c++ - Eigen:线性系统求解器的 vector

Question

我正在使用 Eigen 线性代数库，需要一个 BiCGSTAB 求解器 vector 。不幸的是，扩展这个 vector 非常困难。最小的(不是)工作示例是

#include <Eigen/Eigen>

int main() {
    std::vector< Eigen::BiCGSTAB< Eigen::SparseMatrix< double > > > tmp;
    tmp.emplace_back();
}

并产生错误信息

$ g++ -I/usr/include/eigen3 main.cpp
In file included from /usr/include/c++/12.2.0/vector:63,
                 from /usr/include/c++/12.2.0/functional:62,
                 from /usr/include/eigen3/Eigen/Core:85,
                 from /usr/include/eigen3/Eigen/Dense:1,
                 from /usr/include/eigen3/Eigen/Eigen:1,
                 from main.cpp:1:
/usr/include/c++/12.2.0/bits/stl_uninitialized.h: In instantiation of ‘constexpr bool std::__check_constructible() [with _ValueType = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&&]’:
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:182:4:   required from ‘_ForwardIterator std::uninitialized_copy(_InputIterator, _InputIterator, _ForwardIterator) [with _InputIterator = move_iterator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*]’
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:372:37:   required from ‘_ForwardIterator std::__uninitialized_copy_a(_InputIterator, _InputIterator, _ForwardIterator, allocator<_Tp>&) [with _InputIterator = move_iterator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >]’
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:397:2:   required from ‘_ForwardIterator std::__uninitialized_move_if_noexcept_a(_InputIterator, _InputIterator, _ForwardIterator, _Allocator&) [with _InputIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _Allocator = allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >]’
/usr/include/c++/12.2.0/bits/vector.tcc:487:3:   required from ‘void std::vector<_Tp, _Alloc>::_M_realloc_insert(iterator, _Args&& ...) [with _Args = {}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; iterator = std::vector<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::iterator]’
/usr/include/c++/12.2.0/bits/vector.tcc:123:21:   required from ‘std::vector<_Tp, _Alloc>::reference std::vector<_Tp, _Alloc>::emplace_back(_Args&& ...) [with _Args = {}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; reference = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&]’
main.cpp:5:21:   required from here
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:90:56: error: static assertion failed: result type must be constructible from input type
   90 |       static_assert(is_constructible<_ValueType, _Tp>::value,
      |                                                        ^~~~~
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:90:56: note: ‘std::integral_constant<bool, false>::value’ evaluates to false

尝试 std::move 更糟，即

#include <Eigen/Eigen>
#include <utility>

int main() {
    std::vector< Eigen::BiCGSTAB< Eigen::SparseMatrix< double > > > tmp;

    Eigen::BiCGSTAB< Eigen::SparseMatrix< double > > solver;
    tmp.push_back( std::move( solver ) );
}

导致错误信息

g++ -I/usr/include/eigen3 main.cpp
In file included from /usr/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/c++allocator.h:33,
                 from /usr/include/c++/12.2.0/bits/allocator.h:46,
                 from /usr/include/c++/12.2.0/string:41,
                 from /usr/include/c++/12.2.0/bits/locale_classes.h:40,
                 from /usr/include/c++/12.2.0/bits/ios_base.h:41,
                 from /usr/include/c++/12.2.0/ios:42,
                 from /usr/include/c++/12.2.0/istream:38,
                 from /usr/include/c++/12.2.0/sstream:38,
                 from /usr/include/c++/12.2.0/complex:45,
                 from /usr/include/eigen3/Eigen/Core:50,
                 from /usr/include/eigen3/Eigen/Dense:1,
                 from /usr/include/eigen3/Eigen/Eigen:1,
                 from main.cpp:1:
/usr/include/c++/12.2.0/bits/new_allocator.h: In instantiation of ‘void std::__new_allocator<_Tp>::construct(_Up*, _Args&& ...) [with _Up = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Args = {Eigen::BiCGSTAB<Eigen::SparseMatrix<double, 0, int>, Eigen::DiagonalPreconditioner<double> >}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >]’:
/usr/include/c++/12.2.0/bits/alloc_traits.h:516:17:   required from ‘static void std::allocator_traits<std::allocator<_CharT> >::construct(allocator_type&, _Up*, _Args&& ...) [with _Up = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Args = {Eigen::BiCGSTAB<Eigen::SparseMatrix<double, 0, int>, Eigen::DiagonalPreconditioner<double> >}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; allocator_type = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >]’
/usr/include/c++/12.2.0/bits/vector.tcc:117:30:   required from ‘std::vector<_Tp, _Alloc>::reference std::vector<_Tp, _Alloc>::emplace_back(_Args&& ...) [with _Args = {Eigen::BiCGSTAB<Eigen::SparseMatrix<double, 0, int>, Eigen::DiagonalPreconditioner<double> >}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; reference = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&]’
/usr/include/c++/12.2.0/bits/stl_vector.h:1294:21:   required from ‘void std::vector<_Tp, _Alloc>::push_back(value_type&&) [with _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; value_type = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >]’
main.cpp:9:18:   required from here
/usr/include/c++/12.2.0/bits/new_allocator.h:175:11: error: use of deleted function ‘Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >::BiCGSTAB(const Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&)’
  175 |         { ::new((void *)__p) _Up(std::forward<_Args>(__args)...); }
      |           ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/eigen3/Eigen/IterativeLinearSolvers:42,
                 from /usr/include/eigen3/Eigen/Sparse:31,
                 from /usr/include/eigen3/Eigen/Eigen:2:
/usr/include/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h:158:7: note: ‘Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >::BiCGSTAB(const Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&)’ is implicitly deleted because the default definition would be ill-formed:
  158 | class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >
      |       ^~~~~~~~
/usr/include/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h:158:7: error: use of deleted function ‘Eigen::IterativeSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::IterativeSolverBase(const Eigen::IterativeSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >&)’
In file included from /usr/include/eigen3/Eigen/IterativeLinearSolvers:38:
/usr/include/eigen3/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h:143:7: note: ‘Eigen::IterativeSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::IterativeSolverBase(const Eigen::IterativeSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >&)’ is implicitly deleted because the default definition would be ill-formed:
  143 | class IterativeSolverBase : public SparseSolverBase<Derived>
      |       ^~~~~~~~~~~~~~~~~~~
/usr/include/eigen3/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h:143:7: error: use of deleted function ‘Eigen::SparseSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::SparseSolverBase(const Eigen::SparseSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >&)’
In file included from /usr/include/eigen3/Eigen/SparseCore:64,
                 from /usr/include/eigen3/Eigen/Sparse:26:
/usr/include/eigen3/Eigen/src/SparseCore/SparseSolverBase.h:67:7: note: ‘Eigen::SparseSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::SparseSolverBase(const Eigen::SparseSolverBase<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >&)’ is implicitly deleted because the default definition would be ill-formed:
   67 | class SparseSolverBase : internal::noncopyable
      |       ^~~~~~~~~~~~~~~~
/usr/include/eigen3/Eigen/src/SparseCore/SparseSolverBase.h:67:7: error: ‘Eigen::internal::noncopyable::noncopyable(const Eigen::internal::noncopyable&)’ is private within this context
In file included from /usr/include/eigen3/Eigen/Core:162:
/usr/include/eigen3/Eigen/src/Core/util/Meta.h:424:21: note: declared private here
  424 |   EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);
      |                     ^~~~~~~~~~~
In file included from /usr/include/c++/12.2.0/vector:63,
                 from /usr/include/c++/12.2.0/functional:62,
                 from /usr/include/eigen3/Eigen/Core:85:
/usr/include/c++/12.2.0/bits/stl_uninitialized.h: In instantiation of ‘constexpr bool std::__check_constructible() [with _ValueType = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&&]’:
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:182:4:   required from ‘_ForwardIterator std::uninitialized_copy(_InputIterator, _InputIterator, _ForwardIterator) [with _InputIterator = move_iterator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*]’
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:372:37:   required from ‘_ForwardIterator std::__uninitialized_copy_a(_InputIterator, _InputIterator, _ForwardIterator, allocator<_Tp>&) [with _InputIterator = move_iterator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >]’
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:397:2:   required from ‘_ForwardIterator std::__uninitialized_move_if_noexcept_a(_InputIterator, _InputIterator, _ForwardIterator, _Allocator&) [with _InputIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _ForwardIterator = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >*; _Allocator = allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >]’
/usr/include/c++/12.2.0/bits/vector.tcc:487:3:   required from ‘void std::vector<_Tp, _Alloc>::_M_realloc_insert(iterator, _Args&& ...) [with _Args = {Eigen::BiCGSTAB<Eigen::SparseMatrix<double, 0, int>, Eigen::DiagonalPreconditioner<double> >}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; iterator = std::vector<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >::iterator]’
/usr/include/c++/12.2.0/bits/vector.tcc:123:21:   required from ‘std::vector<_Tp, _Alloc>::reference std::vector<_Tp, _Alloc>::emplace_back(_Args&& ...) [with _Args = {Eigen::BiCGSTAB<Eigen::SparseMatrix<double, 0, int>, Eigen::DiagonalPreconditioner<double> >}; _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; reference = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >&]’
/usr/include/c++/12.2.0/bits/stl_vector.h:1294:21:   required from ‘void std::vector<_Tp, _Alloc>::push_back(value_type&&) [with _Tp = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::BiCGSTAB<Eigen::SparseMatrix<double> > >; value_type = Eigen::BiCGSTAB<Eigen::SparseMatrix<double> >]’
main.cpp:9:18:   required from here
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:90:56: error: static assertion failed: result type must be constructible from input type
   90 |       static_assert(is_constructible<_ValueType, _Tp>::value,
      |                                                        ^~~~~
/usr/include/c++/12.2.0/bits/stl_uninitialized.h:90:56: note: ‘std::integral_constant<bool, false>::value’ evaluates to false

我使用的是 Eigen 3.4 和 g++ 12.2 版。

有什么办法解决这个问题吗？

Answer 1

将我的评论变成正确的答案:

看了代码，发现BiCGSTAB就像所有的求解器都继承自一个旨在防止复制和扩展移动的基类:class SparseSolverBase : internal::noncopyable

我无法说出选择这种设计的确切原因。如果我不得不猜测，我会说一些求解器可能使用自引用属性(保存指向其他成员的指针)，这尤其会破坏固定大小的矩阵。或者使用 Eigen::Map可能会导致复制问题，尤其是复制分配问题。

std::vector仅适用于可移动类型，因为它在重新分配时需要移动。即使调用reserve()事先，代码仍然需要编译，即使它从未被执行。

我想到了三种解决方法:

1. 使用 std::deque .它提供了 vector 拥有的所有方法的超集，但它的实现意味着只要你只调用 emplace_back或 emplace_front而不是例如insert ，它不需要可移动类型。缺点是它在所有单独访问上有点慢

2. 使用 std::vector<std::unique_ptr<Solver>> .效率低于双端队列，但现在您还可以插入、重新洗牌等。

3. 使用 std::unique_ptr<Solver[]>并使用旧的new Solver[count]分配。从 C++14 开始，您可以使用 std::make_unique<Solver[]>(count) .这具有最少的开销，甚至比 vector 还少，但接口(interface)没有那么好(您可以使用 [index] 运算符，但指针甚至不知道数组大小)并且数字在分配后固定