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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
+
+#define EIGEN_WORLD_VERSION 3
+#define EIGEN_MAJOR_VERSION 3
+#define EIGEN_MINOR_VERSION 4
+
+#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))))
+
+// Compiler identification, EIGEN_COMP_*
+
+/// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
+#ifdef __GNUC__
+ #define EIGEN_COMP_GNUC 1
+#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_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
+
+// 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
+
+/// \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 1 if the compiler is IBM XL C++
+#if defined(__IBMCPP__) || defined(__xlc__)
+ #define EIGEN_COMP_IBM 1
+#else
+ #define EIGEN_COMP_IBM 0
+#endif
+
+/// \internal EIGEN_COMP_PGI set to 1 if the compiler is Portland Group Compiler
+#if defined(__PGI)
+ #define EIGEN_COMP_PGI 1
+#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_ARM set to 1 if the compiler is ARM 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(__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__)
+ #define EIGEN_ARCH_ARM64 1
+#else
+ #define EIGEN_ARCH_ARM64 0
+#endif
+
+#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_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 1 if the OS is SUN
+#if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
+ #define EIGEN_OS_SUN 1
+#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
+
+
+
+#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
+
+// 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
+
+#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
+
+// 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
+
+// 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
+
+#if EIGEN_MAX_CPP_VER>=11 && (defined(__cplusplus) && (__cplusplus >= 201103L) || EIGEN_COMP_MSVC >= 1900)
+#define EIGEN_HAS_CXX11 1
+#else
+#define EIGEN_HAS_CXX11 0
+#endif
+
+
+// Do we support r-value references?
+#ifndef EIGEN_HAS_RVALUE_REFERENCES
+#if EIGEN_MAX_CPP_VER>=11 && \
+ (__has_feature(cxx_rvalue_references) || \
+ (defined(__cplusplus) && __cplusplus >= 201103L) || \
+ (EIGEN_COMP_MSVC >= 1600))
+ #define EIGEN_HAS_RVALUE_REFERENCES 1
+#else
+ #define EIGEN_HAS_RVALUE_REFERENCES 0
+#endif
+#endif
+
+// Does the compiler support C99?
+#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)))
+ #define EIGEN_HAS_C99_MATH 1
+#else
+ #define EIGEN_HAS_C99_MATH 0
+#endif
+#endif
+
+// Does the compiler support result_of?
+#ifndef EIGEN_HAS_STD_RESULT_OF
+#if EIGEN_MAX_CPP_VER>=11 && ((__has_feature(cxx_lambdas) || (defined(__cplusplus) && __cplusplus >= 201103L)))
+#define EIGEN_HAS_STD_RESULT_OF 1
+#else
+#define EIGEN_HAS_STD_RESULT_OF 0
+#endif
+#endif
+
+// Does the compiler support variadic templates?
+#ifndef EIGEN_HAS_VARIADIC_TEMPLATES
+#if EIGEN_MAX_CPP_VER>=11 && (__cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900) \
+ && ( !defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (defined __CUDACC_VER__ && __CUDACC_VER__ >= 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
+#else
+#define EIGEN_HAS_VARIADIC_TEMPLATES 0
+#endif
+#endif
+
+// Does the compiler fully support const expressions? (as in c++14)
+#ifndef EIGEN_HAS_CONSTEXPR
+
+#ifdef __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 && (__cplusplus > 199711L && defined(__CUDACC_VER__) && (EIGEN_COMP_CLANG || __CUDACC_VER__ >= 70500))
+ #define EIGEN_HAS_CONSTEXPR 1
+#endif
+#elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (defined(__cplusplus) && __cplusplus >= 201402L) || \
+ (EIGEN_GNUC_AT_LEAST(4,8) && (__cplusplus > 199711L)))
+#define EIGEN_HAS_CONSTEXPR 1
+#endif
+
+#ifndef EIGEN_HAS_CONSTEXPR
+#define EIGEN_HAS_CONSTEXPR 0
+#endif
+
+#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 && ((__cplusplus > 201103L) || (__cplusplus >= 201103L) && (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 && \
+ ((__cplusplus > 201103L) \
+ || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
+ || EIGEN_COMP_MSVC >= 1900)
+ #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) \
+ || (__cplusplus > 201103L) \
+ || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
+ || EIGEN_COMP_MSVC >= 1900)
+ #define EIGEN_HAS_CXX11_NOEXCEPT 1
+ #else
+ #define EIGEN_HAS_CXX11_NOEXCEPT 0
+ #endif
+#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
+
+#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.
+#if EIGEN_COMP_MSVC || EIGEN_COMP_ICC
+#define EIGEN_STRONG_INLINE __forceinline
+#else
+#define EIGEN_STRONG_INLINE inline
+#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)
+#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
+
+// 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
+#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 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
+ #define eigen_plain_assert(x)
+#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 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
+
+
+//------------------------------------------------------------------------------------------
+// Static and dynamic alignment control
+//
+// The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES
+// as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.
+// The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,
+// a default value is automatically computed based on architecture, compiler, and OS.
+//
+// This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}
+// to be used to declare statically aligned buffers.
+//------------------------------------------------------------------------------------------
+
+
+/* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
+ * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
+ * so that vectorization doesn't affect binary compatibility.
+ *
+ * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
+ * vectorized and non-vectorized code.
+ */
+#if (defined __CUDACC__)
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
+#elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
+#elif EIGEN_COMP_MSVC
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
+#elif EIGEN_COMP_SUNCC
+ // FIXME not sure about this one:
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
+#else
+ #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
+#endif
+
+// If the user explicitly disable vectorization, then we also disable alignment
+#if defined(EIGEN_DONT_VECTORIZE)
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
+#elif defined(EIGEN_VECTORIZE_AVX512)
+ // 64 bytes static alignmeent is preferred only if really required
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
+#elif defined(__AVX__)
+ // 32 bytes static alignmeent is preferred only if really required
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32
+#else
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
+#endif
+
+
+// EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense
+#define EIGEN_MIN_ALIGN_BYTES 16
+
+// Defined the boundary (in bytes) on which the data needs to be aligned. Note
+// that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be
+// aligned at all regardless of the value of this #define.
+
+#if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)) && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#error EIGEN_MAX_STATIC_ALIGN_BYTES and EIGEN_DONT_ALIGN[_STATICALLY] are both defined with EIGEN_MAX_STATIC_ALIGN_BYTES!=0. Use EIGEN_MAX_STATIC_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN_STATICALLY.
+#endif
+
+// EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprectated
+// They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0
+#if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)
+ #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES
+ #undef EIGEN_MAX_STATIC_ALIGN_BYTES
+ #endif
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+#endif
+
+#ifndef EIGEN_MAX_STATIC_ALIGN_BYTES
+
+ // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES
+
+ // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
+ // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
+ // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
+ // certain common platform (compiler+architecture combinations) to avoid these problems.
+ // Only static alignment is really problematic (relies on nonstandard compiler extensions),
+ // try to keep heap alignment even when we have to disable static alignment.
+ #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64)
+ #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+ #elif EIGEN_ARCH_ARM_OR_ARM64 && EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_MOST(4, 6)
+ // Old versions of GCC on ARM, at least 4.4, were once seen to have buggy static alignment support.
+ // Not sure which version fixed it, hopefully it doesn't affect 4.7, which is still somewhat in use.
+ // 4.8 and newer seem definitely unaffected.
+ #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+ #else
+ #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
+ #endif
+
+ // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
+ #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
+ && !EIGEN_GCC3_OR_OLDER \
+ && !EIGEN_COMP_SUNCC \
+ && !EIGEN_OS_QNX
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
+ #else
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
+ #endif
+
+ #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+ #else
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+ #endif
+
+#endif
+
+// If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_ALIGN_BYTES
+#if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES
+#undef EIGEN_MAX_STATIC_ALIGN_BYTES
+#define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
+ #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+#endif
+
+// At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.
+// It takes into account both the user choice to explicitly enable/disable alignment (by settting EIGEN_MAX_STATIC_ALIGN_BYTES)
+// and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).
+// Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.
+
+
+// Shortcuts to EIGEN_ALIGN_TO_BOUNDARY
+#define EIGEN_ALIGN8 EIGEN_ALIGN_TO_BOUNDARY(8)
+#define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
+#define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
+#define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)
+#else
+#define EIGEN_ALIGN_MAX
+#endif
+
+
+// Dynamic alignment control
+
+#if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0
+#error EIGEN_MAX_ALIGN_BYTES and EIGEN_DONT_ALIGN are both defined with EIGEN_MAX_ALIGN_BYTES!=0. Use EIGEN_MAX_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN.
+#endif
+
+#ifdef EIGEN_DONT_ALIGN
+ #ifdef EIGEN_MAX_ALIGN_BYTES
+ #undef EIGEN_MAX_ALIGN_BYTES
+ #endif
+ #define EIGEN_MAX_ALIGN_BYTES 0
+#elif !defined(EIGEN_MAX_ALIGN_BYTES)
+ #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+#else
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
+#endif
+
+
+#ifndef EIGEN_UNALIGNED_VECTORIZE
+#define EIGEN_UNALIGNED_VECTORIZE 1
+#endif
+
+//----------------------------------------------------------------------
+
+
+#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
+ #define EIGEN_RESTRICT
+#endif
+#ifndef EIGEN_RESTRICT
+ #define EIGEN_RESTRICT __restrict
+#endif
+
+#ifndef EIGEN_STACK_ALLOCATION_LIMIT
+// 131072 == 128 KB
+#define EIGEN_STACK_ALLOCATION_LIMIT 131072
+#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
+
+#if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 || defined(__CUDACC_VER__)) // for older MSVC versions, as well as 1900 && CUDA 8, using the base operator is sufficient (cf Bugs 1000, 1324)
+ #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 manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+
+/**
+* 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 { 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))
+
+// 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<=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 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 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)
+
+
+#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
+# ifdef __CUDA_ARCH__
+# define EIGEN_THROW_X(X) asm("trap;")
+# define EIGEN_THROW asm("trap;")
+# 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()
+# define EIGEN_EXCEPTION_SPEC(X) throw(X)
+#endif
+
+#endif // EIGEN_MACROS_H