text: // 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 7
  
  #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 || (EIGEN_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 && (EIGEN_COMP_CLANG || EIGEN_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.
  #ifndef EIGEN_STRONG_INLINE
  #if EIGEN_COMP_MSVC || EIGEN_COMP_ICC
  #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)
  #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) if (!(x)) throw std::logic_error(#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 || EIGEN_CUDACC_VER>0)
    // 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()
  #   if EIGEN_COMP_MSVC
        // MSVC does not support exception specifications (warning C4290),
        // and they are deprecated in c++11 anyway.
  #     define EIGEN_EXCEPTION_SPEC(X) throw()
  #   else
  #     define EIGEN_EXCEPTION_SPEC(X) throw(X)
  #   endif
  #endif
  
  #endif // EIGEN_MACROS_H
  