
};
template <typename T, int MatrixOrArrayOptions, int Alignment>
struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
{
T array[1];
EIGEN_DEVICE_FUNC plain_array() {}
EIGEN_DEVICE_FUNC plain_array(constructor_without_unaligned_array_assert) {}
};
struct plain_array_helper {
template<typename T, int Size, int MatrixOrArrayOptions, int Alignment>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static void copy(const plain_array<T, Size, MatrixOrArrayOptions, Alignment>& src, const Eigen::Index size,
plain_array<T, Size, MatrixOrArrayOptions, Alignment>& dst) {
smart_copy(src.array, src.array + size, dst.array);
}
template<typename T, int Size, int MatrixOrArrayOptions, int Alignment>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static void swap(plain_array<T, Size, MatrixOrArrayOptions, Alignment>& a, const Eigen::Index a_size,
plain_array<T, Size, MatrixOrArrayOptions, Alignment>& b, const Eigen::Index b_size) {
if (a_size < b_size) {
std::swap_ranges(b.array, b.array + a_size, a.array);
smart_move(b.array + a_size, b.array + b_size, a.array + a_size);
} else if (a_size > b_size) {
std::swap_ranges(a.array, a.array + b_size, b.array);
smart_move(a.array + b_size, a.array + a_size, b.array + b_size);
} else {
std::swap_ranges(a.array, a.array + a_size, b.array);
}
}
};
} // end namespace internal
/** \internal
*
* \class DenseStorage
* \ingroup Core_Module
*
* \brief Stores the data of a matrix
*
* This class stores the data of fixed-size, dynamic-size or mixed matrices
* in a way as compact as possible.
*
* \sa Matrix
*/
template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage;
// purely fixed-size matrix
template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage
{
internal::plain_array<T,Size,_Options> m_data;
public:
EIGEN_DEVICE_FUNC DenseStorage() {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
}
EIGEN_DEVICE_FUNC
explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()) {}
#if !EIGEN_HAS_CXX11 || defined(EIGEN_DENSE_STORAGE_CTOR_PLUGIN)
EIGEN_DEVICE_FUNC
DenseStorage(const DenseStorage& other) : m_data(other.m_data) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
}
#else
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) = default;
#endif
#if !EIGEN_HAS_CXX11
EIGEN_DEVICE_FUNC
DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other) m_data = other.m_data;
return *this;
}
#else
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) = default;
#endif
#if EIGEN_HAS_RVALUE_REFERENCES
#if !EIGEN_HAS_CXX11
EIGEN_DEVICE_FUNC DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
: m_data(std::move(other.m_data))
{
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
{
if (this != &other)
m_data = std::move(other.m_data);
return *this;
}
#else
EIGEN_DEVICE_FUNC DenseStorage(DenseStorage&&) = default;
EIGEN_DEVICE_FUNC DenseStorage& operator=(DenseStorage&&) = default;
#endif
#endif
EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
eigen_internal_assert(size==rows*cols && rows==_Rows && cols==_Cols);
EIGEN_UNUSED_VARIABLE(size);
EIGEN_UNUSED_VARIABLE(rows);
EIGEN_UNUSED_VARIABLE(cols);
}
EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
numext::swap(m_data, other.m_data);
}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return _Rows;}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return _Cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}
EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}
EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
};
// null matrix
template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
{
public:
EIGEN_DEVICE_FUNC DenseStorage() {}
EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) {}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) {}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) { return *this; }
EIGEN_DEVICE_FUNC DenseStorage(Index,Index,Index) {}
EIGEN_DEVICE_FUNC void swap(DenseStorage& ) {}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return _Rows;}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return _Cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}
EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}
EIGEN_DEVICE_FUNC const T *data() const { return 0; }
EIGEN_DEVICE_FUNC T *data() { return 0; }
};
// more specializations for null matrices; these are necessary to resolve ambiguities
template<typename T, int _Options> class DenseStorage<T, 0, Dynamic, Dynamic, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
template<typename T, int _Rows, int _Options> class DenseStorage<T, 0, _Rows, Dynamic, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
template<typename T, int _Cols, int _Options> class DenseStorage<T, 0, Dynamic, _Cols, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
// dynamic-size matrix with fixed-size storage
template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic, Dynamic, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
Index m_rows;
Index m_cols;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0), m_cols(0) {}
EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows), m_cols(other.m_cols)
{
internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
m_rows = other.m_rows;
m_cols = other.m_cols;
internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data);
}
return *this;
}
EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index cols) : m_rows(rows), m_cols(cols) {}
EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
{
internal::plain_array_helper::swap(m_data, m_rows * m_cols, other.m_data, other.m_rows * other.m_cols);
numext::swap(m_rows,other.m_rows);
numext::swap(m_cols,other.m_cols);
}
EIGEN_DEVICE_FUNC Index rows() const {return m_rows;}
EIGEN_DEVICE_FUNC Index cols() const {return m_cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }
EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }
EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
};
// dynamic-size matrix with fixed-size storage and fixed width
template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Size, Dynamic, _Cols, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
Index m_rows;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0) {}
EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows)
{
internal::plain_array_helper::copy(other.m_data, m_rows * _Cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
m_rows = other.m_rows;
internal::plain_array_helper::copy(other.m_data, m_rows * _Cols, m_data);
}
return *this;
}
EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index) : m_rows(rows) {}
EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
{
internal::plain_array_helper::swap(m_data, m_rows * _Cols, other.m_data, other.m_rows * _Cols);
numext::swap(m_rows, other.m_rows);
}
EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols(void) const EIGEN_NOEXCEPT {return _Cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index) { m_rows = rows; }
EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index) { m_rows = rows; }
EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
};
// dynamic-size matrix with fixed-size storage and fixed height
template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Size, _Rows, Dynamic, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
Index m_cols;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_cols(0) {}
EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::constructor_without_unaligned_array_assert()), m_cols(other.m_cols)
{
internal::plain_array_helper::copy(other.m_data, _Rows * m_cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
m_cols = other.m_cols;
internal::plain_array_helper::copy(other.m_data, _Rows * m_cols, m_data);
}
return *this;
}
EIGEN_DEVICE_FUNC DenseStorage(Index, Index, Index cols) : m_cols(cols) {}
EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
internal::plain_array_helper::swap(m_data, _Rows * m_cols, other.m_data, _Rows * other.m_cols);
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows(void) const EIGEN_NOEXCEPT {return _Rows;}
EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index, Index, Index cols) { m_cols = cols; }
EIGEN_DEVICE_FUNC void resize(Index, Index, Index cols) { m_cols = cols; }
EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
};
// purely dynamic matrix.
template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynamic, _Options>
{
T *m_data;
Index m_rows;
Index m_cols;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(0), m_rows(0), m_cols(0) {}
EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols)
: m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows), m_cols(cols)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
eigen_internal_assert(size==rows*cols && rows>=0 && cols >=0);
}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(other.m_rows*other.m_cols))
, m_rows(other.m_rows)
, m_cols(other.m_cols)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*m_cols)
internal::smart_copy(other.m_data, other.m_data+other.m_rows*other.m_cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
DenseStorage tmp(other);
this->swap(tmp);
}
return *this;
}
#if EIGEN_HAS_RVALUE_REFERENCES
EIGEN_DEVICE_FUNC
DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
: m_data(std::move(other.m_data))
, m_rows(std::move(other.m_rows))
, m_cols(std::move(other.m_cols))
{
other.m_data = nullptr;
other.m_rows = 0;
other.m_cols = 0;
}
EIGEN_DEVICE_FUNC
DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
{
numext::swap(m_data, other.m_data);
numext::swap(m_rows, other.m_rows);
numext::swap(m_cols, other.m_cols);
return *this;
}
#endif
EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
{
numext::swap(m_data,other.m_data);
numext::swap(m_rows,other.m_rows);
numext::swap(m_cols,other.m_cols);
}
EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
void conservativeResize(Index size, Index rows, Index cols)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC void resize(Index size, Index rows, Index cols)
{
if(size != m_rows*m_cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols);
if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
EIGEN_DEVICE_FUNC T *data() { return m_data; }
};
// matrix with dynamic width and fixed height (so that matrix has dynamic size).
template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Rows, Dynamic, _Options>
{
T *m_data;
Index m_cols;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_cols(0) {}
explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(cols)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
eigen_internal_assert(size==rows*cols && rows==_Rows && cols >=0);
EIGEN_UNUSED_VARIABLE(rows);
}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(_Rows*other.m_cols))
, m_cols(other.m_cols)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_cols*_Rows)
internal::smart_copy(other.m_data, other.m_data+_Rows*m_cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
DenseStorage tmp(other);
this->swap(tmp);
}
return *this;
}
#if EIGEN_HAS_RVALUE_REFERENCES
EIGEN_DEVICE_FUNC
DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
: m_data(std::move(other.m_data))
, m_cols(std::move(other.m_cols))
{
other.m_data = nullptr;
other.m_cols = 0;
}
EIGEN_DEVICE_FUNC
DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
{
numext::swap(m_data, other.m_data);
numext::swap(m_cols, other.m_cols);
return *this;
}
#endif
EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
numext::swap(m_data,other.m_data);
numext::swap(m_cols,other.m_cols);
}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return _Rows;}
EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
EIGEN_DEVICE_FUNC void conservativeResize(Index size, Index, Index cols)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index, Index cols)
{
if(size != _Rows*m_cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols);
if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_cols = cols;
}
EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
EIGEN_DEVICE_FUNC T *data() { return m_data; }
};
// matrix with dynamic height and fixed width (so that matrix has dynamic size).
template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dynamic, _Cols, _Options>
{
T *m_data;
Index m_rows;
public:
EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0) {}
explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
eigen_internal_assert(size==rows*cols && rows>=0 && cols == _Cols);
EIGEN_UNUSED_VARIABLE(cols);
}
EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
: m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(other.m_rows*_Cols))
, m_rows(other.m_rows)
{
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*_Cols)
internal::smart_copy(other.m_data, other.m_data+other.m_rows*_Cols, m_data);
}
EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
{
if (this != &other)
{
DenseStorage tmp(other);
this->swap(tmp);
}
return *this;
}
#if EIGEN_HAS_RVALUE_REFERENCES
EIGEN_DEVICE_FUNC
DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
: m_data(std::move(other.m_data))
, m_rows(std::move(other.m_rows))
{
other.m_data = nullptr;
other.m_rows = 0;
}
EIGEN_DEVICE_FUNC
DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
{
numext::swap(m_data, other.m_data);
numext::swap(m_rows, other.m_rows);
return *this;
}
#endif
EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
numext::swap(m_data,other.m_data);
numext::swap(m_rows,other.m_rows);
}
EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) {return _Cols;}
void conservativeResize(Index size, Index rows, Index)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index rows, Index)
{
if(size != m_rows*_Cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows);
if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_rows = rows;
}
EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
EIGEN_DEVICE_FUNC T *data() { return m_data; }
};
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONAL_H
#define EIGEN_DIAGONAL_H
namespace Eigen {
/** \class Diagonal
* \ingroup Core_Module
*
* \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
*
* \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
* \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
* A positive value means a superdiagonal, a negative value means a subdiagonal.
* You can also use DynamicIndex so the index can be set at runtime.
*
* The matrix is not required to be square.
*
* This class represents an expression of the main diagonal, or any sub/super diagonal
* of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
* time this is the only way it is used.
*
* \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
*/
namespace internal {
template<typename MatrixType, int DiagIndex>
struct traits<Diagonal<MatrixType,DiagIndex> >
: traits<MatrixType>
{
typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
typedef typename MatrixType::StorageKind StorageKind;
enum {
RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
: (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
ColsAtCompileTime = 1,
MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
: DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
MatrixType::MaxColsAtCompileTime)
: (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
MaxColsAtCompileTime = 1,
MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags = (unsigned int)_MatrixTypeNested::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions
MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
OuterStrideAtCompileTime = 0
};
};
}
template<typename MatrixType, int _DiagIndex> class Diagonal
: public internal::dense_xpr_base< Diagonal<MatrixType,_DiagIndex> >::type
{
public:
enum { DiagIndex = _DiagIndex };
typedef typename internal::dense_xpr_base<Diagonal>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
EIGEN_DEVICE_FUNC
explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index)
{
eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() );
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
EIGEN_DEVICE_FUNC
inline Index rows() const
{
return m_index.value()<0 ? numext::mini<Index>(m_matrix.cols(),m_matrix.rows()+m_index.value())
: numext::mini<Index>(m_matrix.rows(),m_matrix.cols()-m_index.value());
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return 1; }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT {
return m_matrix.outerStride() + 1;
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return 0; }
typedef typename internal::conditional<
internal::is_lvalue<MatrixType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
EIGEN_DEVICE_FUNC
inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index row, Index)
{
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index row, Index) const
{
return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
}
EIGEN_DEVICE_FUNC
inline CoeffReturnType coeff(Index row, Index) const
{
return m_matrix.coeff(row+rowOffset(), row+colOffset());
}
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index idx)
{
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index idx) const
{
return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
}
EIGEN_DEVICE_FUNC
inline CoeffReturnType coeff(Index idx) const
{
return m_matrix.coeff(idx+rowOffset(), idx+colOffset());
}
EIGEN_DEVICE_FUNC
inline const typename internal::remove_all<typename MatrixType::Nested>::type&
nestedExpression() const
{
return m_matrix;
}
EIGEN_DEVICE_FUNC
inline Index index() const
{
return m_index.value();
}
protected:
typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
private:
// some compilers may fail to optimize std::max etc in case of compile-time constants...
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index absDiagIndex() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index rowOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? 0 : -m_index.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index colOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : 0; }
// trigger a compile-time error if someone try to call packet
template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
};
/** \returns an expression of the main diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* Example: \include MatrixBase_diagonal.cpp
* Output: \verbinclude MatrixBase_diagonal.out
*
* \sa class Diagonal */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalReturnType
MatrixBase<Derived>::diagonal()
{
return DiagonalReturnType(derived());
}
/** This is the const version of diagonal(). */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::ConstDiagonalReturnType
MatrixBase<Derived>::diagonal() const
{
return ConstDiagonalReturnType(derived());
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_int.cpp
* Output: \verbinclude MatrixBase_diagonal_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType
MatrixBase<Derived>::diagonal(Index index)
{
return DiagonalDynamicIndexReturnType(derived(), index);
}
/** This is the const version of diagonal(Index). */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType
MatrixBase<Derived>::diagonal(Index index) const
{
return ConstDiagonalDynamicIndexReturnType(derived(), index);
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_template_int.cpp
* Output: \verbinclude MatrixBase_diagonal_template_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template<typename Derived>
template<int Index_>
EIGEN_DEVICE_FUNC
inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index_>::Type
MatrixBase<Derived>::diagonal()
{
return typename DiagonalIndexReturnType<Index_>::Type(derived());
}
/** This is the const version of diagonal<int>(). */
template<typename Derived>
template<int Index_>
EIGEN_DEVICE_FUNC
inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index_>::Type
MatrixBase<Derived>::diagonal() const
{
return typename ConstDiagonalIndexReturnType<Index_>::Type(derived());
}
} // end namespace Eigen
#endif // EIGEN_DIAGONAL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALMATRIX_H
#define EIGEN_DIAGONALMATRIX_H
namespace Eigen {
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
class DiagonalBase : public EigenBase<Derived>
{
public:
typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::RealScalar RealScalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
IsVectorAtCompileTime = 0,
Flags = NoPreferredStorageOrderBit
};
typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
typedef DenseMatrixType DenseType;
typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
EIGEN_DEVICE_FUNC
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
EIGEN_DEVICE_FUNC
inline Derived& derived() { return *static_cast<Derived*>(this); }
EIGEN_DEVICE_FUNC
DenseMatrixType toDenseMatrix() const { return derived(); }
EIGEN_DEVICE_FUNC
inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
EIGEN_DEVICE_FUNC
inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
EIGEN_DEVICE_FUNC
inline Index rows() const { return diagonal().size(); }
EIGEN_DEVICE_FUNC
inline Index cols() const { return diagonal().size(); }
template<typename MatrixDerived>
EIGEN_DEVICE_FUNC
const Product<Derived,MatrixDerived,LazyProduct>
operator*(const MatrixBase<MatrixDerived> &matrix) const
{
return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
}
typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;
EIGEN_DEVICE_FUNC
inline const InverseReturnType
inverse() const
{
return InverseReturnType(diagonal().cwiseInverse());
}
EIGEN_DEVICE_FUNC
inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
operator*(const Scalar& scalar) const
{
return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
}
EIGEN_DEVICE_FUNC
friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
operator*(const Scalar& scalar, const DiagonalBase& other)
{
return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifdef EIGEN_PARSED_BY_DOXYGEN
inline unspecified_expression_type
#else
inline const DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(DiagonalVectorType,typename OtherDerived::DiagonalVectorType,sum) >
#endif
operator+(const DiagonalBase<OtherDerived>& other) const
{
return (diagonal() + other.diagonal()).asDiagonal();
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifdef EIGEN_PARSED_BY_DOXYGEN
inline unspecified_expression_type
#else
inline const DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(DiagonalVectorType,typename OtherDerived::DiagonalVectorType,difference) >
#endif
operator-(const DiagonalBase<OtherDerived>& other) const
{
return (diagonal() - other.diagonal()).asDiagonal();
}
};
#endif
/** \class DiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a diagonal matrix with its storage
*
* \param _Scalar the type of coefficients
* \param SizeAtCompileTime the dimension of the matrix, or Dynamic
* \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
* to SizeAtCompileTime. Most of the time, you do not need to specify it.
*
* \sa class DiagonalWrapper
*/
namespace internal {
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
: traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
typedef DiagonalShape StorageKind;
enum {
Flags = LvalueBit | NoPreferredStorageOrderBit
};
};
}
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
class DiagonalMatrix
: public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
typedef const DiagonalMatrix& Nested;
typedef _Scalar Scalar;
typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
#endif
protected:
DiagonalVectorType m_diagonal;
public:
/** const version of diagonal(). */
EIGEN_DEVICE_FUNC
inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
/** \returns a reference to the stored vector of diagonal coefficients. */
EIGEN_DEVICE_FUNC
inline DiagonalVectorType& diagonal() { return m_diagonal; }
/** Default constructor without initialization */
EIGEN_DEVICE_FUNC
inline DiagonalMatrix() {}
/** Constructs a diagonal matrix with given dimension */
EIGEN_DEVICE_FUNC
explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
/** 2D constructor. */
EIGEN_DEVICE_FUNC
inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
/** 3D constructor. */
EIGEN_DEVICE_FUNC
inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
#if EIGEN_HAS_CXX11
/** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients. \cpp11
*
* There exists C++98 anologue constructors for fixed-size diagonal matrices having 2 or 3 coefficients.
*
* \warning To construct a diagonal matrix of fixed size, the number of values passed to this
* constructor must match the fixed dimension of \c *this.
*
* \sa DiagonalMatrix(const Scalar&, const Scalar&)
* \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const ArgTypes&... args)
: m_diagonal(a0, a1, a2, args...) {}
/** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer
* lists \cpp11
*/
EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE DiagonalMatrix(const std::initializer_list<std::initializer_list<Scalar>>& list)
: m_diagonal(list) {}
#endif // EIGEN_HAS_CXX11
/** Copy constructor. */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
#endif
/** generic constructor from expression of the diagonal coefficients */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
{}
/** Copy operator. */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
{
m_diagonal = other.diagonal();
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_DEVICE_FUNC
DiagonalMatrix& operator=(const DiagonalMatrix& other)
{
m_diagonal = other.diagonal();
return *this;
}
#endif
/** Resizes to given size. */
EIGEN_DEVICE_FUNC
inline void resize(Index size) { m_diagonal.resize(size); }
/** Sets all coefficients to zero. */
EIGEN_DEVICE_FUNC
inline void setZero() { m_diagonal.setZero(); }
/** Resizes and sets all coefficients to zero. */
EIGEN_DEVICE_FUNC
inline void setZero(Index size) { m_diagonal.setZero(size); }
/** Sets this matrix to be the identity matrix of the current size. */
EIGEN_DEVICE_FUNC
inline void setIdentity() { m_diagonal.setOnes(); }
/** Sets this matrix to be the identity matrix of the given size. */
EIGEN_DEVICE_FUNC
inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
};
/** \class DiagonalWrapper
* \ingroup Core_Module
*
* \brief Expression of a diagonal matrix
*
* \param _DiagonalVectorType the type of the vector of diagonal coefficients
*
* This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
* instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
* and most of the time this is the only way that it is used.
*
* \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
*/
namespace internal {
template<typename _DiagonalVectorType>
struct traits<DiagonalWrapper<_DiagonalVectorType> >
{
typedef _DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::StorageIndex StorageIndex;
typedef DiagonalShape StorageKind;
typedef typename traits<DiagonalVectorType>::XprKind XprKind;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
Flags = (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
};
};
}
template<typename _DiagonalVectorType>
class DiagonalWrapper
: public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef _DiagonalVectorType DiagonalVectorType;
typedef DiagonalWrapper Nested;
#endif
/** Constructor from expression of diagonal coefficients to wrap. */
EIGEN_DEVICE_FUNC
explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
/** \returns a const reference to the wrapped expression of diagonal coefficients. */
EIGEN_DEVICE_FUNC
const DiagonalVectorType& diagonal() const { return m_diagonal; }
protected:
typename DiagonalVectorType::Nested m_diagonal;
};
/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
*
* \only_for_vectors
*
* Example: \include MatrixBase_asDiagonal.cpp
* Output: \verbinclude MatrixBase_asDiagonal.out
*
* \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
**/
template<typename Derived>
EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived>
MatrixBase<Derived>::asDiagonal() const
{
return DiagonalWrapper<const Derived>(derived());
}
/** \returns true if *this is approximately equal to a diagonal matrix,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isDiagonal.cpp
* Output: \verbinclude MatrixBase_isDiagonal.out
*
* \sa asDiagonal()
*/
template<typename Derived>
bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
{
RealScalar absOnDiagonal = numext::abs(coeff(j,j));
if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
}
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < j; ++i)
{
if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
}
return true;
}
namespace internal {
template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };
struct Diagonal2Dense {};
template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };
// Diagonal matrix to Dense assignment
template< typename DstXprType, typename SrcXprType, typename Functor>
struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
{
static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
{
Index dstRows = src.rows();
Index dstCols = src.cols();
if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
dst.resize(dstRows, dstCols);
dst.setZero();
dst.diagonal() = src.diagonal();
}
static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
{ dst.diagonal() += src.diagonal(); }
static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
{ dst.diagonal() -= src.diagonal(); }
};
} // namespace internal
} // end namespace Eigen
#endif // EIGEN_DIAGONALMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALPRODUCT_H
#define EIGEN_DIAGONALPRODUCT_H
namespace Eigen {
/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
*/
template<typename Derived>
template<typename DiagonalDerived>
EIGEN_DEVICE_FUNC inline const Product<Derived, DiagonalDerived, LazyProduct>
MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &a_diagonal) const
{
return Product<Derived, DiagonalDerived, LazyProduct>(derived(),a_diagonal.derived());
}
} // end namespace Eigen
#endif // EIGEN_DIAGONALPRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DOT_H
#define EIGEN_DOT_H
namespace Eigen {
namespace internal {
// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
// looking at the static assertions. Thus this is a trick to get better compile errors.
template<typename T, typename U,
// the NeedToTranspose condition here is taken straight from Assign.h
bool NeedToTranspose = T::IsVectorAtCompileTime
&& U::IsVectorAtCompileTime
&& ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
| // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
// revert to || as soon as not needed anymore.
(int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
>
struct dot_nocheck
{
typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
typedef typename conj_prod::result_type ResScalar;
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE
static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
{
return a.template binaryExpr<conj_prod>(b).sum();
}
};
template<typename T, typename U>
struct dot_nocheck<T, U, true>
{
typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
typedef typename conj_prod::result_type ResScalar;
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE
static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
{
return a.transpose().template binaryExpr<conj_prod>(b).sum();
}
};
} // end namespace internal
/** \fn MatrixBase::dot
* \returns the dot product of *this with other.
*
* \only_for_vectors
*
* \note If the scalar type is complex numbers, then this function returns the hermitian
* (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
* second variable.
*
* \sa squaredNorm(), norm()
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE
typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))
typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
#endif
eigen_assert(size() == other.size());
return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
}
//---------- implementation of L2 norm and related functions ----------
/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the squared Frobenius norm.
* In both cases, it consists in the sum of the square of all the matrix entries.
* For vectors, this is also equals to the dot product of \c *this with itself.
*
* \sa dot(), norm(), lpNorm()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
{
return numext::real((*this).cwiseAbs2().sum());
}
/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
* In both cases, it consists in the square root of the sum of the square of all the matrix entries.
* For vectors, this is also equals to the square root of the dot product of \c *this with itself.
*
* \sa lpNorm(), dot(), squaredNorm()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
{
return numext::sqrt(squaredNorm());
}
/** \returns an expression of the quotient of \c *this by its own norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0),
* then this function returns a copy of the input.
*
* \only_for_vectors
*
* \sa norm(), normalize()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
MatrixBase<Derived>::normalized() const
{
typedef typename internal::nested_eval<Derived,2>::type _Nested;
_Nested n(derived());
RealScalar z = n.squaredNorm();
// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
if(z>RealScalar(0))
return n / numext::sqrt(z);
else
return n;
}
/** Normalizes the vector, i.e. divides it by its own norm.
*
* \only_for_vectors
*
* \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
*
* \sa norm(), normalized()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize()
{
RealScalar z = squaredNorm();
// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
if(z>RealScalar(0))
derived() /= numext::sqrt(z);
}
/** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow.
*
* \only_for_vectors
*
* This method is analogue to the normalized() method, but it reduces the risk of
* underflow and overflow when computing the norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0),
* then this function returns a copy of the input.
*
* \sa stableNorm(), stableNormalize(), normalized()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
MatrixBase<Derived>::stableNormalized() const
{
typedef typename internal::nested_eval<Derived,3>::type _Nested;
_Nested n(derived());
RealScalar w = n.cwiseAbs().maxCoeff();
RealScalar z = (n/w).squaredNorm();
if(z>RealScalar(0))
return n / (numext::sqrt(z)*w);
else
return n;
}
/** Normalizes the vector while avoid underflow and overflow
*
* \only_for_vectors
*
* This method is analogue to the normalize() method, but it reduces the risk of
* underflow and overflow when computing the norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
*
* \sa stableNorm(), stableNormalized(), normalize()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize()
{
RealScalar w = cwiseAbs().maxCoeff();
RealScalar z = (derived()/w).squaredNorm();
if(z>RealScalar(0))
derived() /= numext::sqrt(z)*w;
}
//---------- implementation of other norms ----------
namespace internal {
template<typename Derived, int p>
struct lpNorm_selector
{
typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const MatrixBase<Derived>& m)
{
EIGEN_USING_STD(pow)
return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
}
};
template<typename Derived>
struct lpNorm_selector<Derived, 1>
{
EIGEN_DEVICE_FUNC
static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
{
return m.cwiseAbs().sum();
}
};
template<typename Derived>
struct lpNorm_selector<Derived, 2>
{
EIGEN_DEVICE_FUNC
static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
{
return m.norm();
}
};
template<typename Derived>
struct lpNorm_selector<Derived, Infinity>
{
typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const MatrixBase<Derived>& m)
{
if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0))
return RealScalar(0);
return m.cwiseAbs().maxCoeff();
}
};
} // end namespace internal
/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
* of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
* norm, that is the maximum of the absolute values of the coefficients of \c *this.
*
* In all cases, if \c *this is empty, then the value 0 is returned.
*
* \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
*
* \sa norm()
*/
template<typename Derived>
template<int p>
#ifndef EIGEN_PARSED_BY_DOXYGEN
EIGEN_DEVICE_FUNC inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
#else
EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar
#endif
MatrixBase<Derived>::lpNorm() const
{
return internal::lpNorm_selector<Derived, p>::run(*this);
}
//---------- implementation of isOrthogonal / isUnitary ----------
/** \returns true if *this is approximately orthogonal to \a other,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isOrthogonal.cpp
* Output: \verbinclude MatrixBase_isOrthogonal.out
*/
template<typename Derived>
template<typename OtherDerived>
bool MatrixBase<Derived>::isOrthogonal
(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
{
typename internal::nested_eval<Derived,2>::type nested(derived());
typename internal::nested_eval<OtherDerived,2>::type otherNested(other.derived());
return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
}
/** \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(const RealScalar& prec) const
{
typename internal::nested_eval<Derived,1>::type self(derived());
for(Index i = 0; i < cols(); ++i)
{
if(!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
return false;
for(Index j = 0; j < i; ++j)
if(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec))
return false;
}
return true;
}
} // end namespace Eigen
#endif // EIGEN_DOT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_EIGENBASE_H
#define EIGEN_EIGENBASE_H
namespace Eigen {
/** \class EigenBase
* \ingroup Core_Module
*
* Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
*
* In other words, an EigenBase object is an object that can be copied into a MatrixBase.
*
* Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
*
* Notice that this class is trivial, it is only used to disambiguate overloaded functions.
*
* \sa \blank \ref TopicClassHierarchy
*/
template<typename Derived> struct EigenBase
{
// typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
/** \brief The interface type of indices
* \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
* \sa StorageIndex, \ref TopicPreprocessorDirectives.
* DEPRECATED: Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
* Deprecation is not marked with a doxygen comment because there are too many existing usages to add the deprecation attribute.
*/
typedef Eigen::Index Index;
// FIXME is it needed?
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/** \returns a reference to the derived object */
EIGEN_DEVICE_FUNC
Derived& derived() { return *static_cast<Derived*>(this); }
/** \returns a const reference to the derived object */
EIGEN_DEVICE_FUNC
const Derived& derived() const { return *static_cast<const Derived*>(this); }
EIGEN_DEVICE_FUNC
inline Derived& const_cast_derived() const
{ return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
EIGEN_DEVICE_FUNC
inline const Derived& const_derived() const
{ return *static_cast<const Derived*>(this); }
/** \returns the number of rows. \sa cols(), RowsAtCompileTime */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); }
/** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); }
/** \returns the number of coefficients, which is rows()*cols().
* \sa rows(), cols(), SizeAtCompileTime. */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index size() const EIGEN_NOEXCEPT { return rows() * cols(); }
/** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
template<typename Dest>
EIGEN_DEVICE_FUNC
inline void evalTo(Dest& dst) const
{ derived().evalTo(dst); }
/** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
template<typename Dest>
EIGEN_DEVICE_FUNC
inline void addTo(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(),cols());
evalTo(res);
dst += res;
}
/** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
template<typename Dest>
EIGEN_DEVICE_FUNC
inline void subTo(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(),cols());
evalTo(res);
dst -= res;
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
template<typename Dest>
EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = dst * this->derived();
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
template<typename Dest>
EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = this->derived() * dst;
}
};
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \brief Copies the generic expression \a other into *this.
*
* \details The expression must provide a (templated) evalTo(Derived& dst) const
* function which does the actual job. In practice, this allows any user to write
* its own special matrix without having to modify MatrixBase
*
* \returns a reference to *this.
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
{
call_assignment(derived(), other.derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
{
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
{
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_EIGENBASE_H

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lib/eigen-3.4.0/Eigen/src/Core/ForceAlignedAccess.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FORCEALIGNEDACCESS_H
#define EIGEN_FORCEALIGNEDACCESS_H
namespace Eigen {
/** \class ForceAlignedAccess
* \ingroup Core_Module
*
* \brief Enforce aligned packet loads and stores regardless of what is requested
*
* \param ExpressionType the type of the object of which we are forcing aligned packet access
*
* This class is the return type of MatrixBase::forceAlignedAccess()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::forceAlignedAccess()
*/
namespace internal {
template<typename ExpressionType>
struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
{};
}
template<typename ExpressionType> class ForceAlignedAccess
: public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
{
public:
typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const
{
return m_expression.coeff(row, col);
}
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col)
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const
{
return m_expression.coeff(index);
}
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index)
{
return m_expression.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_expression.template packet<Aligned>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_expression.template packet<Aligned>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
}
EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
protected:
const ExpressionType& m_expression;
private:
ForceAlignedAccess& operator=(const ForceAlignedAccess&);
};
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(),class ForceAlignedAccess
*/
template<typename Derived>
inline const ForceAlignedAccess<Derived>
MatrixBase<Derived>::forceAlignedAccess() const
{
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(), class ForceAlignedAccess
*/
template<typename Derived>
inline ForceAlignedAccess<Derived>
MatrixBase<Derived>::forceAlignedAccess()
{
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template<typename Derived>
template<bool Enable>
inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type
MatrixBase<Derived>::forceAlignedAccessIf() const
{
return derived(); // FIXME This should not work but apparently is never used
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template<typename Derived>
template<bool Enable>
inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type
MatrixBase<Derived>::forceAlignedAccessIf()
{
return derived(); // FIXME This should not work but apparently is never used
}
} // end namespace Eigen
#endif // EIGEN_FORCEALIGNEDACCESS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FUZZY_H
#define EIGEN_FUZZY_H
namespace Eigen {
namespace internal
{
template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isApprox_selector
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
{
typename internal::nested_eval<Derived,2>::type nested(x);
typename internal::nested_eval<OtherDerived,2>::type otherNested(y);
return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
}
};
template<typename Derived, typename OtherDerived>
struct isApprox_selector<Derived, OtherDerived, true>
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
{
return x.matrix() == y.matrix();
}
};
template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_object_selector
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
{
return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
}
};
template<typename Derived, typename OtherDerived>
struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
{
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_scalar_selector
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
{
return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
}
};
template<typename Derived>
struct isMuchSmallerThan_scalar_selector<Derived, true>
{
EIGEN_DEVICE_FUNC
static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
{
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
} // end namespace internal
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
* determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
* are considered to be approximately equal within precision \f$ p \f$ if
* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
* L2 norm).
*
* \note Because of the multiplicativeness of this comparison, one can't use this function
* to check whether \c *this is approximately equal to the zero matrix or vector.
* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
* or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
* RealScalar&, RealScalar) instead.
*
* \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(
const DenseBase<OtherDerived>& other,
const RealScalar& prec
) const
{
return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
/** \returns \c true if the norm of \c *this is much smaller than \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
*
* For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
* the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
* of a reference matrix of same dimensions.
*
* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
*/
template<typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
const typename NumTraits<Scalar>::Real& other,
const RealScalar& prec
) const
{
return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
}
/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm.
*
* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
const DenseBase<OtherDerived>& other,
const RealScalar& prec
) const
{
return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
} // end namespace Eigen
#endif // EIGEN_FUZZY_H

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@ -1,465 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERAL_PRODUCT_H
#define EIGEN_GENERAL_PRODUCT_H
namespace Eigen {
enum {
Large = 2,
Small = 3
};
// Define the threshold value to fallback from the generic matrix-matrix product
// implementation (heavy) to the lightweight coeff-based product one.
// See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
// in products/GeneralMatrixMatrix.h for more details.
// TODO This threshold should also be used in the compile-time selector below.
#ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
// This default value has been obtained on a Haswell architecture.
#define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
#endif
namespace internal {
template<int Rows, int Cols, int Depth> struct product_type_selector;
template<int Size, int MaxSize> struct product_size_category
{
enum {
#ifndef EIGEN_GPU_COMPILE_PHASE
is_large = MaxSize == Dynamic ||
Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
(Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
#else
is_large = 0,
#endif
value = is_large ? Large
: Size == 1 ? 1
: Small
};
};
template<typename Lhs, typename Rhs> struct product_type
{
typedef typename remove_all<Lhs>::type _Lhs;
typedef typename remove_all<Rhs>::type _Rhs;
enum {
MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,
Rows = traits<_Lhs>::RowsAtCompileTime,
MaxCols = traits<_Rhs>::MaxColsAtCompileTime,
Cols = traits<_Rhs>::ColsAtCompileTime,
MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,
traits<_Rhs>::MaxRowsAtCompileTime),
Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,
traits<_Rhs>::RowsAtCompileTime)
};
// the splitting into different lines of code here, introducing the _select enums and the typedef below,
// is to work around an internal compiler error with gcc 4.1 and 4.2.
private:
enum {
rows_select = product_size_category<Rows,MaxRows>::value,
cols_select = product_size_category<Cols,MaxCols>::value,
depth_select = product_size_category<Depth,MaxDepth>::value
};
typedef product_type_selector<rows_select, cols_select, depth_select> selector;
public:
enum {
value = selector::ret,
ret = selector::ret
};
#ifdef EIGEN_DEBUG_PRODUCT
static void debug()
{
EIGEN_DEBUG_VAR(Rows);
EIGEN_DEBUG_VAR(Cols);
EIGEN_DEBUG_VAR(Depth);
EIGEN_DEBUG_VAR(rows_select);
EIGEN_DEBUG_VAR(cols_select);
EIGEN_DEBUG_VAR(depth_select);
EIGEN_DEBUG_VAR(value);
}
#endif
};
/* The following allows to select the kind of product at compile time
* based on the three dimensions of the product.
* This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
// FIXME I'm not sure the current mapping is the ideal one.
template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
template<int M> struct product_type_selector<M, 1, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<int N> struct product_type_selector<1, N, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small,Large,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
} // end namespace internal
/***********************************************************************
* Implementation of Inner Vector Vector Product
***********************************************************************/
// FIXME : maybe the "inner product" could return a Scalar
// instead of a 1x1 matrix ??
// Pro: more natural for the user
// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
// product ends up to a row-vector times col-vector product... To tackle this use
// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
/***********************************************************************
* Implementation of Outer Vector Vector Product
***********************************************************************/
/***********************************************************************
* Implementation of General Matrix Vector Product
***********************************************************************/
/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
* 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
* 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
* 3 - all other cases are handled using a simple loop along the outer-storage direction.
* Therefore we need a lower level meta selector.
* Furthermore, if the matrix is the rhs, then the product has to be transposed.
*/
namespace internal {
template<int Side, int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector;
} // end namespace internal
namespace internal {
template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
template<typename Scalar,int Size,int MaxSize>
struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
{
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
};
template<typename Scalar,int Size>
struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
{
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { return 0; }
};
template<typename Scalar,int Size,int MaxSize>
struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
{
enum {
ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
PacketSize = internal::packet_traits<Scalar>::size
};
#if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;
EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
#else
// Some architectures cannot align on the stack,
// => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
EIGEN_STRONG_INLINE Scalar* data() {
return ForceAlignment
? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
: m_data.array;
}
#endif
};
// The vector is on the left => transposition
template<int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
{
template<typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
{
Transpose<Dest> destT(dest);
enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
::run(rhs.transpose(), lhs.transpose(), destT, alpha);
}
};
template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
{
template<typename Lhs, typename Rhs, typename Dest>
static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
{
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef typename Dest::Scalar ResScalar;
typedef typename Dest::RealScalar RealScalar;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
// make sure Dest is a compile-time vector type (bug 1166)
typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime!=0)
};
typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
if(!MightCannotUseDest)
{
// shortcut if we are sure to be able to use dest directly,
// this ease the compiler to generate cleaner and more optimzized code for most common cases
general_matrix_vector_product
<Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
actualLhs.rows(), actualLhs.cols(),
LhsMapper(actualLhs.data(), actualLhs.outerStride()),
RhsMapper(actualRhs.data(), actualRhs.innerStride()),
dest.data(), 1,
compatibleAlpha);
}
else
{
gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
evalToDest ? dest.data() : static_dest.data());
if(!evalToDest)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
Index size = dest.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
if(!alphaIsCompatible)
{
MappedDest(actualDestPtr, dest.size()).setZero();
compatibleAlpha = RhsScalar(1);
}
else
MappedDest(actualDestPtr, dest.size()) = dest;
}
general_matrix_vector_product
<Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
actualLhs.rows(), actualLhs.cols(),
LhsMapper(actualLhs.data(), actualLhs.outerStride()),
RhsMapper(actualRhs.data(), actualRhs.innerStride()),
actualDestPtr, 1,
compatibleAlpha);
if (!evalToDest)
{
if(!alphaIsCompatible)
dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
else
dest = MappedDest(actualDestPtr, dest.size());
}
}
}
};
template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
{
template<typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
{
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef typename Dest::Scalar ResScalar;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime==0
};
gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
if(!DirectlyUseRhs)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
Index size = actualRhs.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
}
typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
general_matrix_vector_product
<Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
actualLhs.rows(), actualLhs.cols(),
LhsMapper(actualLhs.data(), actualLhs.outerStride()),
RhsMapper(actualRhsPtr, 1),
dest.data(), dest.col(0).innerStride(), //NOTE if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
actualAlpha);
}
};
template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
{
template<typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
{
EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
// TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
typename nested_eval<Rhs,1>::type actual_rhs(rhs);
const Index size = rhs.rows();
for(Index k=0; k<size; ++k)
dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
}
};
template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
{
template<typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
{
EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
const Index rows = dest.rows();
for(Index i=0; i<rows; ++i)
dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
}
};
} // end namespace internal
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \returns the matrix product of \c *this and \a other.
*
* \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
*
* \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Product<Derived, OtherDerived>
MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
{
// A note regarding the function declaration: In MSVC, this function will sometimes
// not be inlined since DenseStorage is an unwindable object for dynamic
// matrices and product types are holding a member to store the result.
// Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
enum {
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
|| OtherDerived::RowsAtCompileTime==Dynamic
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
#ifdef EIGEN_DEBUG_PRODUCT
internal::product_type<Derived,OtherDerived>::debug();
#endif
return Product<Derived, OtherDerived>(derived(), other.derived());
}
/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
*
* The returned product will behave like any other expressions: the coefficients of the product will be
* computed once at a time as requested. This might be useful in some extremely rare cases when only
* a small and no coherent fraction of the result's coefficients have to be computed.
*
* \warning This version of the matrix product can be much much slower. So use it only if you know
* what you are doing and that you measured a true speed improvement.
*
* \sa operator*(const MatrixBase&)
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Product<Derived,OtherDerived,LazyProduct>
MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
{
enum {
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
|| OtherDerived::RowsAtCompileTime==Dynamic
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
}
} // end namespace Eigen
#endif // EIGEN_PRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_GLOBAL_FUNCTIONS_H
#ifdef EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
/** \returns an expression of the coefficient-wise DOC_OP of \a x
DOC_DETAILS
\sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
*/ \
template<typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
NAME(const Eigen::ArrayBase<Derived>& x);
#else
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
template<typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
(NAME)(const Eigen::ArrayBase<Derived>& x) { \
return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
}
#endif // EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
\
template<typename Derived> \
struct NAME##_retval<ArrayBase<Derived> > \
{ \
typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
}; \
template<typename Derived> \
struct NAME##_impl<ArrayBase<Derived> > \
{ \
static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
{ \
return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
} \
};
namespace Eigen
{
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
#if EIGEN_HAS_CXX11_MATH
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh,scalar_asinh_op,inverse hyperbolic sine,\sa ArrayBase::asinh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh,scalar_acosh_op,inverse hyperbolic cosine,\sa ArrayBase::acosh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh,scalar_atanh_op,inverse hyperbolic tangent,\sa ArrayBase::atanh)
#endif
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic,scalar_logistic_op,logistic function,\sa ArrayBase::logistic)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint,scalar_rint_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)
/** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
*
* \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression (\c Derived::Scalar).
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
#ifdef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived,typename ScalarExponent>
inline const CwiseBinaryOp<internal::scalar_pow_op<Derived::Scalar,ScalarExponent>,Derived,Constant<ScalarExponent> >
pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
#else
template <typename Derived,typename ScalarExponent>
EIGEN_DEVICE_FUNC inline
EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<typename Derived::Scalar
EIGEN_COMMA ScalarExponent EIGEN_COMMA
EIGEN_SCALAR_BINARY_SUPPORTED(pow,typename Derived::Scalar,ScalarExponent)>::type,pow))
pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent)
{
typedef typename internal::promote_scalar_arg<typename Derived::Scalar,ScalarExponent,
EIGEN_SCALAR_BINARY_SUPPORTED(pow,typename Derived::Scalar,ScalarExponent)>::type PromotedExponent;
return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedExponent,pow)(x.derived(),
typename internal::plain_constant_type<Derived,PromotedExponent>::type(x.derived().rows(), x.derived().cols(), internal::scalar_constant_op<PromotedExponent>(exponent)));
}
#endif
/** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
*
* This function computes the coefficient-wise power.
*
* Example: \include Cwise_array_power_array.cpp
* Output: \verbinclude Cwise_array_power_array.out
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
template<typename Derived,typename ExponentDerived>
inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents)
{
return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
x.derived(),
exponents.derived()
);
}
/** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
*
* This function computes the coefficient-wise power between a scalar and an array of exponents.
*
* \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
*
* Example: \include Cwise_scalar_power_array.cpp
* Output: \verbinclude Cwise_scalar_power_array.out
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
#ifdef EIGEN_PARSED_BY_DOXYGEN
template<typename Scalar,typename Derived>
inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
#else
template <typename Scalar, typename Derived>
EIGEN_DEVICE_FUNC inline
EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(
const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<typename Derived::Scalar
EIGEN_COMMA Scalar EIGEN_COMMA
EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type,Derived,pow))
pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
typedef typename internal::promote_scalar_arg<typename Derived::Scalar,Scalar,
EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type PromotedScalar;
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar,Derived,pow)(
typename internal::plain_constant_type<Derived,PromotedScalar>::type(exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)), exponents.derived());
}
#endif
namespace internal
{
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
}
}
// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
#endif // EIGEN_GLOBAL_FUNCTIONS_H

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lib/eigen-3.4.0/Eigen/src/Core/IO.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_IO_H
#define EIGEN_IO_H
namespace Eigen {
enum { DontAlignCols = 1 };
enum { StreamPrecision = -1,
FullPrecision = -2 };
namespace internal {
template<typename Derived>
std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);
}
/** \class IOFormat
* \ingroup Core_Module
*
* \brief Stores a set of parameters controlling the way matrices are printed
*
* List of available parameters:
* - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
* The default is the special value \c StreamPrecision which means to use the
* stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
* \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
* type.
* - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which
* allows to disable the alignment of columns, resulting in faster code.
* - \b coeffSeparator string printed between two coefficients of the same row
* - \b rowSeparator string printed between two rows
* - \b rowPrefix string printed at the beginning of each row
* - \b rowSuffix string printed at the end of each row
* - \b matPrefix string printed at the beginning of the matrix
* - \b matSuffix string printed at the end of the matrix
* - \b fill character printed to fill the empty space in aligned columns
*
* Example: \include IOFormat.cpp
* Output: \verbinclude IOFormat.out
*
* \sa DenseBase::format(), class WithFormat
*/
struct IOFormat
{
/** Default constructor, see class IOFormat for the meaning of the parameters */
IOFormat(int _precision = StreamPrecision, int _flags = 0,
const std::string& _coeffSeparator = " ",
const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
const std::string& _matPrefix="", const std::string& _matSuffix="", const char _fill=' ')
: matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
rowSpacer(""), coeffSeparator(_coeffSeparator), fill(_fill), precision(_precision), flags(_flags)
{
// TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline
// don't add rowSpacer if columns are not to be aligned
if((flags & DontAlignCols))
return;
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;
char fill;
int precision;
int flags;
};
/** \class WithFormat
* \ingroup Core_Module
*
* \brief Pseudo expression providing matrix output with given format
*
* \tparam ExpressionType the type of the object on which IO stream operations are performed
*
* This class represents an expression with stream operators controlled by a given IOFormat.
* It is the return type of DenseBase::format()
* and most of the time this is the only way it is used.
*
* See class IOFormat for some examples.
*
* \sa DenseBase::format(), class IOFormat
*/
template<typename ExpressionType>
class WithFormat
{
public:
WithFormat(const ExpressionType& matrix, const IOFormat& format)
: m_matrix(matrix), m_format(format)
{}
friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
{
return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
}
protected:
typename ExpressionType::Nested m_matrix;
IOFormat m_format;
};
namespace internal {
// NOTE: This helper is kept for backward compatibility with previous code specializing
// this internal::significant_decimals_impl structure. In the future we should directly
// call digits10() which has been introduced in July 2016 in 3.3.
template<typename Scalar>
struct significant_decimals_impl
{
static inline int run()
{
return NumTraits<Scalar>::digits10();
}
};
/** \internal
* print the matrix \a _m to the output stream \a s using the output format \a fmt */
template<typename Derived>
std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
{
using internal::is_same;
using internal::conditional;
if(_m.size() == 0)
{
s << fmt.matPrefix << fmt.matSuffix;
return s;
}
typename Derived::Nested m = _m;
typedef typename Derived::Scalar Scalar;
typedef typename
conditional<
is_same<Scalar, char>::value ||
is_same<Scalar, unsigned char>::value ||
is_same<Scalar, numext::int8_t>::value ||
is_same<Scalar, numext::uint8_t>::value,
int,
typename conditional<
is_same<Scalar, std::complex<char> >::value ||
is_same<Scalar, std::complex<unsigned char> >::value ||
is_same<Scalar, std::complex<numext::int8_t> >::value ||
is_same<Scalar, std::complex<numext::uint8_t> >::value,
std::complex<int>,
const Scalar&
>::type
>::type PrintType;
Index width = 0;
std::streamsize explicit_precision;
if(fmt.precision == StreamPrecision)
{
explicit_precision = 0;
}
else if(fmt.precision == FullPrecision)
{
if (NumTraits<Scalar>::IsInteger)
{
explicit_precision = 0;
}
else
{
explicit_precision = significant_decimals_impl<Scalar>::run();
}
}
else
{
explicit_precision = fmt.precision;
}
std::streamsize old_precision = 0;
if(explicit_precision) old_precision = s.precision(explicit_precision);
bool align_cols = !(fmt.flags & DontAlignCols);
if(align_cols)
{
// compute the largest width
for(Index j = 0; j < m.cols(); ++j)
for(Index i = 0; i < m.rows(); ++i)
{
std::stringstream sstr;
sstr.copyfmt(s);
sstr << static_cast<PrintType>(m.coeff(i,j));
width = std::max<Index>(width, Index(sstr.str().length()));
}
}
std::streamsize old_width = s.width();
char old_fill_character = s.fill();
s << fmt.matPrefix;
for(Index i = 0; i < m.rows(); ++i)
{
if (i)
s << fmt.rowSpacer;
s << fmt.rowPrefix;
if(width) {
s.fill(fmt.fill);
s.width(width);
}
s << static_cast<PrintType>(m.coeff(i, 0));
for(Index j = 1; j < m.cols(); ++j)
{
s << fmt.coeffSeparator;
if(width) {
s.fill(fmt.fill);
s.width(width);
}
s << static_cast<PrintType>(m.coeff(i, j));
}
s << fmt.rowSuffix;
if( i < m.rows() - 1)
s << fmt.rowSeparator;
}
s << fmt.matSuffix;
if(explicit_precision) s.precision(old_precision);
if(width) {
s.fill(old_fill_character);
s.width(old_width);
}
return s;
}
} // end namespace internal
/** \relates DenseBase
*
* Outputs the matrix, to the given stream.
*
* If you wish to print the matrix with a format different than the default, use DenseBase::format().
*
* It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
* If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
*
* \sa DenseBase::format()
*/
template<typename Derived>
std::ostream & operator <<
(std::ostream & s,
const DenseBase<Derived> & m)
{
return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
}
} // end namespace Eigen
#endif // EIGEN_IO_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INDEXED_VIEW_H
#define EIGEN_INDEXED_VIEW_H
namespace Eigen {
namespace internal {
template<typename XprType, typename RowIndices, typename ColIndices>
struct traits<IndexedView<XprType, RowIndices, ColIndices> >
: traits<XprType>
{
enum {
RowsAtCompileTime = int(array_size<RowIndices>::value),
ColsAtCompileTime = int(array_size<ColIndices>::value),
MaxRowsAtCompileTime = RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime) : Dynamic,
MaxColsAtCompileTime = ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime) : Dynamic,
XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
: (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
: XprTypeIsRowMajor,
RowIncr = int(get_compile_time_incr<RowIndices>::value),
ColIncr = int(get_compile_time_incr<ColIndices>::value),
InnerIncr = IsRowMajor ? ColIncr : RowIncr,
OuterIncr = IsRowMajor ? RowIncr : ColIncr,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
XprInnerStride = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time<XprType>::ret) : int(outer_stride_at_compile_time<XprType>::ret),
XprOuterstride = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType>::ret) : int(inner_stride_at_compile_time<XprType>::ret),
InnerSize = XprTypeIsRowMajor ? ColsAtCompileTime : RowsAtCompileTime,
IsBlockAlike = InnerIncr==1 && OuterIncr==1,
IsInnerPannel = HasSameStorageOrderAsXprType && is_same<AllRange<InnerSize>,typename conditional<XprTypeIsRowMajor,ColIndices,RowIndices>::type>::value,
InnerStrideAtCompileTime = InnerIncr<0 || InnerIncr==DynamicIndex || XprInnerStride==Dynamic ? Dynamic : XprInnerStride * InnerIncr,
OuterStrideAtCompileTime = OuterIncr<0 || OuterIncr==DynamicIndex || XprOuterstride==Dynamic ? Dynamic : XprOuterstride * OuterIncr,
ReturnAsScalar = is_same<RowIndices,SingleRange>::value && is_same<ColIndices,SingleRange>::value,
ReturnAsBlock = (!ReturnAsScalar) && IsBlockAlike,
ReturnAsIndexedView = (!ReturnAsScalar) && (!ReturnAsBlock),
// FIXME we deal with compile-time strides if and only if we have DirectAccessBit flag,
// but this is too strict regarding negative strides...
DirectAccessMask = (int(InnerIncr)!=UndefinedIncr && int(OuterIncr)!=UndefinedIncr && InnerIncr>=0 && OuterIncr>=0) ? DirectAccessBit : 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
Flags = (traits<XprType>::Flags & (HereditaryBits | DirectAccessMask )) | FlagsLvalueBit | FlagsRowMajorBit | FlagsLinearAccessBit
};
typedef Block<XprType,RowsAtCompileTime,ColsAtCompileTime,IsInnerPannel> BlockType;
};
}
template<typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
class IndexedViewImpl;
/** \class IndexedView
* \ingroup Core_Module
*
* \brief Expression of a non-sequential sub-matrix defined by arbitrary sequences of row and column indices
*
* \tparam XprType the type of the expression in which we are taking the intersections of sub-rows and sub-columns
* \tparam RowIndices the type of the object defining the sequence of row indices
* \tparam ColIndices the type of the object defining the sequence of column indices
*
* This class represents an expression of a sub-matrix (or sub-vector) defined as the intersection
* of sub-sets of rows and columns, that are themself defined by generic sequences of row indices \f$ \{r_0,r_1,..r_{m-1}\} \f$
* and column indices \f$ \{c_0,c_1,..c_{n-1} \}\f$. Let \f$ A \f$ be the nested matrix, then the resulting matrix \f$ B \f$ has \c m
* rows and \c n columns, and its entries are given by: \f$ B(i,j) = A(r_i,c_j) \f$.
*
* The \c RowIndices and \c ColIndices types must be compatible with the following API:
* \code
* <integral type> operator[](Index) const;
* Index size() const;
* \endcode
*
* Typical supported types thus include:
* - std::vector<int>
* - std::valarray<int>
* - std::array<int>
* - Plain C arrays: int[N]
* - Eigen::ArrayXi
* - decltype(ArrayXi::LinSpaced(...))
* - Any view/expressions of the previous types
* - Eigen::ArithmeticSequence
* - Eigen::internal::AllRange (helper for Eigen::all)
* - Eigen::internal::SingleRange (helper for single index)
* - etc.
*
* In typical usages of %Eigen, this class should never be used directly. It is the return type of
* DenseBase::operator()(const RowIndices&, const ColIndices&).
*
* \sa class Block
*/
template<typename XprType, typename RowIndices, typename ColIndices>
class IndexedView : public IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind>
{
public:
typedef typename IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(IndexedView)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedView)
typedef typename internal::ref_selector<XprType>::non_const_type MatrixTypeNested;
typedef typename internal::remove_all<XprType>::type NestedExpression;
template<typename T0, typename T1>
IndexedView(XprType& xpr, const T0& rowIndices, const T1& colIndices)
: m_xpr(xpr), m_rowIndices(rowIndices), m_colIndices(colIndices)
{}
/** \returns number of rows */
Index rows() const { return internal::size(m_rowIndices); }
/** \returns number of columns */
Index cols() const { return internal::size(m_colIndices); }
/** \returns the nested expression */
const typename internal::remove_all<XprType>::type&
nestedExpression() const { return m_xpr; }
/** \returns the nested expression */
typename internal::remove_reference<XprType>::type&
nestedExpression() { return m_xpr; }
/** \returns a const reference to the object storing/generating the row indices */
const RowIndices& rowIndices() const { return m_rowIndices; }
/** \returns a const reference to the object storing/generating the column indices */
const ColIndices& colIndices() const { return m_colIndices; }
protected:
MatrixTypeNested m_xpr;
RowIndices m_rowIndices;
ColIndices m_colIndices;
};
// Generic API dispatcher
template<typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
class IndexedViewImpl
: public internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices> >::type
{
public:
typedef typename internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices> >::type Base;
};
namespace internal {
template<typename ArgType, typename RowIndices, typename ColIndices>
struct unary_evaluator<IndexedView<ArgType, RowIndices, ColIndices>, IndexBased>
: evaluator_base<IndexedView<ArgType, RowIndices, ColIndices> >
{
typedef IndexedView<ArgType, RowIndices, ColIndices> XprType;
enum {
CoeffReadCost = evaluator<ArgType>::CoeffReadCost /* TODO + cost of row/col index */,
FlagsLinearAccessBit = (traits<XprType>::RowsAtCompileTime == 1 || traits<XprType>::ColsAtCompileTime == 1) ? LinearAccessBit : 0,
FlagsRowMajorBit = traits<XprType>::FlagsRowMajorBit,
Flags = (evaluator<ArgType>::Flags & (HereditaryBits & ~RowMajorBit /*| LinearAccessBit | DirectAccessBit*/)) | FlagsLinearAccessBit | FlagsRowMajorBit,
Alignment = 0
};
EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr)
{
EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
}
typedef typename XprType::Scalar Scalar;
typedef typename XprType::CoeffReturnType CoeffReturnType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
CoeffReturnType coeff(Index row, Index col) const
{
return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Scalar& coeffRef(Index row, Index col)
{
return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar& coeffRef(Index index) const
{
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const CoeffReturnType coeff(Index index) const
{
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
return m_argImpl.coeff( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
protected:
evaluator<ArgType> m_argImpl;
const XprType& m_xpr;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_INDEXED_VIEW_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INVERSE_H
#define EIGEN_INVERSE_H
namespace Eigen {
template<typename XprType,typename StorageKind> class InverseImpl;
namespace internal {
template<typename XprType>
struct traits<Inverse<XprType> >
: traits<typename XprType::PlainObject>
{
typedef typename XprType::PlainObject PlainObject;
typedef traits<PlainObject> BaseTraits;
enum {
Flags = BaseTraits::Flags & RowMajorBit
};
};
} // end namespace internal
/** \class Inverse
*
* \brief Expression of the inverse of another expression
*
* \tparam XprType the type of the expression we are taking the inverse
*
* This class represents an abstract expression of A.inverse()
* and most of the time this is the only way it is used.
*
*/
template<typename XprType>
class Inverse : public InverseImpl<XprType,typename internal::traits<XprType>::StorageKind>
{
public:
typedef typename XprType::StorageIndex StorageIndex;
typedef typename XprType::Scalar Scalar;
typedef typename internal::ref_selector<XprType>::type XprTypeNested;
typedef typename internal::remove_all<XprTypeNested>::type XprTypeNestedCleaned;
typedef typename internal::ref_selector<Inverse>::type Nested;
typedef typename internal::remove_all<XprType>::type NestedExpression;
explicit EIGEN_DEVICE_FUNC Inverse(const XprType &xpr)
: m_xpr(xpr)
{}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }
protected:
XprTypeNested m_xpr;
};
// Generic API dispatcher
template<typename XprType, typename StorageKind>
class InverseImpl
: public internal::generic_xpr_base<Inverse<XprType> >::type
{
public:
typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;
typedef typename XprType::Scalar Scalar;
private:
Scalar coeff(Index row, Index col) const;
Scalar coeff(Index i) const;
};
namespace internal {
/** \internal
* \brief Default evaluator for Inverse expression.
*
* This default evaluator for Inverse expression simply evaluate the inverse into a temporary
* by a call to internal::call_assignment_no_alias.
* Therefore, inverse implementers only have to specialize Assignment<Dst,Inverse<...>, ...> for
* there own nested expression.
*
* \sa class Inverse
*/
template<typename ArgType>
struct unary_evaluator<Inverse<ArgType> >
: public evaluator<typename Inverse<ArgType>::PlainObject>
{
typedef Inverse<ArgType> InverseType;
typedef typename InverseType::PlainObject PlainObject;
typedef evaluator<PlainObject> Base;
enum { Flags = Base::Flags | EvalBeforeNestingBit };
unary_evaluator(const InverseType& inv_xpr)
: m_result(inv_xpr.rows(), inv_xpr.cols())
{
::new (static_cast<Base*>(this)) Base(m_result);
internal::call_assignment_no_alias(m_result, inv_xpr);
}
protected:
PlainObject m_result;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_INVERSE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAP_H
#define EIGEN_MAP_H
namespace Eigen {
namespace internal {
template<typename PlainObjectType, int MapOptions, typename StrideType>
struct traits<Map<PlainObjectType, MapOptions, StrideType> >
: public traits<PlainObjectType>
{
typedef traits<PlainObjectType> TraitsBase;
enum {
PlainObjectTypeInnerSize = ((traits<PlainObjectType>::Flags&RowMajorBit)==RowMajorBit)
? PlainObjectType::ColsAtCompileTime
: PlainObjectType::RowsAtCompileTime,
InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
? int(PlainObjectType::InnerStrideAtCompileTime)
: int(StrideType::InnerStrideAtCompileTime),
OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
? (InnerStrideAtCompileTime==Dynamic || PlainObjectTypeInnerSize==Dynamic
? Dynamic
: int(InnerStrideAtCompileTime) * int(PlainObjectTypeInnerSize))
: int(StrideType::OuterStrideAtCompileTime),
Alignment = int(MapOptions)&int(AlignedMask),
Flags0 = TraitsBase::Flags & (~NestByRefBit),
Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
};
private:
enum { Options }; // Expressions don't have Options
};
}
/** \class Map
* \ingroup Core_Module
*
* \brief A matrix or vector expression mapping an existing array of data.
*
* \tparam PlainObjectType the equivalent matrix type of the mapped data
* \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
* The default is \c #Unaligned.
* \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
* of an ordinary, contiguous array. This can be overridden by specifying strides.
* The type passed here must be a specialization of the Stride template, see examples below.
*
* This class represents a matrix or vector expression mapping an existing array of data.
* It can be used to let Eigen interface without any overhead with non-Eigen data structures,
* such as plain C arrays or structures from other libraries. By default, it assumes that the
* data is laid out contiguously in memory. You can however override this by explicitly specifying
* inner and outer strides.
*
* Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
* \include Map_simple.cpp
* Output: \verbinclude Map_simple.out
*
* If you need to map non-contiguous arrays, you can do so by specifying strides:
*
* Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
* increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
* fixed value.
* \include Map_inner_stride.cpp
* Output: \verbinclude Map_inner_stride.out
*
* Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
* as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
* Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
* a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
* is \c Dynamic
* \include Map_outer_stride.cpp
* Output: \verbinclude Map_outer_stride.out
*
* For more details and for an example of specifying both an inner and an outer stride, see class Stride.
*
* \b Tip: to change the array of data mapped by a Map object, you can use the C++
* placement new syntax:
*
* Example: \include Map_placement_new.cpp
* Output: \verbinclude Map_placement_new.out
*
* This class is the return type of PlainObjectBase::Map() but can also be used directly.
*
* \sa PlainObjectBase::Map(), \ref TopicStorageOrders
*/
template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
: public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
{
public:
typedef MapBase<Map> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Map)
typedef typename Base::PointerType PointerType;
typedef PointerType PointerArgType;
EIGEN_DEVICE_FUNC
inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const
{
return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const
{
return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
: internal::traits<Map>::OuterStrideAtCompileTime != Dynamic ? Index(internal::traits<Map>::OuterStrideAtCompileTime)
: IsVectorAtCompileTime ? (this->size() * innerStride())
: int(Flags)&RowMajorBit ? (this->cols() * innerStride())
: (this->rows() * innerStride());
}
/** Constructor in the fixed-size case.
*
* \param dataPtr pointer to the array to map
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC
explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr)), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
/** Constructor in the dynamic-size vector case.
*
* \param dataPtr pointer to the array to map
* \param size the size of the vector expression
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC
inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr), size), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
/** Constructor in the dynamic-size matrix case.
*
* \param dataPtr pointer to the array to map
* \param rows the number of rows of the matrix expression
* \param cols the number of columns of the matrix expression
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC
inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
protected:
StrideType m_stride;
};
} // end namespace Eigen
#endif // EIGEN_MAP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAPBASE_H
#define EIGEN_MAPBASE_H
#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
EIGEN_STATIC_ASSERT((int(internal::evaluator<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
namespace Eigen {
/** \ingroup Core_Module
*
* \brief Base class for dense Map and Block expression with direct access
*
* This base class provides the const low-level accessors (e.g. coeff, coeffRef) of dense
* Map and Block objects with direct access.
* Typical users do not have to directly deal with this class.
*
* This class can be extended by through the macro plugin \c EIGEN_MAPBASE_PLUGIN.
* See \link TopicCustomizing_Plugins customizing Eigen \endlink for details.
*
* The \c Derived class has to provide the following two methods describing the memory layout:
* \code Index innerStride() const; \endcode
* \code Index outerStride() const; \endcode
*
* \sa class Map, class Block
*/
template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
: public internal::dense_xpr_base<Derived>::type
{
public:
typedef typename internal::dense_xpr_base<Derived>::type Base;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
InnerStrideAtCompileTime = internal::traits<Derived>::InnerStrideAtCompileTime,
SizeAtCompileTime = Base::SizeAtCompileTime
};
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef typename internal::conditional<
bool(internal::is_lvalue<Derived>::value),
Scalar *,
const Scalar *>::type
PointerType;
using Base::derived;
// using Base::RowsAtCompileTime;
// using Base::ColsAtCompileTime;
// using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::IsRowMajor;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::eval;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
// bug 217 - compile error on ICC 11.1
using Base::operator=;
typedef typename Base::CoeffReturnType CoeffReturnType;
/** \copydoc DenseBase::rows() */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index rows() const EIGEN_NOEXCEPT { return m_rows.value(); }
/** \copydoc DenseBase::cols() */
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index cols() const EIGEN_NOEXCEPT { return m_cols.value(); }
/** Returns a pointer to the first coefficient of the matrix or vector.
*
* \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
*
* \sa innerStride(), outerStride()
*/
EIGEN_DEVICE_FUNC inline const Scalar* data() const { return m_data; }
/** \copydoc PlainObjectBase::coeff(Index,Index) const */
EIGEN_DEVICE_FUNC
inline const Scalar& coeff(Index rowId, Index colId) const
{
return m_data[colId * colStride() + rowId * rowStride()];
}
/** \copydoc PlainObjectBase::coeff(Index) const */
EIGEN_DEVICE_FUNC
inline const Scalar& coeff(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return m_data[index * innerStride()];
}
/** \copydoc PlainObjectBase::coeffRef(Index,Index) const */
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index rowId, Index colId) const
{
return this->m_data[colId * colStride() + rowId * rowStride()];
}
/** \copydoc PlainObjectBase::coeffRef(Index) const */
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
/** \internal */
template<int LoadMode>
inline PacketScalar packet(Index rowId, Index colId) const
{
return internal::ploadt<PacketScalar, LoadMode>
(m_data + (colId * colStride() + rowId * rowStride()));
}
/** \internal */
template<int LoadMode>
inline PacketScalar packet(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
}
/** \internal Constructor for fixed size matrices or vectors */
EIGEN_DEVICE_FUNC
explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
{
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
checkSanity<Derived>();
}
/** \internal Constructor for dynamically sized vectors */
EIGEN_DEVICE_FUNC
inline MapBase(PointerType dataPtr, Index vecSize)
: m_data(dataPtr),
m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),
m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime))
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
eigen_assert(vecSize >= 0);
eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
checkSanity<Derived>();
}
/** \internal Constructor for dynamically sized matrices */
EIGEN_DEVICE_FUNC
inline MapBase(PointerType dataPtr, Index rows, Index cols)
: m_data(dataPtr), m_rows(rows), m_cols(cols)
{
eigen_assert( (dataPtr == 0)
|| ( rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
checkSanity<Derived>();
}
#ifdef EIGEN_MAPBASE_PLUGIN
#include EIGEN_MAPBASE_PLUGIN
#endif
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
template<typename T>
EIGEN_DEVICE_FUNC
void checkSanity(typename internal::enable_if<(internal::traits<T>::Alignment>0),void*>::type = 0) const
{
#if EIGEN_MAX_ALIGN_BYTES>0
// innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible value:
const Index minInnerStride = InnerStrideAtCompileTime == Dynamic ? 1 : Index(InnerStrideAtCompileTime);
EIGEN_ONLY_USED_FOR_DEBUG(minInnerStride);
eigen_assert(( ((internal::UIntPtr(m_data) % internal::traits<Derived>::Alignment) == 0)
|| (cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits<Derived>::Alignment ) && "data is not aligned");
#endif
}
template<typename T>
EIGEN_DEVICE_FUNC
void checkSanity(typename internal::enable_if<internal::traits<T>::Alignment==0,void*>::type = 0) const
{}
PointerType m_data;
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
};
/** \ingroup Core_Module
*
* \brief Base class for non-const dense Map and Block expression with direct access
*
* This base class provides the non-const low-level accessors (e.g. coeff and coeffRef) of
* dense Map and Block objects with direct access.
* It inherits MapBase<Derived, ReadOnlyAccessors> which defines the const variant for reading specific entries.
*
* \sa class Map, class Block
*/
template<typename Derived> class MapBase<Derived, WriteAccessors>
: public MapBase<Derived, ReadOnlyAccessors>
{
typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
public:
typedef MapBase<Derived, ReadOnlyAccessors> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::PacketScalar PacketScalar;
typedef typename Base::StorageIndex StorageIndex;
typedef typename Base::PointerType PointerType;
using Base::derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
typedef typename internal::conditional<
internal::is_lvalue<Derived>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
EIGEN_DEVICE_FUNC
inline const Scalar* data() const { return this->m_data; }
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
{
return this->m_data[col * colStride() + row * rowStride()];
}
EIGEN_DEVICE_FUNC
inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
template<int StoreMode>
inline void writePacket(Index row, Index col, const PacketScalar& val)
{
internal::pstoret<Scalar, PacketScalar, StoreMode>
(this->m_data + (col * colStride() + row * rowStride()), val);
}
template<int StoreMode>
inline void writePacket(Index index, const PacketScalar& val)
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
internal::pstoret<Scalar, PacketScalar, StoreMode>
(this->m_data + index * innerStride(), val);
}
EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {}
EIGEN_DEVICE_FUNC
Derived& operator=(const MapBase& other)
{
ReadOnlyMapBase::Base::operator=(other);
return derived();
}
// In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
// see bugs 821 and 920.
using ReadOnlyMapBase::Base::operator=;
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
};
#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS
} // end namespace Eigen
#endif // EIGEN_MAPBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATHFUNCTIONSIMPL_H
#define EIGEN_MATHFUNCTIONSIMPL_H
namespace Eigen {
namespace internal {
/** \internal \returns the hyperbolic tan of \a a (coeff-wise)
Doesn't do anything fancy, just a 13/6-degree rational interpolant which
is accurate up to a couple of ulps in the (approximate) range [-8, 8],
outside of which tanh(x) = +/-1 in single precision. The input is clamped
to the range [-c, c]. The value c is chosen as the smallest value where
the approximation evaluates to exactly 1. In the reange [-0.0004, 0.0004]
the approxmation tanh(x) ~= x is used for better accuracy as x tends to zero.
This implementation works on both scalars and packets.
*/
template<typename T>
T generic_fast_tanh_float(const T& a_x)
{
// Clamp the inputs to the range [-c, c]
#ifdef EIGEN_VECTORIZE_FMA
const T plus_clamp = pset1<T>(7.99881172180175781f);
const T minus_clamp = pset1<T>(-7.99881172180175781f);
#else
const T plus_clamp = pset1<T>(7.90531110763549805f);
const T minus_clamp = pset1<T>(-7.90531110763549805f);
#endif
const T tiny = pset1<T>(0.0004f);
const T x = pmax(pmin(a_x, plus_clamp), minus_clamp);
const T tiny_mask = pcmp_lt(pabs(a_x), tiny);
// The monomial coefficients of the numerator polynomial (odd).
const T alpha_1 = pset1<T>(4.89352455891786e-03f);
const T alpha_3 = pset1<T>(6.37261928875436e-04f);
const T alpha_5 = pset1<T>(1.48572235717979e-05f);
const T alpha_7 = pset1<T>(5.12229709037114e-08f);
const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
const T alpha_11 = pset1<T>(2.00018790482477e-13f);
const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
// The monomial coefficients of the denominator polynomial (even).
const T beta_0 = pset1<T>(4.89352518554385e-03f);
const T beta_2 = pset1<T>(2.26843463243900e-03f);
const T beta_4 = pset1<T>(1.18534705686654e-04f);
const T beta_6 = pset1<T>(1.19825839466702e-06f);
// Since the polynomials are odd/even, we need x^2.
const T x2 = pmul(x, x);
// Evaluate the numerator polynomial p.
T p = pmadd(x2, alpha_13, alpha_11);
p = pmadd(x2, p, alpha_9);
p = pmadd(x2, p, alpha_7);
p = pmadd(x2, p, alpha_5);
p = pmadd(x2, p, alpha_3);
p = pmadd(x2, p, alpha_1);
p = pmul(x, p);
// Evaluate the denominator polynomial q.
T q = pmadd(x2, beta_6, beta_4);
q = pmadd(x2, q, beta_2);
q = pmadd(x2, q, beta_0);
// Divide the numerator by the denominator.
return pselect(tiny_mask, x, pdiv(p, q));
}
template<typename RealScalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y)
{
// IEEE IEC 6059 special cases.
if ((numext::isinf)(x) || (numext::isinf)(y))
return NumTraits<RealScalar>::infinity();
if ((numext::isnan)(x) || (numext::isnan)(y))
return NumTraits<RealScalar>::quiet_NaN();
EIGEN_USING_STD(sqrt);
RealScalar p, qp;
p = numext::maxi(x,y);
if(p==RealScalar(0)) return RealScalar(0);
qp = numext::mini(y,x) / p;
return p * sqrt(RealScalar(1) + qp*qp);
}
template<typename Scalar>
struct hypot_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static EIGEN_DEVICE_FUNC
inline RealScalar run(const Scalar& x, const Scalar& y)
{
EIGEN_USING_STD(abs);
return positive_real_hypot<RealScalar>(abs(x), abs(y));
}
};
// Generic complex sqrt implementation that correctly handles corner cases
// according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt
template<typename T>
EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& z) {
// Computes the principal sqrt of the input.
//
// For a complex square root of the number x + i*y. We want to find real
// numbers u and v such that
// (u + i*v)^2 = x + i*y <=>
// u^2 - v^2 + i*2*u*v = x + i*v.
// By equating the real and imaginary parts we get:
// u^2 - v^2 = x
// 2*u*v = y.
//
// For x >= 0, this has the numerically stable solution
// u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
// v = y / (2 * u)
// and for x < 0,
// v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))
// u = y / (2 * v)
//
// Letting w = sqrt(0.5 * (|x| + |z|)),
// if x == 0: u = w, v = sign(y) * w
// if x > 0: u = w, v = y / (2 * w)
// if x < 0: u = |y| / (2 * w), v = sign(y) * w
const T x = numext::real(z);
const T y = numext::imag(z);
const T zero = T(0);
const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));
return
(numext::isinf)(y) ? std::complex<T>(NumTraits<T>::infinity(), y)
: x == zero ? std::complex<T>(w, y < zero ? -w : w)
: x > zero ? std::complex<T>(w, y / (2 * w))
: std::complex<T>(numext::abs(y) / (2 * w), y < zero ? -w : w );
}
// Generic complex rsqrt implementation.
template<typename T>
EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
// Computes the principal reciprocal sqrt of the input.
//
// For a complex reciprocal square root of the number z = x + i*y. We want to
// find real numbers u and v such that
// (u + i*v)^2 = 1 / (x + i*y) <=>
// u^2 - v^2 + i*2*u*v = x/|z|^2 - i*v/|z|^2.
// By equating the real and imaginary parts we get:
// u^2 - v^2 = x/|z|^2
// 2*u*v = y/|z|^2.
//
// For x >= 0, this has the numerically stable solution
// u = sqrt(0.5 * (x + |z|)) / |z|
// v = -y / (2 * u * |z|)
// and for x < 0,
// v = -sign(y) * sqrt(0.5 * (-x + |z|)) / |z|
// u = -y / (2 * v * |z|)
//
// Letting w = sqrt(0.5 * (|x| + |z|)),
// if x == 0: u = w / |z|, v = -sign(y) * w / |z|
// if x > 0: u = w / |z|, v = -y / (2 * w * |z|)
// if x < 0: u = |y| / (2 * w * |z|), v = -sign(y) * w / |z|
const T x = numext::real(z);
const T y = numext::imag(z);
const T zero = T(0);
const T abs_z = numext::hypot(x, y);
const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));
const T woz = w / abs_z;
// Corner cases consistent with 1/sqrt(z) on gcc/clang.
return
abs_z == zero ? std::complex<T>(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
: ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex<T>(zero, zero)
: x == zero ? std::complex<T>(woz, y < zero ? woz : -woz)
: x > zero ? std::complex<T>(woz, -y / (2 * w * abs_z))
: std::complex<T>(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz );
}
template<typename T>
EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z) {
// Computes complex log.
T a = numext::abs(z);
EIGEN_USING_STD(atan2);
T b = atan2(z.imag(), z.real());
return std::complex<T>(numext::log(a), b);
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_MATHFUNCTIONSIMPL_H

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lib/eigen-3.4.0/Eigen/src/Core/Matrix.h
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@ -1,565 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIX_H
#define EIGEN_MATRIX_H
namespace Eigen {
namespace internal {
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
private:
enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };
typedef typename find_best_packet<_Scalar,size>::type PacketScalar;
enum {
row_major_bit = _Options&RowMajor ? RowMajorBit : 0,
is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,
max_size = is_dynamic_size_storage ? Dynamic : _MaxRows*_MaxCols,
default_alignment = compute_default_alignment<_Scalar,max_size>::value,
actual_alignment = ((_Options&DontAlign)==0) ? default_alignment : 0,
required_alignment = unpacket_traits<PacketScalar>::alignment,
packet_access_bit = (packet_traits<_Scalar>::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=required_alignment))) ? PacketAccessBit : 0
};
public:
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef Eigen::Index StorageIndex;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _MaxRows,
MaxColsAtCompileTime = _MaxCols,
Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
Options = _Options,
InnerStrideAtCompileTime = 1,
OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,
// FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
Alignment = actual_alignment
};
};
}
/** \class Matrix
* \ingroup Core_Module
*
* \brief The matrix class, also used for vectors and row-vectors
*
* The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
* Vectors are matrices with one column, and row-vectors are matrices with one row.
*
* The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
*
* The first three template parameters are required:
* \tparam _Scalar Numeric type, e.g. float, double, int or std::complex<float>.
* User defined scalar types are supported as well (see \ref user_defined_scalars "here").
* \tparam _Rows Number of rows, or \b Dynamic
* \tparam _Cols Number of columns, or \b Dynamic
*
* The remaining template parameters are optional -- in most cases you don't have to worry about them.
* \tparam _Options A combination of either \b #RowMajor or \b #ColMajor, and of either
* \b #AutoAlign or \b #DontAlign.
* The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
* for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
* \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
* \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
*
* Eigen provides a number of typedefs covering the usual cases. Here are some examples:
*
* \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
* \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
* \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
*
* \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
* \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
*
* \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
* \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
*
* See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
*
* You can access elements of vectors and matrices using normal subscripting:
*
* \code
* Eigen::VectorXd v(10);
* v[0] = 0.1;
* v[1] = 0.2;
* v(0) = 0.3;
* v(1) = 0.4;
*
* Eigen::MatrixXi m(10, 10);
* m(0, 1) = 1;
* m(0, 2) = 2;
* m(0, 3) = 3;
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
*
* <i><b>Some notes:</b></i>
*
* <dl>
* <dt><b>\anchor dense Dense versus sparse:</b></dt>
* <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
*
* Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
* This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
*
* <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
* <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
* of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
* to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
*
* Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
* variables, and the array of coefficients is allocated dynamically on the heap.
*
* Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
* If you want this behavior, see the Sparse module.</dd>
*
* <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
* <dd>In most cases, one just leaves these parameters to the default values.
* These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
* when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
* exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
* are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
* </dl>
*
* <i><b>ABI and storage layout</b></i>
*
* The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
* <table class="manual">
* <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>
* <tr><td>\code Matrix<T,Dynamic,Dynamic> \endcode</td><td>\code
* struct {
* T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
* Eigen::Index rows, cols;
* };
* \endcode</td></tr>
* <tr class="alt"><td>\code
* Matrix<T,Dynamic,1>
* Matrix<T,1,Dynamic> \endcode</td><td>\code
* struct {
* T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
* Eigen::Index size;
* };
* \endcode</td></tr>
* <tr><td>\code Matrix<T,Rows,Cols> \endcode</td><td>\code
* struct {
* T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0
* };
* \endcode</td></tr>
* <tr class="alt"><td>\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \endcode</td><td>\code
* struct {
* T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
* Eigen::Index rows, cols;
* };
* \endcode</td></tr>
* </table>
* Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two
* smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
*
* \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
* \ref TopicStorageOrders
*/
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Matrix
: public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
public:
/** \brief Base class typedef.
* \sa PlainObjectBase
*/
typedef PlainObjectBase<Matrix> Base;
enum { Options = _Options };
EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
typedef typename Base::PlainObject PlainObject;
using Base::base;
using Base::coeffRef;
/**
* \brief Assigns matrices to each other.
*
* \note This is a special case of the templated operator=. Its purpose is
* to prevent a default operator= from hiding the templated operator=.
*
* \callgraph
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
{
return Base::_set(other);
}
/** \internal
* \brief Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other)
{
return Base::_set(other);
}
/* Here, doxygen failed to copy the brief information when using \copydoc */
/**
* \brief Copies the generic expression \a other into *this.
* \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
{
return Base::operator=(other);
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
{
return Base::operator=(func);
}
/** \brief Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Matrix() : Base()
{
Base::_check_template_params();
EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
}
// FIXME is it still needed
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
explicit Matrix(internal::constructor_without_unaligned_array_assert)
: Base(internal::constructor_without_unaligned_array_assert())
{ Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
#if EIGEN_HAS_RVALUE_REFERENCES
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
: Base(std::move(other))
{
Base::_check_template_params();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
{
Base::operator=(std::move(other));
return *this;
}
#endif
#if EIGEN_HAS_CXX11
/** \copydoc PlainObjectBase(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&... args)
*
* Example: \include Matrix_variadic_ctor_cxx11.cpp
* Output: \verbinclude Matrix_variadic_ctor_cxx11.out
*
* \sa Matrix(const std::initializer_list<std::initializer_list<Scalar>>&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
: Base(a0, a1, a2, a3, args...) {}
/** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11
*
* In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
*
* Example: \include Matrix_initializer_list_23_cxx11.cpp
* Output: \verbinclude Matrix_initializer_list_23_cxx11.out
*
* Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered.
*
* In the case of a compile-time column vector, implicit transposition from a single row is allowed.
* Therefore <code>VectorXd{{1,2,3,4,5}}</code> is legal and the more verbose syntax
* <code>RowVectorXd{{1},{2},{3},{4},{5}}</code> can be avoided:
*
* Example: \include Matrix_initializer_list_vector_cxx11.cpp
* Output: \verbinclude Matrix_initializer_list_vector_cxx11.out
*
* In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes,
* and implicit transposition is allowed for compile-time vectors only.
*
* \sa Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE Matrix(const std::initializer_list<std::initializer_list<Scalar>>& list) : Base(list) {}
#endif // end EIGEN_HAS_CXX11
#ifndef EIGEN_PARSED_BY_DOXYGEN
// This constructor is for both 1x1 matrices and dynamic vectors
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
explicit Matrix(const T& x)
{
Base::_check_template_params();
Base::template _init1<T>(x);
}
template<typename T0, typename T1>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Matrix(const T0& x, const T1& y)
{
Base::_check_template_params();
Base::template _init2<T0,T1>(x, y);
}
#else
/** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */
EIGEN_DEVICE_FUNC
explicit Matrix(const Scalar *data);
/** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* This is useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead.
*
* \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance,
* calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&).
* For fixed-size \c 1x1 matrices it is therefore recommended to use the default
* constructor Matrix() instead, especially when using one of the non standard
* \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
*/
EIGEN_STRONG_INLINE explicit Matrix(Index dim);
/** \brief Constructs an initialized 1x1 matrix with the given coefficient
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
Matrix(const Scalar& x);
/** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size matrices. For fixed-size matrices,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead.
*
* \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance,
* calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y).
* For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default
* constructor Matrix() instead, especially when using one of the non standard
* \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
*/
EIGEN_DEVICE_FUNC
Matrix(Index rows, Index cols);
/** \brief Constructs an initialized 2D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
Matrix(const Scalar& x, const Scalar& y);
#endif // end EIGEN_PARSED_BY_DOXYGEN
/** \brief Constructs an initialized 3D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
}
/** \brief Constructs an initialized 4D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
*/
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
m_storage.data()[3] = w;
}
/** \brief Copy constructor */
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other)
{ }
/** \brief Copy constructor for generic expressions.
* \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
*/
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
: Base(other.derived())
{ }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index innerStride() const EIGEN_NOEXCEPT { return 1; }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
/////////// Geometry module ///////////
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
// allow to extend Matrix outside Eigen
#ifdef EIGEN_MATRIX_PLUGIN
#include EIGEN_MATRIX_PLUGIN
#endif
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
};
/** \defgroup matrixtypedefs Global matrix typedefs
*
* \ingroup Core_Module
*
* %Eigen defines several typedef shortcuts for most common matrix and vector types.
*
* The general patterns are the following:
*
* \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
* and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
* for complex double.
*
* For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
*
* There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
* a fixed-size vector of 4 complex floats.
*
* With \cpp11, template alias are also defined for common sizes.
* They follow the same pattern as above except that the scalar type suffix is replaced by a
* template parameter, i.e.:
* - `MatrixSize<Type>` where `Size` can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size.
* - `MatrixXSize<Type>` and `MatrixSizeX<Type>` where `Size` can be \c 2,\c 3,\c 4 for hybrid dynamic/fixed matrices.
* - `VectorSize<Type>` and `RowVectorSize<Type>` for column and row vectors.
*
* With \cpp11, you can also use fully generic column and row vector types: `Vector<Type,Size>` and `RowVector<Type,Size>`.
*
* \sa class Matrix
*/
#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_TYPEDEFS
#undef EIGEN_MAKE_FIXED_TYPEDEFS
#if EIGEN_HAS_CXX11
#define EIGEN_MAKE_TYPEDEFS(Size, SizeSuffix) \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Matrix##SizeSuffix = Matrix<Type, Size, Size>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Vector##SizeSuffix = Matrix<Type, Size, 1>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using RowVector##SizeSuffix = Matrix<Type, 1, Size>;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Size) \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Matrix##Size##X = Matrix<Type, Size, Dynamic>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Matrix##X##Size = Matrix<Type, Dynamic, Size>;
EIGEN_MAKE_TYPEDEFS(2, 2)
EIGEN_MAKE_TYPEDEFS(3, 3)
EIGEN_MAKE_TYPEDEFS(4, 4)
EIGEN_MAKE_TYPEDEFS(Dynamic, X)
EIGEN_MAKE_FIXED_TYPEDEFS(2)
EIGEN_MAKE_FIXED_TYPEDEFS(3)
EIGEN_MAKE_FIXED_TYPEDEFS(4)
/** \ingroup matrixtypedefs
* \brief \cpp11 */
template <typename Type, int Size>
using Vector = Matrix<Type, Size, 1>;
/** \ingroup matrixtypedefs
* \brief \cpp11 */
template <typename Type, int Size>
using RowVector = Matrix<Type, 1, Size>;
#undef EIGEN_MAKE_TYPEDEFS
#undef EIGEN_MAKE_FIXED_TYPEDEFS
#endif // EIGEN_HAS_CXX11
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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lib/eigen-3.4.0/Eigen/src/Core/MatrixBase.h
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@ -1,547 +0,0 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
namespace Eigen {
/** \class MatrixBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and expressions
*
* This class is the base that is inherited by all matrix, vector, and related expression
* types. Most of the Eigen API is contained in this class, and its base classes. Other important
* classes for the Eigen API are Matrix, and VectorwiseOp.
*
* Note that some methods are defined in other modules such as the \ref LU_Module LU module
* for all functions related to matrix inversions.
*
* \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
*
* When writing a function taking Eigen objects as argument, if you want your function
* to take as argument any matrix, vector, or expression, just let it take a
* MatrixBase argument. As an example, here is a function printFirstRow which, given
* a matrix, vector, or expression \a x, prints the first row of \a x.
*
* \code
template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
*
* \sa \blank \ref TopicClassHierarchy
*/
template<typename Derived> class MatrixBase
: public DenseBase<Derived>
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef MatrixBase StorageBaseType;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::eval;
using Base::operator-;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
typedef typename Base::RowXpr RowXpr;
typedef typename Base::ColXpr ColXpr;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** type of the equivalent square matrix */
typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** \returns the size of the main diagonal, which is min(rows(),cols()).
* \sa rows(), cols(), SizeAtCompileTime. */
EIGEN_DEVICE_FUNC
inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); }
typedef typename Base::PlainObject PlainObject;
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
/** \internal the return type of MatrixBase::adjoint() */
typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
ConstTransposeReturnType
>::type AdjointReturnType;
/** \internal Return type of eigenvalues() */
typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
/** \internal the return type of identity */
typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,PlainObject> IdentityReturnType;
/** \internal the return type of unit vectors */
typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
#define EIGEN_DOC_UNARY_ADDONS(X,Y)
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# ifdef EIGEN_MATRIXBASE_PLUGIN
# include EIGEN_MATRIXBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_UNARY_ADDONS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const MatrixBase& other);
// We cannot inherit here via Base::operator= since it is causing
// trouble with MSVC.
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator=(const DenseBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
Derived& operator=(const ReturnByValue<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator+=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Derived& operator-=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
const Product<Derived,OtherDerived>
operator*(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
const Product<Derived,OtherDerived,LazyProduct>
lazyProduct(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
Derived& operator*=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheLeft(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheRight(const EigenBase<OtherDerived>& other);
template<typename DiagonalDerived>
EIGEN_DEVICE_FUNC
const Product<Derived, DiagonalDerived, LazyProduct>
operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
dot(const MatrixBase<OtherDerived>& other) const;
EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
EIGEN_DEVICE_FUNC RealScalar norm() const;
RealScalar stableNorm() const;
RealScalar blueNorm() const;
RealScalar hypotNorm() const;
EIGEN_DEVICE_FUNC const PlainObject normalized() const;
EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
EIGEN_DEVICE_FUNC void normalize();
EIGEN_DEVICE_FUNC void stableNormalize();
EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
EIGEN_DEVICE_FUNC void adjointInPlace();
typedef Diagonal<Derived> DiagonalReturnType;
EIGEN_DEVICE_FUNC
DiagonalReturnType diagonal();
typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
EIGEN_DEVICE_FUNC
ConstDiagonalReturnType diagonal() const;
template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
template<int Index>
EIGEN_DEVICE_FUNC
typename DiagonalIndexReturnType<Index>::Type diagonal();
template<int Index>
EIGEN_DEVICE_FUNC
typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
EIGEN_DEVICE_FUNC
DiagonalDynamicIndexReturnType diagonal(Index index);
EIGEN_DEVICE_FUNC
ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
template<unsigned int Mode>
EIGEN_DEVICE_FUNC
typename TriangularViewReturnType<Mode>::Type triangularView();
template<unsigned int Mode>
EIGEN_DEVICE_FUNC
typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC
typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC
typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
EIGEN_DEVICE_FUNC
const DiagonalWrapper<const Derived> asDiagonal() const;
const PermutationWrapper<const Derived> asPermutation() const;
EIGEN_DEVICE_FUNC
Derived& setIdentity();
EIGEN_DEVICE_FUNC
Derived& setIdentity(Index rows, Index cols);
EIGEN_DEVICE_FUNC Derived& setUnit(Index i);
EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i);
bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived>
bool isOrthogonal(const MatrixBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
/** \returns true if each coefficients of \c *this and \a other are all exactly equal.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator!= */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const
{ return cwiseEqual(other).all(); }
/** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator== */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const
{ return cwiseNotEqual(other).any(); }
NoAlias<Derived,Eigen::MatrixBase > EIGEN_DEVICE_FUNC noalias();
// TODO forceAlignedAccess is temporarily disabled
// Need to find a nicer workaround.
inline const Derived& forceAlignedAccess() const { return derived(); }
inline Derived& forceAlignedAccess() { return derived(); }
template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }
template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }
EIGEN_DEVICE_FUNC Scalar trace() const;
template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
/** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
/** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }
/////////// LU module ///////////
inline const FullPivLU<PlainObject> fullPivLu() const;
inline const PartialPivLU<PlainObject> partialPivLu() const;
inline const PartialPivLU<PlainObject> lu() const;
EIGEN_DEVICE_FUNC
inline const Inverse<Derived> inverse() const;
template<typename ResultType>
inline void computeInverseAndDetWithCheck(
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
template<typename ResultType>
inline void computeInverseWithCheck(
ResultType& inverse,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
EIGEN_DEVICE_FUNC
Scalar determinant() const;
/////////// Cholesky module ///////////
inline const LLT<PlainObject> llt() const;
inline const LDLT<PlainObject> ldlt() const;
/////////// QR module ///////////
inline const HouseholderQR<PlainObject> householderQr() const;
inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;
/////////// Eigenvalues module ///////////
inline EigenvaluesReturnType eigenvalues() const;
inline RealScalar operatorNorm() const;
/////////// SVD module ///////////
inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
inline BDCSVD<PlainObject> bdcSvd(unsigned int computationOptions = 0) const;
/////////// Geometry module ///////////
#ifndef EIGEN_PARSED_BY_DOXYGEN
/// \internal helper struct to form the return type of the cross product
template<typename OtherDerived> struct cross_product_return_type {
typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
};
#endif // EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifndef EIGEN_PARSED_BY_DOXYGEN
inline typename cross_product_return_type<OtherDerived>::type
#else
inline PlainObject
#endif
cross(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
EIGEN_DEVICE_FUNC
inline PlainObject unitOrthogonal(void) const;
EIGEN_DEVICE_FUNC
inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?)
enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
: ColsAtCompileTime==1 ? Vertical : Horizontal };
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
EIGEN_DEVICE_FUNC
inline HomogeneousReturnType homogeneous() const;
enum {
SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
};
typedef Block<const Derived,
internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
EIGEN_DEVICE_FUNC
inline const HNormalizedReturnType hnormalized() const;
////////// Householder module ///////////
EIGEN_DEVICE_FUNC
void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void makeHouseholder(EssentialPart& essential,
Scalar& tau, RealScalar& beta) const;
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void applyHouseholderOnTheLeft(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void applyHouseholderOnTheRight(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
///////// Jacobi module /////////
template<typename OtherScalar>
EIGEN_DEVICE_FUNC
void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
template<typename OtherScalar>
EIGEN_DEVICE_FUNC
void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
///////// SparseCore module /////////
template<typename OtherDerived>
EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
{
return other.cwiseProduct(derived());
}
///////// MatrixFunctions module /////////
typedef typename internal::stem_function<Scalar>::type StemFunction;
#define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
/** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
const ReturnType<Derived> Name() const;
#define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
/** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
const ReturnType<Derived> Name(Argument) const;
EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
/** \brief Helper function for the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>.*/
const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
#if EIGEN_HAS_CXX11_MATH
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine)
#endif
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p)
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase)
private:
EIGEN_DEVICE_FUNC explicit MatrixBase(int);
EIGEN_DEVICE_FUNC MatrixBase(int,int);
template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
};
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** replaces \c *this by \c *this * \a other.
*
* \returns a reference to \c *this
*
* Example: \include MatrixBase_applyOnTheRight.cpp
* Output: \verbinclude MatrixBase_applyOnTheRight.out
*/
template<typename Derived>
template<typename OtherDerived>
inline Derived&
MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheRight(derived());
return derived();
}
/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
*
* Example: \include MatrixBase_applyOnTheRight.cpp
* Output: \verbinclude MatrixBase_applyOnTheRight.out
*/
template<typename Derived>
template<typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheRight(derived());
}
/** replaces \c *this by \a other * \c *this.
*
* Example: \include MatrixBase_applyOnTheLeft.cpp
* Output: \verbinclude MatrixBase_applyOnTheLeft.out
*/
template<typename Derived>
template<typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheLeft(derived());
}
} // end namespace Eigen
#endif // EIGEN_MATRIXBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NESTBYVALUE_H
#define EIGEN_NESTBYVALUE_H
namespace Eigen {
namespace internal {
template<typename ExpressionType>
struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
{
enum {
Flags = traits<ExpressionType>::Flags & ~NestByRefBit
};
};
}
/** \class NestByValue
* \ingroup Core_Module
*
* \brief Expression which must be nested by value
*
* \tparam 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> class NestByValue
: public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
{
public:
typedef typename internal::dense_xpr_base<NestByValue>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
EIGEN_DEVICE_FUNC const ExpressionType& nestedExpression() const { return m_expression; }
protected:
const ExpressionType m_expression;
};
/** \returns an expression of the temporary version of *this.
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline const NestByValue<Derived>
DenseBase<Derived>::nestByValue() const
{
return NestByValue<Derived>(derived());
}
namespace internal {
// Evaluator of Solve -> eval into a temporary
template<typename ArgType>
struct evaluator<NestByValue<ArgType> >
: public evaluator<ArgType>
{
typedef evaluator<ArgType> Base;
EIGEN_DEVICE_FUNC explicit evaluator(const NestByValue<ArgType>& xpr)
: Base(xpr.nestedExpression())
{}
};
}
} // end namespace Eigen
#endif // EIGEN_NESTBYVALUE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NOALIAS_H
#define EIGEN_NOALIAS_H
namespace Eigen {
/** \class NoAlias
* \ingroup Core_Module
*
* \brief Pseudo expression providing an operator = assuming no aliasing
*
* \tparam ExpressionType the type of the object on which to do the lazy assignment
*
* This class represents an expression with special assignment operators
* assuming no aliasing between the target expression and the source expression.
* More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
* It is the return type of MatrixBase::noalias()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::noalias()
*/
template<typename ExpressionType, template <typename> class StorageBase>
class NoAlias
{
public:
typedef typename ExpressionType::Scalar Scalar;
EIGEN_DEVICE_FUNC
explicit NoAlias(ExpressionType& expression) : m_expression(expression) {}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
{
call_assignment_no_alias(m_expression, other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
return m_expression;
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
{
call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
return m_expression;
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
{
call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
return m_expression;
}
EIGEN_DEVICE_FUNC
ExpressionType& expression() const
{
return m_expression;
}
protected:
ExpressionType& m_expression;
};
/** \returns a pseudo expression of \c *this with an operator= assuming
* no aliasing between \c *this and the source expression.
*
* More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
* Currently, even though several expressions may alias, only product
* expressions have this flag. Therefore, noalias() is only useful when
* the source expression contains a matrix product.
*
* Here are some examples where noalias is useful:
* \code
* D.noalias() = A * B;
* D.noalias() += A.transpose() * B;
* D.noalias() -= 2 * A * B.adjoint();
* \endcode
*
* On the other hand the following example will lead to a \b wrong result:
* \code
* A.noalias() = A * B;
* \endcode
* because the result matrix A is also an operand of the matrix product. Therefore,
* there is no alternative than evaluating A * B in a temporary, that is the default
* behavior when you write:
* \code
* A = A * B;
* \endcode
*
* \sa class NoAlias
*/
template<typename Derived>
NoAlias<Derived,MatrixBase> EIGEN_DEVICE_FUNC MatrixBase<Derived>::noalias()
{
return NoAlias<Derived, Eigen::MatrixBase >(derived());
}
} // end namespace Eigen
#endif // EIGEN_NOALIAS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H
namespace Eigen {
namespace internal {
// default implementation of digits10(), based on numeric_limits if specialized,
// 0 for integer types, and log10(epsilon()) otherwise.
template< typename T,
bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_digits10_impl
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() { return std::numeric_limits<T>::digits10; }
};
template<typename T>
struct default_digits10_impl<T,false,false> // Floating point
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() {
using std::log10;
using std::ceil;
typedef typename NumTraits<T>::Real Real;
return int(ceil(-log10(NumTraits<Real>::epsilon())));
}
};
template<typename T>
struct default_digits10_impl<T,false,true> // Integer
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() { return 0; }
};
// default implementation of digits(), based on numeric_limits if specialized,
// 0 for integer types, and log2(epsilon()) otherwise.
template< typename T,
bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_digits_impl
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() { return std::numeric_limits<T>::digits; }
};
template<typename T>
struct default_digits_impl<T,false,false> // Floating point
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() {
using std::log;
using std::ceil;
typedef typename NumTraits<T>::Real Real;
return int(ceil(-log(NumTraits<Real>::epsilon())/log(static_cast<Real>(2))));
}
};
template<typename T>
struct default_digits_impl<T,false,true> // Integer
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static int run() { return 0; }
};
} // end namespace internal
namespace numext {
/** \internal bit-wise cast without changing the underlying bit representation. */
// TODO: Replace by std::bit_cast (available in C++20)
template <typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
#if EIGEN_HAS_TYPE_TRAITS
// The behaviour of memcpy is not specified for non-trivially copyable types
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED);
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
THIS_TYPE_IS_NOT_SUPPORTED);
#endif
EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED);
Tgt tgt;
EIGEN_USING_STD(memcpy)
memcpy(&tgt, &src, sizeof(Tgt));
return tgt;
}
} // namespace numext
/** \class NumTraits
* \ingroup Core_Module
*
* \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
*
* \tparam T the numeric type at hand
*
* This class stores enums, typedefs and static methods giving information about a numeric type.
*
* The provided data consists of:
* \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
* then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
* is a typedef to \a U.
* \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
* such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
* \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
* take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
* only intended as a helper for code that needs to explicitly promote types.
* \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex<U>, Literal is defined as \c U.
* Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
* \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
* this means, just use \a T here.
* \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
* type, and to 0 otherwise.
* \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
* and to \c 0 otherwise.
* \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
* to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
* Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost.
* \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
* \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
* be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
* \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>,
* it returns a \a Real instead of a \a T.
* \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
* value by the fuzzy comparison operators.
* \li highest() and lowest() functions returning the highest and lowest possible values respectively.
* \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point). This is
* the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a>
* which is used as the default implementation if specialized.
* \li digits10() function returning the number of decimal digits that can be represented without change. This is
* the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
* which is used as the default implementation if specialized.
* \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
* such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent to
* <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
* <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
* \li infinity() function returning a representation of positive infinity, if available.
* \li quiet_NaN function returning a non-signaling "not-a-number", if available.
*/
template<typename T> struct GenericNumTraits
{
enum {
IsInteger = std::numeric_limits<T>::is_integer,
IsSigned = std::numeric_limits<T>::is_signed,
IsComplex = 0,
RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
ReadCost = 1,
AddCost = 1,
MulCost = 1
};
typedef T Real;
typedef typename internal::conditional<
IsInteger,
typename internal::conditional<sizeof(T)<=2, float, double>::type,
T
>::type NonInteger;
typedef T Nested;
typedef T Literal;
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline Real epsilon()
{
return numext::numeric_limits<T>::epsilon();
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline int digits10()
{
return internal::default_digits10_impl<T>::run();
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline int digits()
{
return internal::default_digits_impl<T>::run();
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline int min_exponent()
{
return numext::numeric_limits<T>::min_exponent;
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline int max_exponent()
{
return numext::numeric_limits<T>::max_exponent;
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline Real dummy_precision()
{
// make sure to override this for floating-point types
return Real(0);
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline T highest() {
return (numext::numeric_limits<T>::max)();
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline T lowest() {
return IsInteger ? (numext::numeric_limits<T>::min)()
: static_cast<T>(-(numext::numeric_limits<T>::max)());
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline T infinity() {
return numext::numeric_limits<T>::infinity();
}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline T quiet_NaN() {
return numext::numeric_limits<T>::quiet_NaN();
}
};
template<typename T> struct NumTraits : GenericNumTraits<T>
{};
template<> struct NumTraits<float>
: GenericNumTraits<float>
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline float dummy_precision() { return 1e-5f; }
};
template<> struct NumTraits<double> : GenericNumTraits<double>
{
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline double dummy_precision() { return 1e-12; }
};
template<> struct NumTraits<long double>
: GenericNumTraits<long double>
{
EIGEN_CONSTEXPR
static inline long double dummy_precision() { return 1e-15l; }
};
template<typename _Real> struct NumTraits<std::complex<_Real> >
: GenericNumTraits<std::complex<_Real> >
{
typedef _Real Real;
typedef typename NumTraits<_Real>::Literal Literal;
enum {
IsComplex = 1,
RequireInitialization = NumTraits<_Real>::RequireInitialization,
ReadCost = 2 * NumTraits<_Real>::ReadCost,
AddCost = 2 * NumTraits<Real>::AddCost,
MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
};
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline int digits10() { return NumTraits<Real>::digits10(); }
};
template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
{
typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
typedef ArrayType & Nested;
typedef typename NumTraits<Scalar>::Literal Literal;
enum {
IsComplex = NumTraits<Scalar>::IsComplex,
IsInteger = NumTraits<Scalar>::IsInteger,
IsSigned = NumTraits<Scalar>::IsSigned,
RequireInitialization = 1,
ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
};
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
EIGEN_CONSTEXPR
static inline int digits10() { return NumTraits<Scalar>::digits10(); }
};
template<> struct NumTraits<std::string>
: GenericNumTraits<std::string>
{
enum {
RequireInitialization = 1,
ReadCost = HugeCost,
AddCost = HugeCost,
MulCost = HugeCost
};
EIGEN_CONSTEXPR
static inline int digits10() { return 0; }
private:
static inline std::string epsilon();
static inline std::string dummy_precision();
static inline std::string lowest();
static inline std::string highest();
static inline std::string infinity();
static inline std::string quiet_NaN();
};
// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
template<> struct NumTraits<void> {};
template<> struct NumTraits<bool> : GenericNumTraits<bool> {};
} // end namespace Eigen
#endif // EIGEN_NUMTRAITS_H

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lib/eigen-3.4.0/Eigen/src/Core/PartialReduxEvaluator.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PARTIALREDUX_H
#define EIGEN_PARTIALREDUX_H
namespace Eigen {
namespace internal {
/***************************************************************************
*
* This file provides evaluators for partial reductions.
* There are two modes:
*
* - scalar path: simply calls the respective function on the column or row.
* -> nothing special here, all the tricky part is handled by the return
* types of VectorwiseOp's members. They embed the functor calling the
* respective DenseBase's member function.
*
* - vectorized path: implements a packet-wise reductions followed by
* some (optional) processing of the outcome, e.g., division by n for mean.
*
* For the vectorized path let's observe that the packet-size and outer-unrolling
* are both decided by the assignement logic. So all we have to do is to decide
* on the inner unrolling.
*
* For the unrolling, we can reuse "internal::redux_vec_unroller" from Redux.h,
* but be need to be careful to specify correct increment.
*
***************************************************************************/
/* logic deciding a strategy for unrolling of vectorized paths */
template<typename Func, typename Evaluator>
struct packetwise_redux_traits
{
enum {
OuterSize = int(Evaluator::IsRowMajor) ? Evaluator::RowsAtCompileTime : Evaluator::ColsAtCompileTime,
Cost = OuterSize == Dynamic ? HugeCost
: OuterSize * Evaluator::CoeffReadCost + (OuterSize-1) * functor_traits<Func>::Cost,
Unrolling = Cost <= EIGEN_UNROLLING_LIMIT ? CompleteUnrolling : NoUnrolling
};
};
/* Value to be returned when size==0 , by default let's return 0 */
template<typename PacketType,typename Func>
EIGEN_DEVICE_FUNC
PacketType packetwise_redux_empty_value(const Func& ) { return pset1<PacketType>(0); }
/* For products the default is 1 */
template<typename PacketType,typename Scalar>
EIGEN_DEVICE_FUNC
PacketType packetwise_redux_empty_value(const scalar_product_op<Scalar,Scalar>& ) { return pset1<PacketType>(1); }
/* Perform the actual reduction */
template<typename Func, typename Evaluator,
int Unrolling = packetwise_redux_traits<Func, Evaluator>::Unrolling
>
struct packetwise_redux_impl;
/* Perform the actual reduction with unrolling */
template<typename Func, typename Evaluator>
struct packetwise_redux_impl<Func, Evaluator, CompleteUnrolling>
{
typedef redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
typedef typename Evaluator::Scalar Scalar;
template<typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
PacketType run(const Evaluator &eval, const Func& func, Index /*size*/)
{
return redux_vec_unroller<Func, Evaluator, 0, packetwise_redux_traits<Func, Evaluator>::OuterSize>::template run<PacketType>(eval,func);
}
};
/* Add a specialization of redux_vec_unroller for size==0 at compiletime.
* This specialization is not required for general reductions, which is
* why it is defined here.
*/
template<typename Func, typename Evaluator, int Start>
struct redux_vec_unroller<Func, Evaluator, Start, 0>
{
template<typename PacketType>
EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE PacketType run(const Evaluator &, const Func& f)
{
return packetwise_redux_empty_value<PacketType>(f);
}
};
/* Perform the actual reduction for dynamic sizes */
template<typename Func, typename Evaluator>
struct packetwise_redux_impl<Func, Evaluator, NoUnrolling>
{
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
template<typename PacketType>
EIGEN_DEVICE_FUNC
static PacketType run(const Evaluator &eval, const Func& func, Index size)
{
if(size==0)
return packetwise_redux_empty_value<PacketType>(func);
const Index size4 = (size-1)&(~3);
PacketType p = eval.template packetByOuterInner<Unaligned,PacketType>(0,0);
Index i = 1;
// This loop is optimized for instruction pipelining:
// - each iteration generates two independent instructions
// - thanks to branch prediction and out-of-order execution we have independent instructions across loops
for(; i<size4; i+=4)
p = func.packetOp(p,
func.packetOp(
func.packetOp(eval.template packetByOuterInner<Unaligned,PacketType>(i+0,0),eval.template packetByOuterInner<Unaligned,PacketType>(i+1,0)),
func.packetOp(eval.template packetByOuterInner<Unaligned,PacketType>(i+2,0),eval.template packetByOuterInner<Unaligned,PacketType>(i+3,0))));
for(; i<size; ++i)
p = func.packetOp(p, eval.template packetByOuterInner<Unaligned,PacketType>(i,0));
return p;
}
};
template< typename ArgType, typename MemberOp, int Direction>
struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
: evaluator_base<PartialReduxExpr<ArgType, MemberOp, Direction> >
{
typedef PartialReduxExpr<ArgType, MemberOp, Direction> XprType;
typedef typename internal::nested_eval<ArgType,1>::type ArgTypeNested;
typedef typename internal::add_const_on_value_type<ArgTypeNested>::type ConstArgTypeNested;
typedef typename internal::remove_all<ArgTypeNested>::type ArgTypeNestedCleaned;
typedef typename ArgType::Scalar InputScalar;
typedef typename XprType::Scalar Scalar;
enum {
TraversalSize = Direction==int(Vertical) ? int(ArgType::RowsAtCompileTime) : int(ArgType::ColsAtCompileTime)
};
typedef typename MemberOp::template Cost<int(TraversalSize)> CostOpType;
enum {
CoeffReadCost = TraversalSize==Dynamic ? HugeCost
: TraversalSize==0 ? 1
: int(TraversalSize) * int(evaluator<ArgType>::CoeffReadCost) + int(CostOpType::value),
_ArgFlags = evaluator<ArgType>::Flags,
_Vectorizable = bool(int(_ArgFlags)&PacketAccessBit)
&& bool(MemberOp::Vectorizable)
&& (Direction==int(Vertical) ? bool(_ArgFlags&RowMajorBit) : (_ArgFlags&RowMajorBit)==0)
&& (TraversalSize!=0),
Flags = (traits<XprType>::Flags&RowMajorBit)
| (evaluator<ArgType>::Flags&(HereditaryBits&(~RowMajorBit)))
| (_Vectorizable ? PacketAccessBit : 0)
| LinearAccessBit,
Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized
};
EIGEN_DEVICE_FUNC explicit evaluator(const XprType xpr)
: m_arg(xpr.nestedExpression()), m_functor(xpr.functor())
{
EIGEN_INTERNAL_CHECK_COST_VALUE(TraversalSize==Dynamic ? HugeCost : (TraversalSize==0 ? 1 : int(CostOpType::value)));
EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
}
typedef typename XprType::CoeffReturnType CoeffReturnType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar coeff(Index i, Index j) const
{
return coeff(Direction==Vertical ? j : i);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar coeff(Index index) const
{
return m_functor(m_arg.template subVector<DirectionType(Direction)>(index));
}
template<int LoadMode,typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
PacketType packet(Index i, Index j) const
{
return packet<LoadMode,PacketType>(Direction==Vertical ? j : i);
}
template<int LoadMode,typename PacketType>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
PacketType packet(Index idx) const
{
enum { PacketSize = internal::unpacket_traits<PacketType>::size };
typedef Block<const ArgTypeNestedCleaned,
Direction==Vertical ? int(ArgType::RowsAtCompileTime) : int(PacketSize),
Direction==Vertical ? int(PacketSize) : int(ArgType::ColsAtCompileTime),
true /* InnerPanel */> PanelType;
PanelType panel(m_arg,
Direction==Vertical ? 0 : idx,
Direction==Vertical ? idx : 0,
Direction==Vertical ? m_arg.rows() : Index(PacketSize),
Direction==Vertical ? Index(PacketSize) : m_arg.cols());
// FIXME
// See bug 1612, currently if PacketSize==1 (i.e. complex<double> with 128bits registers) then the storage-order of panel get reversed
// and methods like packetByOuterInner do not make sense anymore in this context.
// So let's just by pass "vectorization" in this case:
if(PacketSize==1)
return internal::pset1<PacketType>(coeff(idx));
typedef typename internal::redux_evaluator<PanelType> PanelEvaluator;
PanelEvaluator panel_eval(panel);
typedef typename MemberOp::BinaryOp BinaryOp;
PacketType p = internal::packetwise_redux_impl<BinaryOp,PanelEvaluator>::template run<PacketType>(panel_eval,m_functor.binaryFunc(),m_arg.outerSize());
return p;
}
protected:
ConstArgTypeNested m_arg;
const MemberOp m_functor;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_PARTIALREDUX_H

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lib/eigen-3.4.0/Eigen/src/Core/PermutationMatrix.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PERMUTATIONMATRIX_H
#define EIGEN_PERMUTATIONMATRIX_H
namespace Eigen {
namespace internal {
enum PermPermProduct_t {PermPermProduct};
} // end namespace internal
/** \class PermutationBase
* \ingroup Core_Module
*
* \brief Base class for permutations
*
* \tparam Derived the derived class
*
* This class is the base class for all expressions representing a permutation matrix,
* internally stored as a vector of integers.
* The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
* \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
* \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
* This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
* \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
*
* Permutation matrices are square and invertible.
*
* Notice that in addition to the member functions and operators listed here, there also are non-member
* operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
* on either side.
*
* \sa class PermutationMatrix, class PermutationWrapper
*/
template<typename Derived>
class PermutationBase : public EigenBase<Derived>
{
typedef internal::traits<Derived> Traits;
typedef EigenBase<Derived> Base;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
enum {
Flags = Traits::Flags,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::StorageIndex StorageIndex;
typedef Matrix<StorageIndex,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
DenseMatrixType;
typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,StorageIndex>
PlainPermutationType;
typedef PlainPermutationType PlainObject;
using Base::derived;
typedef Inverse<Derived> InverseReturnType;
typedef void Scalar;
#endif
/** Copies the other permutation into *this */
template<typename OtherDerived>
Derived& operator=(const PermutationBase<OtherDerived>& other)
{
indices() = other.indices();
return derived();
}
/** Assignment from the Transpositions \a tr */
template<typename OtherDerived>
Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
{
setIdentity(tr.size());
for(Index k=size()-1; k>=0; --k)
applyTranspositionOnTheRight(k,tr.coeff(k));
return derived();
}
/** \returns the number of rows */
inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }
/** \returns the number of columns */
inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }
/** \returns the size of a side of the respective square matrix, i.e., the number of indices */
inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (Index i=0; i<rows(); ++i)
other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
}
#endif
/** \returns a Matrix object initialized from this permutation matrix. Notice that it
* is inefficient to return this Matrix object by value. For efficiency, favor using
* the Matrix constructor taking EigenBase objects.
*/
DenseMatrixType toDenseMatrix() const
{
return derived();
}
/** const version of indices(). */
const IndicesType& indices() const { return derived().indices(); }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return derived().indices(); }
/** Resizes to given size.
*/
inline void resize(Index newSize)
{
indices().resize(newSize);
}
/** Sets *this to be the identity permutation matrix */
void setIdentity()
{
StorageIndex n = StorageIndex(size());
for(StorageIndex i = 0; i < n; ++i)
indices().coeffRef(i) = i;
}
/** Sets *this to be the identity permutation matrix of given size.
*/
void setIdentity(Index newSize)
{
resize(newSize);
setIdentity();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the left.
*
* \returns a reference to *this.
*
* \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
* this has linear complexity and requires a lot of branching.
*
* \sa applyTranspositionOnTheRight(Index,Index)
*/
Derived& applyTranspositionOnTheLeft(Index i, Index j)
{
eigen_assert(i>=0 && j>=0 && i<size() && j<size());
for(Index k = 0; k < size(); ++k)
{
if(indices().coeff(k) == i) indices().coeffRef(k) = StorageIndex(j);
else if(indices().coeff(k) == j) indices().coeffRef(k) = StorageIndex(i);
}
return derived();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the right.
*
* \returns a reference to *this.
*
* This is a fast operation, it only consists in swapping two indices.
*
* \sa applyTranspositionOnTheLeft(Index,Index)
*/
Derived& applyTranspositionOnTheRight(Index i, Index j)
{
eigen_assert(i>=0 && j>=0 && i<size() && j<size());
std::swap(indices().coeffRef(i), indices().coeffRef(j));
return derived();
}
/** \returns the inverse permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
inline InverseReturnType inverse() const
{ return InverseReturnType(derived()); }
/** \returns the tranpose permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
inline InverseReturnType transpose() const
{ return InverseReturnType(derived()); }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
protected:
template<typename OtherDerived>
void assignTranspose(const PermutationBase<OtherDerived>& other)
{
for (Index i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
}
template<typename Lhs,typename Rhs>
void assignProduct(const Lhs& lhs, const Rhs& rhs)
{
eigen_assert(lhs.cols() == rhs.rows());
for (Index i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
}
#endif
public:
/** \returns the product permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
template<typename Other>
inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
{ return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
/** \returns the product of a permutation with another inverse permutation.
*
* \note \blank \note_try_to_help_rvo
*/
template<typename Other>
inline PlainPermutationType operator*(const InverseImpl<Other,PermutationStorage>& other) const
{ return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
/** \returns the product of an inverse permutation with another permutation.
*
* \note \blank \note_try_to_help_rvo
*/
template<typename Other> friend
inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other, const PermutationBase& perm)
{ return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
/** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.
*
* This function is O(\c n) procedure allocating a buffer of \c n booleans.
*/
Index determinant() const
{
Index res = 1;
Index n = size();
Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
mask.fill(false);
Index r = 0;
while(r < n)
{
// search for the next seed
while(r<n && mask[r]) r++;
if(r>=n)
break;
// we got one, let's follow it until we are back to the seed
Index k0 = r++;
mask.coeffRef(k0) = true;
for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
{
mask.coeffRef(k) = true;
res = -res;
}
}
return res;
}
protected:
};
namespace internal {
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >
: traits<Matrix<_StorageIndex,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef PermutationStorage StorageKind;
typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
typedef _StorageIndex StorageIndex;
typedef void Scalar;
};
}
/** \class PermutationMatrix
* \ingroup Core_Module
*
* \brief Permutation matrix
*
* \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
* \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
* \tparam _StorageIndex the integer type of the indices
*
* This class represents a permutation matrix, internally stored as a vector of integers.
*
* \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
*/
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >
{
typedef PermutationBase<PermutationMatrix> Base;
typedef internal::traits<PermutationMatrix> Traits;
public:
typedef const PermutationMatrix& Nested;
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
typedef typename Traits::StorageIndex StorageIndex;
#endif
inline PermutationMatrix()
{}
/** Constructs an uninitialized permutation matrix of given size.
*/
explicit inline PermutationMatrix(Index size) : m_indices(size)
{
eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
}
/** Copy constructor. */
template<typename OtherDerived>
inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
: m_indices(other.indices()) {}
/** Generic constructor from expression of the indices. The indices
* array has the meaning that the permutations sends each integer i to indices[i].
*
* \warning It is your responsibility to check that the indices array that you passes actually
* describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
* array's size.
*/
template<typename Other>
explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices)
{}
/** Convert the Transpositions \a tr to a permutation matrix */
template<typename Other>
explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
: m_indices(tr.size())
{
*this = tr;
}
/** Copies the other permutation into *this */
template<typename Other>
PermutationMatrix& operator=(const PermutationBase<Other>& other)
{
m_indices = other.indices();
return *this;
}
/** Assignment from the Transpositions \a tr */
template<typename Other>
PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
{
return Base::operator=(tr.derived());
}
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Other>
PermutationMatrix(const InverseImpl<Other,PermutationStorage>& other)
: m_indices(other.derived().nestedExpression().size())
{
eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
StorageIndex end = StorageIndex(m_indices.size());
for (StorageIndex i=0; i<end;++i)
m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
}
template<typename Lhs,typename Rhs>
PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
: m_indices(lhs.indices().size())
{
Base::assignProduct(lhs,rhs);
}
#endif
protected:
IndicesType m_indices;
};
namespace internal {
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>
struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess> >
: traits<Matrix<_StorageIndex,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef PermutationStorage StorageKind;
typedef Map<const Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
typedef _StorageIndex StorageIndex;
typedef void Scalar;
};
}
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>
class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess>
: public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess> >
{
typedef PermutationBase<Map> Base;
typedef internal::traits<Map> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
typedef typename IndicesType::Scalar StorageIndex;
#endif
inline Map(const StorageIndex* indicesPtr)
: m_indices(indicesPtr)
{}
inline Map(const StorageIndex* indicesPtr, Index size)
: m_indices(indicesPtr,size)
{}
/** Copies the other permutation into *this */
template<typename Other>
Map& operator=(const PermutationBase<Other>& other)
{ return Base::operator=(other.derived()); }
/** Assignment from the Transpositions \a tr */
template<typename Other>
Map& operator=(const TranspositionsBase<Other>& tr)
{ return Base::operator=(tr.derived()); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
Map& operator=(const Map& other)
{
m_indices = other.m_indices;
return *this;
}
#endif
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
protected:
IndicesType m_indices;
};
template<typename _IndicesType> class TranspositionsWrapper;
namespace internal {
template<typename _IndicesType>
struct traits<PermutationWrapper<_IndicesType> >
{
typedef PermutationStorage StorageKind;
typedef void Scalar;
typedef typename _IndicesType::Scalar StorageIndex;
typedef _IndicesType IndicesType;
enum {
RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
Flags = 0
};
};
}
/** \class PermutationWrapper
* \ingroup Core_Module
*
* \brief Class to view a vector of integers as a permutation matrix
*
* \tparam _IndicesType the type of the vector of integer (can be any compatible expression)
*
* This class allows to view any vector expression of integers as a permutation matrix.
*
* \sa class PermutationBase, class PermutationMatrix
*/
template<typename _IndicesType>
class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
{
typedef PermutationBase<PermutationWrapper> Base;
typedef internal::traits<PermutationWrapper> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
#endif
inline PermutationWrapper(const IndicesType& indices)
: m_indices(indices)
{}
/** const version of indices(). */
const typename internal::remove_all<typename IndicesType::Nested>::type&
indices() const { return m_indices; }
protected:
typename IndicesType::Nested m_indices;
};
/** \returns the matrix with the permutation applied to the columns.
*/
template<typename MatrixDerived, typename PermutationDerived>
EIGEN_DEVICE_FUNC
const Product<MatrixDerived, PermutationDerived, AliasFreeProduct>
operator*(const MatrixBase<MatrixDerived> &matrix,
const PermutationBase<PermutationDerived>& permutation)
{
return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>
(matrix.derived(), permutation.derived());
}
/** \returns the matrix with the permutation applied to the rows.
*/
template<typename PermutationDerived, typename MatrixDerived>
EIGEN_DEVICE_FUNC
const Product<PermutationDerived, MatrixDerived, AliasFreeProduct>
operator*(const PermutationBase<PermutationDerived> &permutation,
const MatrixBase<MatrixDerived>& matrix)
{
return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>
(permutation.derived(), matrix.derived());
}
template<typename PermutationType>
class InverseImpl<PermutationType, PermutationStorage>
: public EigenBase<Inverse<PermutationType> >
{
typedef typename PermutationType::PlainPermutationType PlainPermutationType;
typedef internal::traits<PermutationType> PermTraits;
protected:
InverseImpl() {}
public:
typedef Inverse<PermutationType> InverseType;
using EigenBase<Inverse<PermutationType> >::derived;
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename PermutationType::DenseMatrixType DenseMatrixType;
enum {
RowsAtCompileTime = PermTraits::RowsAtCompileTime,
ColsAtCompileTime = PermTraits::ColsAtCompileTime,
MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
};
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (Index i=0; i<derived().rows();++i)
other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
}
#endif
/** \return the equivalent permutation matrix */
PlainPermutationType eval() const { return derived(); }
DenseMatrixType toDenseMatrix() const { return derived(); }
/** \returns the matrix with the inverse permutation applied to the columns.
*/
template<typename OtherDerived> friend
const Product<OtherDerived, InverseType, AliasFreeProduct>
operator*(const MatrixBase<OtherDerived>& matrix, const InverseType& trPerm)
{
return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());
}
/** \returns the matrix with the inverse permutation applied to the rows.
*/
template<typename OtherDerived>
const Product<InverseType, OtherDerived, AliasFreeProduct>
operator*(const MatrixBase<OtherDerived>& matrix) const
{
return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());
}
};
template<typename Derived>
const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
{
return derived();
}
namespace internal {
template<> struct AssignmentKind<DenseShape,PermutationShape> { typedef EigenBase2EigenBase Kind; };
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_PERMUTATIONMATRIX_H

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