为什么 std::less<Eigen::VectorXd> 编译失败？
Why does std::less<Eigen::VectorXd> fail to compile?
我为 Eigen::VectorXd 实现了一个比较运算符 operator<，有时，我需要将一个比较函数传递给另一个我的函数，我厌倦了将 operator< 包装成[](const VectorXd& v1, const VectorXd& v2)->bool{return v1 < v2}，所以我认为 std::less class 会很有用，因为据我了解，只要定义了 operator<，它就可以生成 lambda 函数。
但是，我发现 std::less<VectorXd> 对我不起作用，例如，下面的代码可以正常工作：
#include "Eigen/Dense"
#include <iostream>
#include <functional>
using namespace std;
using namespace Eigen;
struct T
{
int x;
};
bool operator<(const T& t1, const T& t2)
{
return t1.x < t2.x;
}
bool operator<(const VectorXd& v1, const VectorXd& v2)
{
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
int main()
{
T t1, t2;
t1.x = 3;
t2.x = 2;
auto ft = std::less<T>();
cout << ft(t1, t2) << endl;
return EXIT_SUCCESS;
}
但是，如果我这样使用 std::less<VectorXd>：
#include "Eigen/Dense"
#include <iostream>
#include <functional>
using namespace std;
using namespace Eigen;
struct T
{
int x;
};
bool operator<(const T& t1, const T& t2)
{
return t1.x < t2.x;
}
bool operator<(const VectorXd& v1, const VectorXd& v2)
{
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
int main()
{
T t1, t2;
t1.x = 3;
t2.x = 2;
auto ft = std::less<T>();
cout << ft(t1, t2) << endl;
VectorXd v1(3);
VectorXd v2(3);
v1 << 1, 2, 3;
v2 << 2, 3, 4;
auto fv = std::less<VectorXd>();
cout << fv(v1, v2) << endl;
return EXIT_SUCCESS;
}
代码编译失败，我收到如下错误信息：
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h: In instantiation of ‘bool std::less<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = Eigen::Matrix<double, -1, 1>]’:
test.cpp:36:26: required from here
/usr/include/c++/5/bits/stl_function.h:387:20: error: no match for ‘operator<’ (operand types are ‘const Eigen::Matrix<double, -1, 1>’ and ‘const Eigen::Matrix<double, -1, 1>’)
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:64:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_pair.h:220:5: note: candidate: template<class _T1, class _T2> constexpr bool std::operator<(const std::pair<_T1, _T2>&, const std::pair<_T1, _T2>&)
operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
^
/usr/include/c++/5/bits/stl_pair.h:220:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::pair<_T1, _T2>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:298:5: note: candidate: template<class _Iterator> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_Iterator>&)
operator<(const reverse_iterator<_Iterator>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:298:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::reverse_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:348:5: note: candidate: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_IteratorR>&)
operator<(const reverse_iterator<_IteratorL>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:348:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::reverse_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:1089:5: note: candidate: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::move_iterator<_Iterator>&, const std::move_iterator<_IteratorR>&)
operator<(const move_iterator<_IteratorL>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:1089:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::move_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:1095:5: note: candidate: template<class _Iterator> bool std::operator<(const std::move_iterator<_Iterator>&, const std::move_iterator<_Iterator>&)
operator<(const move_iterator<_Iterator>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:1095:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::move_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:4987:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&, const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&)
operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
^
/usr/include/c++/5/bits/basic_string.h:4987:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:4999:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&, const _CharT*)
operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
^
/usr/include/c++/5/bits/basic_string.h:4999:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:5011:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const _CharT*, const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&)
operator<(const _CharT* __lhs,
^
/usr/include/c++/5/bits/basic_string.h:5011:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: mismatched types ‘const _CharT*’ and ‘Eigen::Matrix<double, -1, 1>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/ios_base.h:46:0,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/system_error:200:3: note: candidate: bool std::operator<(const std::error_code&, const std::error_code&)
operator<(const error_code& __lhs, const error_code& __rhs) noexcept
^
/usr/include/c++/5/system_error:200:3: note: no known conversion for argument 1 from ‘const Eigen::Matrix<double, -1, 1>’ to ‘const std::error_code&’
/usr/include/c++/5/system_error:274:3: note: candidate: bool std::operator<(const std::error_condition&, const std::error_condition&)
operator<(const error_condition& __lhs,
^
/usr/include/c++/5/system_error:274:3: note: no known conversion for argument 1 from ‘const Eigen::Matrix<double, -1, 1>’ to ‘const std::error_condition&’
In file included from /usr/include/c++/5/tuple:39:0,
from /usr/include/c++/5/functional:55,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:262,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/array:250:5: note: candidate: template<class _Tp, long unsigned int _Nm> bool std::operator<(const std::array<_Tp, _Nm>&, const std::array<_Tp, _Nm>&)
operator<(const array<_Tp, _Nm>& __a, const array<_Tp, _Nm>& __b)
^
/usr/include/c++/5/array:250:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::array<_Tp, _Nm>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/functional:55:0,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:262,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/tuple:928:5: note: candidate: template<class ... _TElements, class ... _UElements> constexpr bool std::operator<(const std::tuple<_Elements ...>&, const std::tuple<_Elements ...>&)
operator<(const tuple<_TElements...>& __t,
^
/usr/include/c++/5/tuple:928:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::tuple<_Elements ...>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/vector:64:0,
from /usr/include/c++/5/bits/random.h:34,
from /usr/include/c++/5/random:49,
from /usr/include/c++/5/bits/stl_algo.h:66,
from /usr/include/c++/5/algorithm:62,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:269,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_vector.h:1528:5: note: candidate: template<class _Tp, class _Alloc> bool std::operator<(const std::vector<_Tp, _Alloc>&, const std::vector<_Tp, _Alloc>&)
operator<(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
^
/usr/include/c++/5/bits/stl_vector.h:1528:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::vector<_Tp, _Alloc>’
{ return __x < __y; }
^
make: *** [try] Error 1
我正在使用 g++ 5.4.0 和 Eigen 3.3
事情是这样的。您的 T 无法可靠地重现情况。您省略了名称空间，这非常重要。与 Eigen 的情况更接近的例子是：
namespace Foo {
struct T
{
int x;
};
}
bool operator<(const Foo::T& t1, const Foo::T& t2)
{
return t1.x < t2.x;
}
并且它会产生完全相同的错误。这是因为模板只会考虑在模板 定义 点（而不是实例化）或 argument dependent lookup 类型上找到的此运算符的重载操作数。
要使依赖于参数的查找起作用，运算符和类型必须在相同的命名空间中定义，而您的显然不是。
所以这是怎么回事，你包括了functional。这在您的翻译单元中定义了模板 std::less。那时，Eigen::VectorXd的operator<已经看不到了。所以后面定义的时候模板定义就不会考虑了。
当您实例化模板时，它会尝试在它意识到的那些重载中寻找合适的重载，然后通过 ADL。由于您的 operator< 不在 Eigen 命名空间内，因此 ADL 也找不到它。
长话短说，为库类型重载运算符是不切实际的。你应该做的是定义一个自定义比较器类型：
struct VectorXdCompare {
bool operator()(const VectorXd& v1, const VectorXd& v2) {
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
};
并在标准库需要时将 VectorXdCompare 作为类型传递。
我为 Eigen::VectorXd 实现了一个比较运算符 operator<，有时，我需要将一个比较函数传递给另一个我的函数，我厌倦了将 operator< 包装成[](const VectorXd& v1, const VectorXd& v2)->bool{return v1 < v2}，所以我认为 std::less class 会很有用，因为据我了解，只要定义了 operator<，它就可以生成 lambda 函数。
但是，我发现 std::less<VectorXd> 对我不起作用，例如，下面的代码可以正常工作：
#include "Eigen/Dense"
#include <iostream>
#include <functional>
using namespace std;
using namespace Eigen;
struct T
{
int x;
};
bool operator<(const T& t1, const T& t2)
{
return t1.x < t2.x;
}
bool operator<(const VectorXd& v1, const VectorXd& v2)
{
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
int main()
{
T t1, t2;
t1.x = 3;
t2.x = 2;
auto ft = std::less<T>();
cout << ft(t1, t2) << endl;
return EXIT_SUCCESS;
}
但是，如果我这样使用 std::less<VectorXd>：
#include "Eigen/Dense"
#include <iostream>
#include <functional>
using namespace std;
using namespace Eigen;
struct T
{
int x;
};
bool operator<(const T& t1, const T& t2)
{
return t1.x < t2.x;
}
bool operator<(const VectorXd& v1, const VectorXd& v2)
{
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
int main()
{
T t1, t2;
t1.x = 3;
t2.x = 2;
auto ft = std::less<T>();
cout << ft(t1, t2) << endl;
VectorXd v1(3);
VectorXd v2(3);
v1 << 1, 2, 3;
v2 << 2, 3, 4;
auto fv = std::less<VectorXd>();
cout << fv(v1, v2) << endl;
return EXIT_SUCCESS;
}
代码编译失败，我收到如下错误信息：
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h: In instantiation of ‘bool std::less<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = Eigen::Matrix<double, -1, 1>]’:
test.cpp:36:26: required from here
/usr/include/c++/5/bits/stl_function.h:387:20: error: no match for ‘operator<’ (operand types are ‘const Eigen::Matrix<double, -1, 1>’ and ‘const Eigen::Matrix<double, -1, 1>’)
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:64:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_pair.h:220:5: note: candidate: template<class _T1, class _T2> constexpr bool std::operator<(const std::pair<_T1, _T2>&, const std::pair<_T1, _T2>&)
operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
^
/usr/include/c++/5/bits/stl_pair.h:220:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::pair<_T1, _T2>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:298:5: note: candidate: template<class _Iterator> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_Iterator>&)
operator<(const reverse_iterator<_Iterator>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:298:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::reverse_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:348:5: note: candidate: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_IteratorR>&)
operator<(const reverse_iterator<_IteratorL>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:348:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::reverse_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:1089:5: note: candidate: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::move_iterator<_Iterator>&, const std::move_iterator<_IteratorR>&)
operator<(const move_iterator<_IteratorL>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:1089:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::move_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/stl_algobase.h:67:0,
from /usr/include/c++/5/bits/char_traits.h:39,
from /usr/include/c++/5/ios:40,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_iterator.h:1095:5: note: candidate: template<class _Iterator> bool std::operator<(const std::move_iterator<_Iterator>&, const std::move_iterator<_Iterator>&)
operator<(const move_iterator<_Iterator>& __x,
^
/usr/include/c++/5/bits/stl_iterator.h:1095:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::move_iterator<_Iterator>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:4987:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&, const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&)
operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
^
/usr/include/c++/5/bits/basic_string.h:4987:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:4999:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&, const _CharT*)
operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
^
/usr/include/c++/5/bits/basic_string.h:4999:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/string:52:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/basic_string.h:5011:5: note: candidate: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const _CharT*, const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&)
operator<(const _CharT* __lhs,
^
/usr/include/c++/5/bits/basic_string.h:5011:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: mismatched types ‘const _CharT*’ and ‘Eigen::Matrix<double, -1, 1>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/bits/ios_base.h:46:0,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/system_error:200:3: note: candidate: bool std::operator<(const std::error_code&, const std::error_code&)
operator<(const error_code& __lhs, const error_code& __rhs) noexcept
^
/usr/include/c++/5/system_error:200:3: note: no known conversion for argument 1 from ‘const Eigen::Matrix<double, -1, 1>’ to ‘const std::error_code&’
/usr/include/c++/5/system_error:274:3: note: candidate: bool std::operator<(const std::error_condition&, const std::error_condition&)
operator<(const error_condition& __lhs,
^
/usr/include/c++/5/system_error:274:3: note: no known conversion for argument 1 from ‘const Eigen::Matrix<double, -1, 1>’ to ‘const std::error_condition&’
In file included from /usr/include/c++/5/tuple:39:0,
from /usr/include/c++/5/functional:55,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:262,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/array:250:5: note: candidate: template<class _Tp, long unsigned int _Nm> bool std::operator<(const std::array<_Tp, _Nm>&, const std::array<_Tp, _Nm>&)
operator<(const array<_Tp, _Nm>& __a, const array<_Tp, _Nm>& __b)
^
/usr/include/c++/5/array:250:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::array<_Tp, _Nm>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/functional:55:0,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:262,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/tuple:928:5: note: candidate: template<class ... _TElements, class ... _UElements> constexpr bool std::operator<(const std::tuple<_Elements ...>&, const std::tuple<_Elements ...>&)
operator<(const tuple<_TElements...>& __t,
^
/usr/include/c++/5/tuple:928:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::tuple<_Elements ...>’
{ return __x < __y; }
^
In file included from /usr/include/c++/5/vector:64:0,
from /usr/include/c++/5/bits/random.h:34,
from /usr/include/c++/5/random:49,
from /usr/include/c++/5/bits/stl_algo.h:66,
from /usr/include/c++/5/algorithm:62,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:269,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_vector.h:1528:5: note: candidate: template<class _Tp, class _Alloc> bool std::operator<(const std::vector<_Tp, _Alloc>&, const std::vector<_Tp, _Alloc>&)
operator<(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
^
/usr/include/c++/5/bits/stl_vector.h:1528:5: note: template argument deduction/substitution failed:
In file included from /usr/include/c++/5/string:48:0,
from /usr/include/c++/5/bits/locale_classes.h:40,
from /usr/include/c++/5/bits/ios_base.h:41,
from /usr/include/c++/5/ios:42,
from /usr/include/c++/5/istream:38,
from /usr/include/c++/5/sstream:38,
from /usr/include/c++/5/complex:45,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Core:80,
from /home/alaya/.softwares/linear_algebra/eigen3.3/include/eigen3/Eigen/Dense:1,
from test.cpp:1:
/usr/include/c++/5/bits/stl_function.h:387:20: note: ‘const Eigen::Matrix<double, -1, 1>’ is not derived from ‘const std::vector<_Tp, _Alloc>’
{ return __x < __y; }
^
make: *** [try] Error 1
我正在使用 g++ 5.4.0 和 Eigen 3.3
事情是这样的。您的 T 无法可靠地重现情况。您省略了名称空间，这非常重要。与 Eigen 的情况更接近的例子是：
namespace Foo {
struct T
{
int x;
};
}
bool operator<(const Foo::T& t1, const Foo::T& t2)
{
return t1.x < t2.x;
}
并且它会产生完全相同的错误。这是因为模板只会考虑在模板 定义 点（而不是实例化）或 argument dependent lookup 类型上找到的此运算符的重载操作数。
要使依赖于参数的查找起作用，运算符和类型必须在相同的命名空间中定义，而您的显然不是。
所以这是怎么回事，你包括了functional。这在您的翻译单元中定义了模板 std::less。那时，Eigen::VectorXd的operator<已经看不到了。所以后面定义的时候模板定义就不会考虑了。
当您实例化模板时，它会尝试在它意识到的那些重载中寻找合适的重载，然后通过 ADL。由于您的 operator< 不在 Eigen 命名空间内，因此 ADL 也找不到它。
长话短说，为库类型重载运算符是不切实际的。你应该做的是定义一个自定义比较器类型：
struct VectorXdCompare {
bool operator()(const VectorXd& v1, const VectorXd& v2) {
return (v1.array() <= v2.array()).all() and (v1 != v2);
}
};
并在标准库需要时将 VectorXdCompare 作为类型传递。