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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 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_MACROS_H
+#define EIGEN_MACROS_H
+
+//------------------------------------------------------------------------------------------
+// Eigen version and basic defaults
+//------------------------------------------------------------------------------------------
+
+#define EIGEN_WORLD_VERSION 3
+#define EIGEN_MAJOR_VERSION 4
+#define EIGEN_MINOR_VERSION 0
+
+#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
+ (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
+ EIGEN_MINOR_VERSION>=z))))
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
+#else
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
+#endif
+
+#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
+#endif
+
+// Upperbound on the C++ version to use.
+// Expected values are 03, 11, 14, 17, etc.
+// By default, let's use an arbitrarily large C++ version.
+#ifndef EIGEN_MAX_CPP_VER
+#define EIGEN_MAX_CPP_VER 99
+#endif
+
+/** Allows to disable some optimizations which might affect the accuracy of the result.
+ * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
+ * They currently include:
+ * - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.
+ */
+#ifndef EIGEN_FAST_MATH
+#define EIGEN_FAST_MATH 1
+#endif
+
+#ifndef EIGEN_STACK_ALLOCATION_LIMIT
+// 131072 == 128 KB
+#define EIGEN_STACK_ALLOCATION_LIMIT 131072
+#endif
+
+//------------------------------------------------------------------------------------------
+// Compiler identification, EIGEN_COMP_*
+//------------------------------------------------------------------------------------------
+
+/// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
+#ifdef __GNUC__
+ #define EIGEN_COMP_GNUC (__GNUC__*10+__GNUC_MINOR__)
+#else
+ #define EIGEN_COMP_GNUC 0
+#endif
+
+/// \internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang
+#if defined(__clang__)
+ #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)
+#else
+ #define EIGEN_COMP_CLANG 0
+#endif
+
+/// \internal EIGEN_COMP_CASTXML set to 1 if being preprocessed by CastXML
+#if defined(__castxml__)
+ #define EIGEN_COMP_CASTXML 1
+#else
+ #define EIGEN_COMP_CASTXML 0
+#endif
+
+/// \internal EIGEN_COMP_LLVM set to 1 if the compiler backend is llvm
+#if defined(__llvm__)
+ #define EIGEN_COMP_LLVM 1
+#else
+ #define EIGEN_COMP_LLVM 0
+#endif
+
+/// \internal EIGEN_COMP_ICC set to __INTEL_COMPILER if the compiler is Intel compiler, 0 otherwise
+#if defined(__INTEL_COMPILER)
+ #define EIGEN_COMP_ICC __INTEL_COMPILER
+#else
+ #define EIGEN_COMP_ICC 0
+#endif
+
+/// \internal EIGEN_COMP_MINGW set to 1 if the compiler is mingw
+#if defined(__MINGW32__)
+ #define EIGEN_COMP_MINGW 1
+#else
+ #define EIGEN_COMP_MINGW 0
+#endif
+
+/// \internal EIGEN_COMP_SUNCC set to 1 if the compiler is Solaris Studio
+#if defined(__SUNPRO_CC)
+ #define EIGEN_COMP_SUNCC 1
+#else
+ #define EIGEN_COMP_SUNCC 0
+#endif
+
+/// \internal EIGEN_COMP_MSVC set to _MSC_VER if the compiler is Microsoft Visual C++, 0 otherwise.
+#if defined(_MSC_VER)
+ #define EIGEN_COMP_MSVC _MSC_VER
+#else
+ #define EIGEN_COMP_MSVC 0
+#endif
+
+#if defined(__NVCC__)
+#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)
+ #define EIGEN_COMP_NVCC ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))
+#elif defined(__CUDACC_VER__)
+ #define EIGEN_COMP_NVCC __CUDACC_VER__
+#else
+ #error "NVCC did not define compiler version."
+#endif
+#else
+ #define EIGEN_COMP_NVCC 0
+#endif
+
+// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
+// name ver MSC_VER
+// 2008 9 1500
+// 2010 10 1600
+// 2012 11 1700
+// 2013 12 1800
+// 2015 14 1900
+// "15" 15 1900
+// 2017-14.1 15.0 1910
+// 2017-14.11 15.3 1911
+// 2017-14.12 15.5 1912
+// 2017-14.13 15.6 1913
+// 2017-14.14 15.7 1914
+
+/// \internal EIGEN_COMP_MSVC_LANG set to _MSVC_LANG if the compiler is Microsoft Visual C++, 0 otherwise.
+#if defined(_MSVC_LANG)
+ #define EIGEN_COMP_MSVC_LANG _MSVC_LANG
+#else
+ #define EIGEN_COMP_MSVC_LANG 0
+#endif
+
+// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC_LANG:
+// MSVC option Standard MSVC_LANG
+// /std:c++14 (default as of VS 2019) C++14 201402L
+// /std:c++17 C++17 201703L
+// /std:c++latest >C++17 >201703L
+
+/// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl
+#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
+ #define EIGEN_COMP_MSVC_STRICT _MSC_VER
+#else
+ #define EIGEN_COMP_MSVC_STRICT 0
+#endif
+
+/// \internal EIGEN_COMP_IBM set to xlc version if the compiler is IBM XL C++
+// XLC version
+// 3.1 0x0301
+// 4.5 0x0405
+// 5.0 0x0500
+// 12.1 0x0C01
+#if defined(__IBMCPP__) || defined(__xlc__) || defined(__ibmxl__)
+ #define EIGEN_COMP_IBM __xlC__
+#else
+ #define EIGEN_COMP_IBM 0
+#endif
+
+/// \internal EIGEN_COMP_PGI set to PGI version if the compiler is Portland Group Compiler
+#if defined(__PGI)
+ #define EIGEN_COMP_PGI (__PGIC__*100+__PGIC_MINOR__)
+#else
+ #define EIGEN_COMP_PGI 0
+#endif
+
+/// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
+#if defined(__CC_ARM) || defined(__ARMCC_VERSION)
+ #define EIGEN_COMP_ARM 1
+#else
+ #define EIGEN_COMP_ARM 0
+#endif
+
+/// \internal EIGEN_COMP_EMSCRIPTEN set to 1 if the compiler is Emscripten Compiler
+#if defined(__EMSCRIPTEN__)
+ #define EIGEN_COMP_EMSCRIPTEN 1
+#else
+ #define EIGEN_COMP_EMSCRIPTEN 0
+#endif
+
+
+/// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
+#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN)
+ #define EIGEN_COMP_GNUC_STRICT 1
+#else
+ #define EIGEN_COMP_GNUC_STRICT 0
+#endif
+
+
+#if EIGEN_COMP_GNUC
+ #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
+ #define EIGEN_GNUC_AT_MOST(x,y) ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
+ #define EIGEN_GNUC_AT(x,y) ( __GNUC__==x && __GNUC_MINOR__==y )
+#else
+ #define EIGEN_GNUC_AT_LEAST(x,y) 0
+ #define EIGEN_GNUC_AT_MOST(x,y) 0
+ #define EIGEN_GNUC_AT(x,y) 0
+#endif
+
+// FIXME: could probably be removed as we do not support gcc 3.x anymore
+#if EIGEN_COMP_GNUC && (__GNUC__ <= 3)
+#define EIGEN_GCC3_OR_OLDER 1
+#else
+#define EIGEN_GCC3_OR_OLDER 0
+#endif
+
+
+
+//------------------------------------------------------------------------------------------
+// Architecture identification, EIGEN_ARCH_*
+//------------------------------------------------------------------------------------------
+
+
+#if defined(__x86_64__) || (defined(_M_X64) && !defined(_M_ARM64EC)) || defined(__amd64)
+ #define EIGEN_ARCH_x86_64 1
+#else
+ #define EIGEN_ARCH_x86_64 0
+#endif
+
+#if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)
+ #define EIGEN_ARCH_i386 1
+#else
+ #define EIGEN_ARCH_i386 0
+#endif
+
+#if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386
+ #define EIGEN_ARCH_i386_OR_x86_64 1
+#else
+ #define EIGEN_ARCH_i386_OR_x86_64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM set to 1 if the architecture is ARM
+#if defined(__arm__)
+ #define EIGEN_ARCH_ARM 1
+#else
+ #define EIGEN_ARCH_ARM 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM64 set to 1 if the architecture is ARM64
+#if defined(__aarch64__) || defined(_M_ARM64) || defined(_M_ARM64EC)
+ #define EIGEN_ARCH_ARM64 1
+#else
+ #define EIGEN_ARCH_ARM64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM_OR_ARM64 set to 1 if the architecture is ARM or ARM64
+#if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64
+ #define EIGEN_ARCH_ARM_OR_ARM64 1
+#else
+ #define EIGEN_ARCH_ARM_OR_ARM64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARMV8 set to 1 if the architecture is armv8 or greater.
+#if EIGEN_ARCH_ARM_OR_ARM64 && defined(__ARM_ARCH) && __ARM_ARCH >= 8
+#define EIGEN_ARCH_ARMV8 1
+#else
+#define EIGEN_ARCH_ARMV8 0
+#endif
+
+
+/// \internal EIGEN_HAS_ARM64_FP16 set to 1 if the architecture provides an IEEE
+/// compliant Arm fp16 type
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16
+ #if defined(__ARM_FP16_FORMAT_IEEE)
+ #define EIGEN_HAS_ARM64_FP16 1
+ #else
+ #define EIGEN_HAS_ARM64_FP16 0
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC set to 1 if the architecture
+/// supports Neon vector intrinsics for fp16.
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+ #if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
+ #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 1
+ #else
+ #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 0
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC set to 1 if the architecture
+/// supports Neon scalar intrinsics for fp16.
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
+ #if defined(__ARM_FEATURE_FP16_SCALAR_ARITHMETIC)
+ #define EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC 1
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_ARCH_MIPS set to 1 if the architecture is MIPS
+#if defined(__mips__) || defined(__mips)
+ #define EIGEN_ARCH_MIPS 1
+#else
+ #define EIGEN_ARCH_MIPS 0
+#endif
+
+/// \internal EIGEN_ARCH_SPARC set to 1 if the architecture is SPARC
+#if defined(__sparc__) || defined(__sparc)
+ #define EIGEN_ARCH_SPARC 1
+#else
+ #define EIGEN_ARCH_SPARC 0
+#endif
+
+/// \internal EIGEN_ARCH_IA64 set to 1 if the architecture is Intel Itanium
+#if defined(__ia64__)
+ #define EIGEN_ARCH_IA64 1
+#else
+ #define EIGEN_ARCH_IA64 0
+#endif
+
+/// \internal EIGEN_ARCH_PPC set to 1 if the architecture is PowerPC
+#if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC)
+ #define EIGEN_ARCH_PPC 1
+#else
+ #define EIGEN_ARCH_PPC 0
+#endif
+
+
+
+//------------------------------------------------------------------------------------------
+// Operating system identification, EIGEN_OS_*
+//------------------------------------------------------------------------------------------
+
+/// \internal EIGEN_OS_UNIX set to 1 if the OS is a unix variant
+#if defined(__unix__) || defined(__unix)
+ #define EIGEN_OS_UNIX 1
+#else
+ #define EIGEN_OS_UNIX 0
+#endif
+
+/// \internal EIGEN_OS_LINUX set to 1 if the OS is based on Linux kernel
+#if defined(__linux__)
+ #define EIGEN_OS_LINUX 1
+#else
+ #define EIGEN_OS_LINUX 0
+#endif
+
+/// \internal EIGEN_OS_ANDROID set to 1 if the OS is Android
+// note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.
+#if defined(__ANDROID__) || defined(ANDROID)
+ #define EIGEN_OS_ANDROID 1
+#else
+ #define EIGEN_OS_ANDROID 0
+#endif
+
+/// \internal EIGEN_OS_GNULINUX set to 1 if the OS is GNU Linux and not Linux-based OS (e.g., not android)
+#if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)
+ #define EIGEN_OS_GNULINUX 1
+#else
+ #define EIGEN_OS_GNULINUX 0
+#endif
+
+/// \internal EIGEN_OS_BSD set to 1 if the OS is a BSD variant
+#if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)
+ #define EIGEN_OS_BSD 1
+#else
+ #define EIGEN_OS_BSD 0
+#endif
+
+/// \internal EIGEN_OS_MAC set to 1 if the OS is MacOS
+#if defined(__APPLE__)
+ #define EIGEN_OS_MAC 1
+#else
+ #define EIGEN_OS_MAC 0
+#endif
+
+/// \internal EIGEN_OS_QNX set to 1 if the OS is QNX
+#if defined(__QNX__)
+ #define EIGEN_OS_QNX 1
+#else
+ #define EIGEN_OS_QNX 0
+#endif
+
+/// \internal EIGEN_OS_WIN set to 1 if the OS is Windows based
+#if defined(_WIN32)
+ #define EIGEN_OS_WIN 1
+#else
+ #define EIGEN_OS_WIN 0
+#endif
+
+/// \internal EIGEN_OS_WIN64 set to 1 if the OS is Windows 64bits
+#if defined(_WIN64)
+ #define EIGEN_OS_WIN64 1
+#else
+ #define EIGEN_OS_WIN64 0
+#endif
+
+/// \internal EIGEN_OS_WINCE set to 1 if the OS is Windows CE
+#if defined(_WIN32_WCE)
+ #define EIGEN_OS_WINCE 1
+#else
+ #define EIGEN_OS_WINCE 0
+#endif
+
+/// \internal EIGEN_OS_CYGWIN set to 1 if the OS is Windows/Cygwin
+#if defined(__CYGWIN__)
+ #define EIGEN_OS_CYGWIN 1
+#else
+ #define EIGEN_OS_CYGWIN 0
+#endif
+
+/// \internal EIGEN_OS_WIN_STRICT set to 1 if the OS is really Windows and not some variants
+#if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )
+ #define EIGEN_OS_WIN_STRICT 1
+#else
+ #define EIGEN_OS_WIN_STRICT 0
+#endif
+
+/// \internal EIGEN_OS_SUN set to __SUNPRO_C if the OS is SUN
+// compiler solaris __SUNPRO_C
+// version studio
+// 5.7 10 0x570
+// 5.8 11 0x580
+// 5.9 12 0x590
+// 5.10 12.1 0x5100
+// 5.11 12.2 0x5110
+// 5.12 12.3 0x5120
+#if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
+ #define EIGEN_OS_SUN __SUNPRO_C
+#else
+ #define EIGEN_OS_SUN 0
+#endif
+
+/// \internal EIGEN_OS_SOLARIS set to 1 if the OS is Solaris
+#if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))
+ #define EIGEN_OS_SOLARIS 1
+#else
+ #define EIGEN_OS_SOLARIS 0
+#endif
+
+
+//------------------------------------------------------------------------------------------
+// Detect GPU compilers and architectures
+//------------------------------------------------------------------------------------------
+
+// NVCC is not supported as the target platform for HIPCC
+// Note that this also makes EIGEN_CUDACC and EIGEN_HIPCC mutually exclusive
+#if defined(__NVCC__) && defined(__HIPCC__)
+ #error "NVCC as the target platform for HIPCC is currently not supported."
+#endif
+
+#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
+ // Means the compiler is either nvcc or clang with CUDA enabled
+ #define EIGEN_CUDACC __CUDACC__
+#endif
+
+#if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA)
+ // Means we are generating code for the device
+ #define EIGEN_CUDA_ARCH __CUDA_ARCH__
+#endif
+
+#if defined(EIGEN_CUDACC)
+#include <cuda.h>
+ #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
+#else
+ #define EIGEN_CUDA_SDK_VER 0
+#endif
+
+#if defined(__HIPCC__) && !defined(EIGEN_NO_HIP)
+ // Means the compiler is HIPCC (analogous to EIGEN_CUDACC, but for HIP)
+ #define EIGEN_HIPCC __HIPCC__
+
+ // We need to include hip_runtime.h here because it pulls in
+ // ++ hip_common.h which contains the define for __HIP_DEVICE_COMPILE__
+ // ++ host_defines.h which contains the defines for the __host__ and __device__ macros
+ #include <hip/hip_runtime.h>
+
+ #if defined(__HIP_DEVICE_COMPILE__)
+ // analogous to EIGEN_CUDA_ARCH, but for HIP
+ #define EIGEN_HIP_DEVICE_COMPILE __HIP_DEVICE_COMPILE__
+ #endif
+
+ // For HIP (ROCm 3.5 and higher), we need to explicitly set the launch_bounds attribute
+ // value to 1024. The compiler assigns a default value of 256 when the attribute is not
+ // specified. This results in failures on the HIP platform, for cases when a GPU kernel
+ // without an explicit launch_bounds attribute is called with a threads_per_block value
+ // greater than 256.
+ //
+ // This is a regression in functioanlity and is expected to be fixed within the next
+ // couple of ROCm releases (compiler will go back to using 1024 value as the default)
+ //
+ // In the meantime, we will use a "only enabled for HIP" macro to set the launch_bounds
+ // attribute.
+
+ #define EIGEN_HIP_LAUNCH_BOUNDS_1024 __launch_bounds__(1024)
+
+#endif
+
+#if !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
+#define EIGEN_HIP_LAUNCH_BOUNDS_1024
+#endif // !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
+
+// Unify CUDA/HIPCC
+
+#if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
+//
+// If either EIGEN_CUDACC or EIGEN_HIPCC is defined, then define EIGEN_GPUCC
+//
+#define EIGEN_GPUCC
+//
+// EIGEN_HIPCC implies the HIP compiler and is used to tweak Eigen code for use in HIP kernels
+// EIGEN_CUDACC implies the CUDA compiler and is used to tweak Eigen code for use in CUDA kernels
+//
+// In most cases the same tweaks are required to the Eigen code to enable in both the HIP and CUDA kernels.
+// For those cases, the corresponding code should be guarded with
+// #if defined(EIGEN_GPUCC)
+// instead of
+// #if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
+//
+// For cases where the tweak is specific to HIP, the code should be guarded with
+// #if defined(EIGEN_HIPCC)
+//
+// For cases where the tweak is specific to CUDA, the code should be guarded with
+// #if defined(EIGEN_CUDACC)
+//
+#endif
+
+#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// If either EIGEN_CUDA_ARCH or EIGEN_HIP_DEVICE_COMPILE is defined, then define EIGEN_GPU_COMPILE_PHASE
+//
+#define EIGEN_GPU_COMPILE_PHASE
+//
+// GPU compilers (HIPCC, NVCC) typically do two passes over the source code,
+// + one to compile the source for the "host" (ie CPU)
+// + another to compile the source for the "device" (ie. GPU)
+//
+// Code that needs to enabled only during the either the "host" or "device" compilation phase
+// needs to be guarded with a macro that indicates the current compilation phase
+//
+// EIGEN_HIP_DEVICE_COMPILE implies the device compilation phase in HIP
+// EIGEN_CUDA_ARCH implies the device compilation phase in CUDA
+//
+// In most cases, the "host" / "device" specific code is the same for both HIP and CUDA
+// For those cases, the code should be guarded with
+// #if defined(EIGEN_GPU_COMPILE_PHASE)
+// instead of
+// #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// For cases where the tweak is specific to HIP, the code should be guarded with
+// #if defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// For cases where the tweak is specific to CUDA, the code should be guarded with
+// #if defined(EIGEN_CUDA_ARCH)
+//
+#endif
+
+#if defined(EIGEN_USE_SYCL) && defined(__SYCL_DEVICE_ONLY__)
+// EIGEN_USE_SYCL is a user-defined macro while __SYCL_DEVICE_ONLY__ is a compiler-defined macro.
+// In most cases we want to check if both macros are defined which can be done using the define below.
+#define SYCL_DEVICE_ONLY
+#endif
+
+//------------------------------------------------------------------------------------------
+// Detect Compiler/Architecture/OS specific features
+//------------------------------------------------------------------------------------------
+
+#if EIGEN_GNUC_AT_MOST(4,3) && !EIGEN_COMP_CLANG
+ // see bug 89
+ #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
+#else
+ #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
+#endif
+
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+# define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+#else
+# define EIGEN_HAS_BUILTIN(x) 0
+#endif
+
+// A Clang feature extension to determine compiler features.
+// We use it to determine 'cxx_rvalue_references'
+#ifndef __has_feature
+# define __has_feature(x) 0
+#endif
+
+// Some old compilers do not support template specializations like:
+// template<typename T,int N> void foo(const T x[N]);
+#if !( EIGEN_COMP_CLANG && ( (EIGEN_COMP_CLANG<309) \
+ || (defined(__apple_build_version__) && (__apple_build_version__ < 9000000))) \
+ || EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC<49)
+#define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 1
+#else
+#define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 0
+#endif
+
+// The macro EIGEN_CPLUSPLUS is a replacement for __cplusplus/_MSVC_LANG that
+// works for both platforms, indicating the C++ standard version number.
+//
+// With MSVC, without defining /Zc:__cplusplus, the __cplusplus macro will
+// report 199711L regardless of the language standard specified via /std.
+// We need to rely on _MSVC_LANG instead, which is only available after
+// VS2015.3.
+#if EIGEN_COMP_MSVC_LANG > 0
+#define EIGEN_CPLUSPLUS EIGEN_COMP_MSVC_LANG
+#elif EIGEN_COMP_MSVC >= 1900
+#define EIGEN_CPLUSPLUS 201103L
+#elif defined(__cplusplus)
+#define EIGEN_CPLUSPLUS __cplusplus
+#else
+#define EIGEN_CPLUSPLUS 0
+#endif
+
+// The macro EIGEN_COMP_CXXVER defines the c++ verson expected by the compiler.
+// For instance, if compiling with gcc and -std=c++17, then EIGEN_COMP_CXXVER
+// is defined to 17.
+#if EIGEN_CPLUSPLUS > 201703L
+ #define EIGEN_COMP_CXXVER 20
+#elif EIGEN_CPLUSPLUS > 201402L
+ #define EIGEN_COMP_CXXVER 17
+#elif EIGEN_CPLUSPLUS > 201103L
+ #define EIGEN_COMP_CXXVER 14
+#elif EIGEN_CPLUSPLUS >= 201103L
+ #define EIGEN_COMP_CXXVER 11
+#else
+ #define EIGEN_COMP_CXXVER 03
+#endif
+
+#ifndef EIGEN_HAS_CXX14_VARIABLE_TEMPLATES
+ #if defined(__cpp_variable_templates) && __cpp_variable_templates >= 201304 && EIGEN_MAX_CPP_VER>=14
+ #define EIGEN_HAS_CXX14_VARIABLE_TEMPLATES 1
+ #else
+ #define EIGEN_HAS_CXX14_VARIABLE_TEMPLATES 0
+ #endif
+#endif
+
+
+// The macros EIGEN_HAS_CXX?? defines a rough estimate of available c++ features
+// but in practice we should not rely on them but rather on the availabilty of
+// individual features as defined later.
+// This is why there is no EIGEN_HAS_CXX17.
+// FIXME: get rid of EIGEN_HAS_CXX14 and maybe even EIGEN_HAS_CXX11.
+#if EIGEN_MAX_CPP_VER>=11 && EIGEN_COMP_CXXVER>=11
+#define EIGEN_HAS_CXX11 1
+#else
+#define EIGEN_HAS_CXX11 0
+#endif
+
+#if EIGEN_MAX_CPP_VER>=14 && EIGEN_COMP_CXXVER>=14
+#define EIGEN_HAS_CXX14 1
+#else
+#define EIGEN_HAS_CXX14 0
+#endif
+
+// Do we support r-value references?
+#ifndef EIGEN_HAS_RVALUE_REFERENCES
+#if EIGEN_MAX_CPP_VER>=11 && \
+ (__has_feature(cxx_rvalue_references) || \
+ (EIGEN_COMP_CXXVER >= 11) || (EIGEN_COMP_MSVC >= 1600))
+ #define EIGEN_HAS_RVALUE_REFERENCES 1
+#else
+ #define EIGEN_HAS_RVALUE_REFERENCES 0
+#endif
+#endif
+
+// Does the compiler support C99?
+// Need to include <cmath> to make sure _GLIBCXX_USE_C99 gets defined
+#include <cmath>
+#ifndef EIGEN_HAS_C99_MATH
+#if EIGEN_MAX_CPP_VER>=11 && \
+ ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901)) \
+ || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
+ || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)) \
+ || (EIGEN_COMP_MSVC >= 1900) || defined(SYCL_DEVICE_ONLY))
+ #define EIGEN_HAS_C99_MATH 1
+#else
+ #define EIGEN_HAS_C99_MATH 0
+#endif
+#endif
+
+// Does the compiler support result_of?
+// result_of was deprecated in c++17 and removed in c++ 20
+#ifndef EIGEN_HAS_STD_RESULT_OF
+#if EIGEN_HAS_CXX11 && EIGEN_COMP_CXXVER < 17
+#define EIGEN_HAS_STD_RESULT_OF 1
+#else
+#define EIGEN_HAS_STD_RESULT_OF 0
+#endif
+#endif
+
+// Does the compiler support std::hash?
+#ifndef EIGEN_HAS_STD_HASH
+// The std::hash struct is defined in C++11 but is not labelled as a __device__
+// function and is not constexpr, so cannot be used on device.
+#if EIGEN_HAS_CXX11 && !defined(EIGEN_GPU_COMPILE_PHASE)
+#define EIGEN_HAS_STD_HASH 1
+#else
+#define EIGEN_HAS_STD_HASH 0
+#endif
+#endif // EIGEN_HAS_STD_HASH
+
+#ifndef EIGEN_HAS_STD_INVOKE_RESULT
+#if EIGEN_MAX_CPP_VER >= 17 && EIGEN_COMP_CXXVER >= 17
+#define EIGEN_HAS_STD_INVOKE_RESULT 1
+#else
+#define EIGEN_HAS_STD_INVOKE_RESULT 0
+#endif
+#endif
+
+#ifndef EIGEN_HAS_ALIGNAS
+#if EIGEN_MAX_CPP_VER>=11 && EIGEN_HAS_CXX11 && \
+ ( __has_feature(cxx_alignas) \
+ || EIGEN_HAS_CXX14 \
+ || (EIGEN_COMP_MSVC >= 1800) \
+ || (EIGEN_GNUC_AT_LEAST(4,8)) \
+ || (EIGEN_COMP_CLANG>=305) \
+ || (EIGEN_COMP_ICC>=1500) \
+ || (EIGEN_COMP_PGI>=1500) \
+ || (EIGEN_COMP_SUNCC>=0x5130))
+#define EIGEN_HAS_ALIGNAS 1
+#else
+#define EIGEN_HAS_ALIGNAS 0
+#endif
+#endif
+
+// Does the compiler support type_traits?
+// - full support of type traits was added only to GCC 5.1.0.
+// - 20150626 corresponds to the last release of 4.x libstdc++
+#ifndef EIGEN_HAS_TYPE_TRAITS
+#if EIGEN_MAX_CPP_VER>=11 && (EIGEN_HAS_CXX11 || EIGEN_COMP_MSVC >= 1700) \
+ && ((!EIGEN_COMP_GNUC_STRICT) || EIGEN_GNUC_AT_LEAST(5, 1)) \
+ && ((!defined(__GLIBCXX__)) || __GLIBCXX__ > 20150626)
+#define EIGEN_HAS_TYPE_TRAITS 1
+#define EIGEN_INCLUDE_TYPE_TRAITS
+#else
+#define EIGEN_HAS_TYPE_TRAITS 0
+#endif
+#endif
+
+// Does the compiler support variadic templates?
+#ifndef EIGEN_HAS_VARIADIC_TEMPLATES
+#if EIGEN_MAX_CPP_VER>=11 && (EIGEN_COMP_CXXVER >= 11) \
+ && (!defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (EIGEN_COMP_NVCC >= 80000) )
+ // ^^ Disable the use of variadic templates when compiling with versions of nvcc older than 8.0 on ARM devices:
+ // this prevents nvcc from crashing when compiling Eigen on Tegra X1
+#define EIGEN_HAS_VARIADIC_TEMPLATES 1
+#elif EIGEN_MAX_CPP_VER>=11 && (EIGEN_COMP_CXXVER >= 11) && defined(SYCL_DEVICE_ONLY)
+#define EIGEN_HAS_VARIADIC_TEMPLATES 1
+#else
+#define EIGEN_HAS_VARIADIC_TEMPLATES 0
+#endif
+#endif
+
+// Does the compiler fully support const expressions? (as in c++14)
+#ifndef EIGEN_HAS_CONSTEXPR
+ #if defined(EIGEN_CUDACC)
+ // Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above
+ #if EIGEN_MAX_CPP_VER>=14 && (EIGEN_COMP_CXXVER >= 11 && (EIGEN_COMP_CLANG || EIGEN_COMP_NVCC >= 70500))
+ #define EIGEN_HAS_CONSTEXPR 1
+ #endif
+ #elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (EIGEN_COMP_CXXVER >= 14) || \
+ (EIGEN_GNUC_AT_LEAST(4,8) && (EIGEN_COMP_CXXVER >= 11)) || \
+ (EIGEN_COMP_CLANG >= 306 && (EIGEN_COMP_CXXVER >= 11)))
+ #define EIGEN_HAS_CONSTEXPR 1
+ #endif
+
+ #ifndef EIGEN_HAS_CONSTEXPR
+ #define EIGEN_HAS_CONSTEXPR 0
+ #endif
+
+#endif // EIGEN_HAS_CONSTEXPR
+
+#if EIGEN_HAS_CONSTEXPR
+#define EIGEN_CONSTEXPR constexpr
+#else
+#define EIGEN_CONSTEXPR
+#endif
+
+// Does the compiler support C++11 math?
+// Let's be conservative and enable the default C++11 implementation only if we are sure it exists
+#ifndef EIGEN_HAS_CXX11_MATH
+ #if EIGEN_MAX_CPP_VER>=11 && ((EIGEN_COMP_CXXVER > 11) || (EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC) \
+ && (EIGEN_ARCH_i386_OR_x86_64) && (EIGEN_OS_GNULINUX || EIGEN_OS_WIN_STRICT || EIGEN_OS_MAC))
+ #define EIGEN_HAS_CXX11_MATH 1
+ #else
+ #define EIGEN_HAS_CXX11_MATH 0
+ #endif
+#endif
+
+// Does the compiler support proper C++11 containers?
+#ifndef EIGEN_HAS_CXX11_CONTAINERS
+ #if EIGEN_MAX_CPP_VER>=11 && \
+ ((EIGEN_COMP_CXXVER > 11) \
+ || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC>=1400)))
+ #define EIGEN_HAS_CXX11_CONTAINERS 1
+ #else
+ #define EIGEN_HAS_CXX11_CONTAINERS 0
+ #endif
+#endif
+
+// Does the compiler support C++11 noexcept?
+#ifndef EIGEN_HAS_CXX11_NOEXCEPT
+ #if EIGEN_MAX_CPP_VER>=11 && \
+ (__has_feature(cxx_noexcept) \
+ || (EIGEN_COMP_CXXVER > 11) \
+ || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC>=1400)))
+ #define EIGEN_HAS_CXX11_NOEXCEPT 1
+ #else
+ #define EIGEN_HAS_CXX11_NOEXCEPT 0
+ #endif
+#endif
+
+#ifndef EIGEN_HAS_CXX11_ATOMIC
+ #if EIGEN_MAX_CPP_VER>=11 && \
+ (__has_feature(cxx_atomic) \
+ || (EIGEN_COMP_CXXVER > 11) \
+ || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_MSVC==0 || EIGEN_COMP_MSVC >= 1700)))
+ #define EIGEN_HAS_CXX11_ATOMIC 1
+ #else
+ #define EIGEN_HAS_CXX11_ATOMIC 0
+ #endif
+#endif
+
+#ifndef EIGEN_HAS_CXX11_OVERRIDE_FINAL
+ #if EIGEN_MAX_CPP_VER>=11 && \
+ (EIGEN_COMP_CXXVER >= 11 || EIGEN_COMP_MSVC >= 1700)
+ #define EIGEN_HAS_CXX11_OVERRIDE_FINAL 1
+ #else
+ #define EIGEN_HAS_CXX11_OVERRIDE_FINAL 0
+ #endif
+#endif
+
+// NOTE: the required Apple's clang version is very conservative
+// and it could be that XCode 9 works just fine.
+// NOTE: the MSVC version is based on https://en.cppreference.com/w/cpp/compiler_support
+// and not tested.
+#ifndef EIGEN_HAS_CXX17_OVERALIGN
+#if EIGEN_MAX_CPP_VER>=17 && EIGEN_COMP_CXXVER>=17 && ( \
+ (EIGEN_COMP_MSVC >= 1912) \
+ || (EIGEN_GNUC_AT_LEAST(7,0)) \
+ || ((!defined(__apple_build_version__)) && (EIGEN_COMP_CLANG>=500)) \
+ || (( defined(__apple_build_version__)) && (__apple_build_version__>=10000000)) \
+ )
+#define EIGEN_HAS_CXX17_OVERALIGN 1
+#else
+#define EIGEN_HAS_CXX17_OVERALIGN 0
+#endif
+#endif
+
+#if defined(EIGEN_CUDACC) && EIGEN_HAS_CONSTEXPR
+ // While available already with c++11, this is useful mostly starting with c++14 and relaxed constexpr rules
+ #if defined(__NVCC__)
+ // nvcc considers constexpr functions as __host__ __device__ with the option --expt-relaxed-constexpr
+ #ifdef __CUDACC_RELAXED_CONSTEXPR__
+ #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
+ #endif
+ #elif defined(__clang__) && defined(__CUDA__) && __has_feature(cxx_relaxed_constexpr)
+ // clang++ always considers constexpr functions as implicitly __host__ __device__
+ #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
+ #endif
+#endif
+
+// Does the compiler support the __int128 and __uint128_t extensions for 128-bit
+// integer arithmetic?
+//
+// Clang and GCC define __SIZEOF_INT128__ when these extensions are supported,
+// but we avoid using them in certain cases:
+//
+// * Building using Clang for Windows, where the Clang runtime library has
+// 128-bit support only on LP64 architectures, but Windows is LLP64.
+#ifndef EIGEN_HAS_BUILTIN_INT128
+#if defined(__SIZEOF_INT128__) && !(EIGEN_OS_WIN && EIGEN_COMP_CLANG)
+#define EIGEN_HAS_BUILTIN_INT128 1
+#else
+#define EIGEN_HAS_BUILTIN_INT128 0
+#endif
+#endif
+
+//------------------------------------------------------------------------------------------
+// Preprocessor programming helpers
+//------------------------------------------------------------------------------------------
+
+// This macro can be used to prevent from macro expansion, e.g.:
+// std::max EIGEN_NOT_A_MACRO(a,b)
+#define EIGEN_NOT_A_MACRO
+
+#define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
+
+// concatenate two tokens
+#define EIGEN_CAT2(a,b) a ## b
+#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
+
+#define EIGEN_COMMA ,
+
+// convert a token to a string
+#define EIGEN_MAKESTRING2(a) #a
+#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
+
+// EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
+// but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
+// but GCC is still doing fine with just inline.
+#ifndef EIGEN_STRONG_INLINE
+#if (EIGEN_COMP_MSVC || EIGEN_COMP_ICC) && !defined(EIGEN_GPUCC)
+#define EIGEN_STRONG_INLINE __forceinline
+#else
+#define EIGEN_STRONG_INLINE inline
+#endif
+#endif
+
+// EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
+// attribute to maximize inlining. This should only be used when really necessary: in particular,
+// it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
+// FIXME with the always_inline attribute,
+// gcc 3.4.x and 4.1 reports the following compilation error:
+// Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
+// : function body not available
+// See also bug 1367
+#if EIGEN_GNUC_AT_LEAST(4,2) && !defined(SYCL_DEVICE_ONLY)
+#define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
+#else
+#define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_DONT_INLINE __attribute__((noinline))
+#elif EIGEN_COMP_MSVC
+#define EIGEN_DONT_INLINE __declspec(noinline)
+#else
+#define EIGEN_DONT_INLINE
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_PERMISSIVE_EXPR __extension__
+#else
+#define EIGEN_PERMISSIVE_EXPR
+#endif
+
+// GPU stuff
+
+// Disable some features when compiling with GPU compilers (NVCC/clang-cuda/SYCL/HIPCC)
+#if defined(EIGEN_CUDACC) || defined(SYCL_DEVICE_ONLY) || defined(EIGEN_HIPCC)
+ // Do not try asserts on device code
+ #ifndef EIGEN_NO_DEBUG
+ #define EIGEN_NO_DEBUG
+ #endif
+
+ #ifdef EIGEN_INTERNAL_DEBUGGING
+ #undef EIGEN_INTERNAL_DEBUGGING
+ #endif
+
+ #ifdef EIGEN_EXCEPTIONS
+ #undef EIGEN_EXCEPTIONS
+ #endif
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+ #ifndef EIGEN_DONT_VECTORIZE
+ #define EIGEN_DONT_VECTORIZE
+ #endif
+ #define EIGEN_DEVICE_FUNC __attribute__((flatten)) __attribute__((always_inline))
+// All functions callable from CUDA/HIP code must be qualified with __device__
+#elif defined(EIGEN_GPUCC)
+ #define EIGEN_DEVICE_FUNC __host__ __device__
+#else
+ #define EIGEN_DEVICE_FUNC
+#endif
+
+
+// this macro allows to get rid of linking errors about multiply defined functions.
+// - static is not very good because it prevents definitions from different object files to be merged.
+// So static causes the resulting linked executable to be bloated with multiple copies of the same function.
+// - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
+#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC inline
+
+#ifdef NDEBUG
+# ifndef EIGEN_NO_DEBUG
+# define EIGEN_NO_DEBUG
+# endif
+#endif
+
+// eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
+#ifdef EIGEN_NO_DEBUG
+ #ifdef SYCL_DEVICE_ONLY // used to silence the warning on SYCL device
+ #define eigen_plain_assert(x) EIGEN_UNUSED_VARIABLE(x)
+ #else
+ #define eigen_plain_assert(x)
+ #endif
+#else
+ #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
+ namespace Eigen {
+ namespace internal {
+ inline bool copy_bool(bool b) { return b; }
+ }
+ }
+ #define eigen_plain_assert(x) assert(x)
+ #else
+ // work around bug 89
+ #include <cstdlib> // for abort
+ #include <iostream> // for std::cerr
+
+ namespace Eigen {
+ namespace internal {
+ // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
+ // see bug 89.
+ namespace {
+ EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
+ }
+ inline void assert_fail(const char *condition, const char *function, const char *file, int line)
+ {
+ std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
+ abort();
+ }
+ }
+ }
+ #define eigen_plain_assert(x) \
+ do { \
+ if(!Eigen::internal::copy_bool(x)) \
+ Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
+ } while(false)
+ #endif
+#endif
+
+// eigen_assert can be overridden
+#ifndef eigen_assert
+#define eigen_assert(x) eigen_plain_assert(x)
+#endif
+
+#ifdef EIGEN_INTERNAL_DEBUGGING
+#define eigen_internal_assert(x) eigen_assert(x)
+#else
+#define eigen_internal_assert(x)
+#endif
+
+#ifdef EIGEN_NO_DEBUG
+#define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
+#else
+#define EIGEN_ONLY_USED_FOR_DEBUG(x)
+#endif
+
+#ifndef EIGEN_NO_DEPRECATED_WARNING
+ #if EIGEN_COMP_GNUC
+ #define EIGEN_DEPRECATED __attribute__((deprecated))
+ #elif EIGEN_COMP_MSVC
+ #define EIGEN_DEPRECATED __declspec(deprecated)
+ #else
+ #define EIGEN_DEPRECATED
+ #endif
+#else
+ #define EIGEN_DEPRECATED
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_UNUSED __attribute__((unused))
+#else
+#define EIGEN_UNUSED
+#endif
+
+// Suppresses 'unused variable' warnings.
+namespace Eigen {
+ namespace internal {
+ template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ignore_unused_variable(const T&) {}
+ }
+}
+#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
+
+#if !defined(EIGEN_ASM_COMMENT)
+ #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
+ #define EIGEN_ASM_COMMENT(X) __asm__("#" X)
+ #else
+ #define EIGEN_ASM_COMMENT(X)
+ #endif
+#endif
+
+
+// Acts as a barrier preventing operations involving `X` from crossing. This
+// occurs, for example, in the fast rounding trick where a magic constant is
+// added then subtracted, which is otherwise compiled away with -ffast-math.
+//
+// See bug 1674
+#if !defined(EIGEN_OPTIMIZATION_BARRIER)
+ #if EIGEN_COMP_GNUC
+ // According to https://gcc.gnu.org/onlinedocs/gcc/Constraints.html:
+ // X: Any operand whatsoever.
+ // r: A register operand is allowed provided that it is in a general
+ // register.
+ // g: Any register, memory or immediate integer operand is allowed, except
+ // for registers that are not general registers.
+ // w: (AArch32/AArch64) Floating point register, Advanced SIMD vector
+ // register or SVE vector register.
+ // x: (SSE) Any SSE register.
+ // (AArch64) Like w, but restricted to registers 0 to 15 inclusive.
+ // v: (PowerPC) An Altivec vector register.
+ // wa:(PowerPC) A VSX register.
+ //
+ // "X" (uppercase) should work for all cases, though this seems to fail for
+ // some versions of GCC for arm/aarch64 with
+ // "error: inconsistent operand constraints in an 'asm'"
+ // Clang x86_64/arm/aarch64 seems to require "g" to support both scalars and
+ // vectors, otherwise
+ // "error: non-trivial scalar-to-vector conversion, possible invalid
+ // constraint for vector type"
+ //
+ // GCC for ppc64le generates an internal compiler error with x/X/g.
+ // GCC for AVX generates an internal compiler error with X.
+ //
+ // Tested on icc/gcc/clang for sse, avx, avx2, avx512dq
+ // gcc for arm, aarch64,
+ // gcc for ppc64le,
+ // both vectors and scalars.
+ //
+ // Note that this is restricted to plain types - this will not work
+ // directly for std::complex<T>, Eigen::half, Eigen::bfloat16. For these,
+ // you will need to apply to the underlying POD type.
+ #if EIGEN_ARCH_PPC && EIGEN_COMP_GNUC_STRICT
+ // This seems to be broken on clang. Packet4f is loaded into a single
+ // register rather than a vector, zeroing out some entries. Integer
+ // types also generate a compile error.
+ // General, Altivec, VSX.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+r,v,wa" (X));
+ #elif EIGEN_ARCH_ARM_OR_ARM64
+ // General, NEON.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+g,w" (X));
+ #elif EIGEN_ARCH_i386_OR_x86_64
+ // General, SSE.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+g,x" (X));
+ #else
+ // Not implemented for other architectures.
+ #define EIGEN_OPTIMIZATION_BARRIER(X)
+ #endif
+ #else
+ // Not implemented for other compilers.
+ #define EIGEN_OPTIMIZATION_BARRIER(X)
+ #endif
+#endif
+
+#if EIGEN_COMP_MSVC
+ // NOTE MSVC often gives C4127 warnings with compiletime if statements. See bug 1362.
+ // This workaround is ugly, but it does the job.
+# define EIGEN_CONST_CONDITIONAL(cond) (void)0, cond
+#else
+# define EIGEN_CONST_CONDITIONAL(cond) cond
+#endif
+
+#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
+ #define EIGEN_RESTRICT
+#endif
+#ifndef EIGEN_RESTRICT
+ #define EIGEN_RESTRICT __restrict
+#endif
+
+
+#ifndef EIGEN_DEFAULT_IO_FORMAT
+#ifdef EIGEN_MAKING_DOCS
+// format used in Eigen's documentation
+// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
+#else
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
+#endif
+#endif
+
+// just an empty macro !
+#define EIGEN_EMPTY
+
+
+// When compiling CUDA/HIP device code with NVCC or HIPCC
+// pull in math functions from the global namespace.
+// In host mode, and when device code is compiled with clang,
+// use the std versions.
+#if (defined(EIGEN_CUDA_ARCH) && defined(__NVCC__)) || defined(EIGEN_HIP_DEVICE_COMPILE)
+ #define EIGEN_USING_STD(FUNC) using ::FUNC;
+#else
+ #define EIGEN_USING_STD(FUNC) using std::FUNC;
+#endif
+
+#if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 || (EIGEN_COMP_MSVC == 1900 && EIGEN_COMP_NVCC))
+ // For older MSVC versions, as well as 1900 && CUDA 8, using the base operator is necessary,
+ // otherwise we get duplicate definition errors
+ // For later MSVC versions, we require explicit operator= definition, otherwise we get
+ // use of implicitly deleted operator errors.
+ // (cf Bugs 920, 1000, 1324, 2291)
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =;
+#elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
+ template <typename OtherDerived> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
+#else
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
+ { \
+ Base::operator=(other); \
+ return *this; \
+ }
+#endif
+
+
+/**
+ * \internal
+ * \brief Macro to explicitly define the default copy constructor.
+ * This is necessary, because the implicit definition is deprecated if the copy-assignment is overridden.
+ */
+#if EIGEN_HAS_CXX11
+#define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS) CLASS(const CLASS&) = default;
+#else
+#define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS)
+#endif
+
+
+
+/** \internal
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ * With C++11 or later this also default-implements the copy-constructor
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+ EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(Derived)
+
+/** \internal
+ * \brief Macro to manually define default constructors and destructors.
+ * This is necessary when the copy constructor is re-defined.
+ * For empty helper classes this should usually be protected, to avoid accidentally creating empty objects.
+ *
+ * Hiding the default destructor lead to problems in C++03 mode together with boost::multiprecision
+ */
+#if EIGEN_HAS_CXX11
+#define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived) \
+ Derived() = default; \
+ ~Derived() = default;
+#else
+#define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived) \
+ Derived() {}; \
+ /* ~Derived() {}; */
+#endif
+
+
+
+
+
+/**
+* Just a side note. Commenting within defines works only by documenting
+* behind the object (via '!<'). Comments cannot be multi-line and thus
+* we have these extra long lines. What is confusing doxygen over here is
+* that we use '\' and basically have a bunch of typedefs with their
+* documentation in a single line.
+**/
+
+#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+ typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
+ typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
+ typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
+ typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
+ typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
+ enum CompileTimeTraits \
+ { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
+ ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
+ Flags = Eigen::internal::traits<Derived>::Flags, \
+ SizeAtCompileTime = Base::SizeAtCompileTime, \
+ MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
+ IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
+ using Base::derived; \
+ using Base::const_cast_derived;
+
+
+// FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
+#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+ typedef typename Base::PacketScalar PacketScalar;
+
+
+#define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
+#define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
+
+// EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
+// followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
+// finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
+#define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
+ : ((int)a == 1 || (int)b == 1) ? 1 \
+ : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
+ : ((int)a <= (int)b) ? (int)a : (int)b)
+
+// EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
+// now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
+// (between 0 and 3), it is not more than 3.
+#define EIGEN_SIZE_MIN_PREFER_FIXED(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
+ : ((int)a == 1 || (int)b == 1) ? 1 \
+ : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
+ : ((int)a == Dynamic) ? (int)b \
+ : ((int)b == Dynamic) ? (int)a \
+ : ((int)a <= (int)b) ? (int)a : (int)b)
+
+// see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
+#define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
+ : ((int)a >= (int)b) ? (int)a : (int)b)
+
+#define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
+
+#define EIGEN_IMPLIES(a,b) (!(a) || (b))
+
+#if EIGEN_HAS_BUILTIN(__builtin_expect) || EIGEN_COMP_GNUC
+#define EIGEN_PREDICT_FALSE(x) (__builtin_expect(x, false))
+#define EIGEN_PREDICT_TRUE(x) (__builtin_expect(false || (x), true))
+#else
+#define EIGEN_PREDICT_FALSE(x) (x)
+#define EIGEN_PREDICT_TRUE(x) (x)
+#endif
+
+// the expression type of a standard coefficient wise binary operation
+#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
+ CwiseBinaryOp< \
+ EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
+ typename internal::traits<LHS>::Scalar, \
+ typename internal::traits<RHS>::Scalar \
+ >, \
+ const LHS, \
+ const RHS \
+ >
+
+#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
+ template<typename OtherDerived> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
+ (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+ { \
+ return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
+ }
+
+#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
+ (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB> > >::value)
+
+#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
+ CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
+ const typename internal::plain_constant_type<EXPR,SCALAR>::type>
+
+#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
+ CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
+ const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
+
+// Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010")
+#if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC_STRICT<=1600)
+#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type
+#else
+#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X
+#endif
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
+ template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+ EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME))\
+ (METHOD)(const T& scalar) const { \
+ typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
+ return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
+ typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
+ }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+ template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend \
+ EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME)) \
+ (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
+ typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
+ return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
+ typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
+ }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
+ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
+
+
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL) && !defined(EIGEN_HIP_DEVICE_COMPILE)
+ #define EIGEN_EXCEPTIONS
+#endif
+
+
+#ifdef EIGEN_EXCEPTIONS
+# define EIGEN_THROW_X(X) throw X
+# define EIGEN_THROW throw
+# define EIGEN_TRY try
+# define EIGEN_CATCH(X) catch (X)
+#else
+# if defined(EIGEN_CUDA_ARCH)
+# define EIGEN_THROW_X(X) asm("trap;")
+# define EIGEN_THROW asm("trap;")
+# elif defined(EIGEN_HIP_DEVICE_COMPILE)
+# define EIGEN_THROW_X(X) asm("s_trap 0")
+# define EIGEN_THROW asm("s_trap 0")
+# else
+# define EIGEN_THROW_X(X) std::abort()
+# define EIGEN_THROW std::abort()
+# endif
+# define EIGEN_TRY if (true)
+# define EIGEN_CATCH(X) else
+#endif
+
+
+#if EIGEN_HAS_CXX11_NOEXCEPT
+# define EIGEN_INCLUDE_TYPE_TRAITS
+# define EIGEN_NOEXCEPT noexcept
+# define EIGEN_NOEXCEPT_IF(x) noexcept(x)
+# define EIGEN_NO_THROW noexcept(true)
+# define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
+#else
+# define EIGEN_NOEXCEPT
+# define EIGEN_NOEXCEPT_IF(x)
+# define EIGEN_NO_THROW throw()
+# if EIGEN_COMP_MSVC || EIGEN_COMP_CXXVER>=17
+ // MSVC does not support exception specifications (warning C4290),
+ // and they are deprecated in c++11 anyway. This is even an error in c++17.
+# define EIGEN_EXCEPTION_SPEC(X) throw()
+# else
+# define EIGEN_EXCEPTION_SPEC(X) throw(X)
+# endif
+#endif
+
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+// The all function is used to enable a variadic version of eigen_assert which can take a parameter pack as its input.
+namespace Eigen {
+namespace internal {
+
+inline bool all(){ return true; }
+
+template<typename T, typename ...Ts>
+bool all(T t, Ts ... ts){ return t && all(ts...); }
+
+}
+}
+#endif
+
+#if EIGEN_HAS_CXX11_OVERRIDE_FINAL
+// provide override and final specifiers if they are available:
+# define EIGEN_OVERRIDE override
+# define EIGEN_FINAL final
+#else
+# define EIGEN_OVERRIDE
+# define EIGEN_FINAL
+#endif
+
+// Wrapping #pragma unroll in a macro since it is required for SYCL
+#if defined(SYCL_DEVICE_ONLY)
+ #if defined(_MSC_VER)
+ #define EIGEN_UNROLL_LOOP __pragma(unroll)
+ #else
+ #define EIGEN_UNROLL_LOOP _Pragma("unroll")
+ #endif
+#else
+ #define EIGEN_UNROLL_LOOP
+#endif
+
+#endif // EIGEN_MACROS_H