Eigen Sparse LU solver - c++

Question

I am using the Eigen library in C++ for solving sparse linear equations: Ax=b where, A is a square sparse matrix and b is a rectangular sparse matrix. I have multiple instances of the A matrices and each one has multiple right hand sides b. Hence, I want to factorize all the A matrices once and store them followed by solution for each A with each b.
I tried to use the C++ vector for storing all the solvers. This is a sample code I have written:
vector<Eigen::SparseMatrix<double>> A;
//fill in all A matrices
vector<Eigen::SparseLU<Eigen::SparseMatrix<double>>> solver_A;
Eigen::SparseLU<Eigen::SparseMatrix<double>> solver;
for (int i=0;i<A.size();i++){
solver.analyzePattern(A[i]);
solver.factorize(A[i]);
solver_A.push_back(solver);
}
//Later, solver_A entries are to be used to solve for various right hand sides
I am using 3.3.7 version of Eigen and compiling in linux with gcc compiler and c++17 standard. I am getting the following compilation error due to the solver_A.push_back(solver) line:
<pre>/usr/include/c++/7/ext/new_allocator.h: In instantiation of ‘<b>void __gnu_cxx::new_allocator<_Tp>::construct(_Up*, _Args&& ...) [with _Up = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Args = {const Eigen::SparseLU<Eigen::SparseMatrix<double, 0, int>, Eigen::COLAMDOrdering<int> >&}; _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >]</b>’:
<b>/usr/include/c++/7/bits/alloc_traits.h:475:4:</b> required from ‘<b>static void std::allocator_traits<std::allocator<_CharT> >::construct(std::allocator_traits<std::allocator<_CharT> >::allocator_type&, _Up*, _Args&& ...) [with _Up = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Args = {const Eigen::SparseLU<Eigen::SparseMatrix<double, 0, int>, Eigen::COLAMDOrdering<int> >&}; _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >; std::allocator_traits<std::allocator<_CharT> >::allocator_type = std::allocator<Eigen::SparseLU<Eigen::SparseMatrix<double> > >]</b>’
<b>/usr/include/c++/7/bits/stl_vector.h:943:30:</b> required from ‘<b>void std::vector<_Tp, _Alloc>::push_back(const value_type&) [with _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::SparseLU<Eigen::SparseMatrix<double> > >; std::vector<_Tp, _Alloc>::value_type = Eigen::SparseLU<Eigen::SparseMatrix<double> >]</b>’
<b>header_files/coefficient_computations.cpp:476:51:</b> required from here
<b>/usr/include/c++/7/ext/new_allocator.h:136:4:</b> <font color="#EF2929"><b>error: </b></font>‘Eigen::SparseLU<_MatrixType, _OrderingType>::SparseLU(const Eigen::SparseLU<_MatrixType, _OrderingType>&) [with _MatrixType = Eigen::SparseMatrix<double>; _O<b>rderingType = Eigen::COLAMDOrdering<int>]</b>’ is private within this context
{ <font color="#EF2929"><b>::new((void *)__p) _Up(std::forward<_Args>(__args)...)</b></font>; }
<font color="#EF2929"><b>^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</b></font>
In file included from <b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/SparseLU:44:0</b>,
from <b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/Sparse:31</b>,
from <b>../Eigen_3_3_7/unsupported/Eigen/SparseExtra:13</b>,
from <b>header_files/general_functions.hpp:17</b>,
from <b>header_files/coefficient_computations.hpp:17</b>,
from <b>header_files/coefficient_computations.cpp:2</b>:
<b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/src/SparseLU/SparseLU.h:393:5:</b> <font color="#34E2E2"><b>note: </b></font>declared private here
<font color="#34E2E2"><b>SparseLU</b></font> (const SparseLU& );
<font color="#34E2E2"><b>^~~~~~~~</b></font>
In file included from <b>/usr/include/c++/7/vector:62:0</b>,
from <b>header_files/coefficient_computations.hpp:13</b>,
from <b>header_files/coefficient_computations.cpp:2</b>:
/usr/include/c++/7/bits/stl_construct.h: In instantiation of ‘<b>void std::_Construct(_T1*, _Args&& ...) [with _T1 = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Args = {Eigen::SparseLU<Eigen::SparseMatrix<double, 0, int>, Eigen::COLAMDOrdering<int> >}]</b>’:
<b>/usr/include/c++/7/bits/stl_uninitialized.h:83:18:</b> required from ‘<b>static _ForwardIterator std::__uninitialized_copy<_TrivialValueTypes>::__uninit_copy(_InputIterator, _InputIterator, _ForwardIterator) [with _InputIterator = std::move_iterator<Eigen::SparseLU<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::SparseLU<Eigen::SparseMatrix<double> >*; bool _TrivialValueTypes = false]</b>’
<b>/usr/include/c++/7/bits/stl_uninitialized.h:134:15:</b> required from ‘<b>_ForwardIterator std::uninitialized_copy(_InputIterator, _InputIterator, _ForwardIterator) [with _InputIterator = std::move_iterator<Eigen::SparseLU<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::SparseLU<Eigen::SparseMatrix<double> >*]</b>’
<b>/usr/include/c++/7/bits/stl_uninitialized.h:289:37:</b> required from ‘<b>_ForwardIterator std::__uninitialized_copy_a(_InputIterator, _InputIterator, _ForwardIterator, std::allocator<_Tp>&) [with _InputIterator = std::move_iterator<Eigen::SparseLU<Eigen::SparseMatrix<double> >*>; _ForwardIterator = Eigen::SparseLU<Eigen::SparseMatrix<double> >*; _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >]</b>’
<b>/usr/include/c++/7/bits/stl_uninitialized.h:311:2:</b> required from ‘<b>_ForwardIterator std::__uninitialized_move_if_noexcept_a(_InputIterator, _InputIterator, _ForwardIterator, _Allocator&) [with _InputIterator = Eigen::SparseLU<Eigen::SparseMatrix<double> >*; _ForwardIterator = Eigen::SparseLU<Eigen::SparseMatrix<double> >*; _Allocator = std::allocator<Eigen::SparseLU<Eigen::SparseMatrix<double> > >]</b>’
<b>/usr/include/c++/7/bits/vector.tcc:426:6:</b> required from ‘<b>void std::vector<_Tp, _Alloc>::_M_realloc_insert(std::vector<_Tp, _Alloc>::iterator, _Args&& ...) [with _Args = {const Eigen::SparseLU<Eigen::SparseMatrix<double, 0, int>, Eigen::COLAMDOrdering<int> >&}; _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::SparseLU<Eigen::SparseMatrix<double> > >; std::vector<_Tp, _Alloc>::iterator = __gnu_cxx::__normal_iterator<Eigen::SparseLU<Eigen::SparseMatrix<double> >*, std::vector<Eigen::SparseLU<Eigen::SparseMatrix<double> > > >; typename std::_Vector_base<_Tp, _Alloc>::pointer = Eigen::SparseLU<Eigen::SparseMatrix<double> >*]</b>’
<b>/usr/include/c++/7/bits/stl_vector.h:948:21:</b> required from ‘<b>void std::vector<_Tp, _Alloc>::push_back(const value_type&) [with _Tp = Eigen::SparseLU<Eigen::SparseMatrix<double> >; _Alloc = std::allocator<Eigen::SparseLU<Eigen::SparseMatrix<double> > >; std::vector<_Tp, _Alloc>::value_type = Eigen::SparseLU<Eigen::SparseMatrix<double> >]</b>’
<b>header_files/coefficient_computations.cpp:476:51:</b> required from here
<b>/usr/include/c++/7/bits/stl_construct.h:75:7:</b> <font color="#EF2929"><b>error: </b></font>‘Eigen::SparseLU<_MatrixType, _OrderingType>::SparseLU(const Eigen::SparseLU<_MatrixType, _OrderingType>&) [with _MatrixType = Eigen::SparseMatrix<double>; _O<b>rderingType = Eigen::COLAMDOrdering<int>]</b>’ is private within this context
{ <font color="#EF2929"><b>::new(static_cast<void*>(__p)) _T1(std::forward<_Args>(__args)...)</b></font>; }
<font color="#EF2929"><b>^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</b></font>
In file included from <b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/SparseLU:44:0</b>,
from <b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/Sparse:31</b>,
from <b>../Eigen_3_3_7/unsupported/Eigen/SparseExtra:13</b>,
from <b>header_files/general_functions.hpp:17</b>,
from <b>header_files/coefficient_computations.hpp:17</b>,
from <b>header_files/coefficient_computations.cpp:2</b>:
<b>../Eigen_3_3_7/unsupported/Eigen/../../Eigen/src/SparseLU/SparseLU.h:393:5:</b> <font color="#34E2E2"><b>note: </b></font>declared private here
<font color="#34E2E2"><b>SparseLU</b></font> (const SparseLU& );
<font color="#34E2E2"><b>^~~~~~~~</b></font>
</pre>
The compilation is successful if the line "solver_A.push_back(solver)" is commented. Any help is appreciated either to fix this issue or with alternate solution.

Answer 1

vector::push_back requires the vector elements to be either copy or move constructible. SparseLU is neither of both because it has a private copy constructor (https://eigen.tuxfamily.org/dox/SparseLU_8h_source.html):
private:
// Disable copy constructor
SparseLU (const SparseLU& );
You can work around that in a number of ways. For example, by constructing the vector of solvers with the appropriate size so that it would need not to grow dynamically (https://godbolt.org/z/vS85P8):
vector<Eigen::SparseMatrix<double>> A;
vector<Eigen::SparseLU<Eigen::SparseMatrix<double>>> solver_A(A.size());
for (int i=0;i<A.size();i++) {
solver_A[i].analyzePattern(A[i]);
solver_A[i].factorize(A[i]);
}
If that’s not possible, another option would be to wrap your solvers into a movable type, for example a std::unique_ptr<Eigen::SparseMatrix<double>>.
As a side note, you can use compute instead of analyzePattern and then factorize.

Answer 2

Another possibility is to use std::deque together with the emplace_back method.
Note that the same is not possible with std::vector because here the vector::emplace_back may move the existing elements. deque::emplace_back doesn't need to do this.
I don't know, what algorithm you are implementing but I had a similar problem and thought I needed to store the solvers. In my case it was instead possible to use the solvers one after another (and never again for the same matrix), so I could use one solver instead of a vector. That's probably a better way if it is possible as it is less heavy on memory, as each solver demands 500 bytes on the stack alone.