# Solving Linear Equations using Eigen

I am trying to solve linear equations in c++ using the Eigen library. For the simple equation Ax=b, I have a sparse matrix A that is n x n, and known values for b which is n x 1, but I need to find the values for x. I tried using

x = A.colPivHouseholderQr().solve(b);

but this solves it for a dense matrix and since my "n" value is quite large, I need to find a way to do this using an implementation that is specific to sparse matrices. I looked into using SparseLU but I've been having trouble trying figure out the syntax behind it. Eigen online says to write something like this :

SparseLU<SparseMatrix<scalar>, COLAMDOrdering<Index>> solver;
solver.analyzePattern(A);
solver.factorize(A);
x = solver.solve(b);

but when I run this, I get errors saying that they don't know what scalar and Index are. Has anyone used SparseLU and know the syntax behind implementing it?

• I'm not sure where you found this example. But instead of "scalar" you would need some floating point type, typically, double. Instead of "Index" you would typically use int. – Bill Greene Nov 19 '15 at 1:47
• This seems like a programming issue, rather than a computational science one, and it would be impossible to answer it without you saying what exactly the "errors" were. – Kirill Nov 19 '15 at 2:12
• Please post the errors as the solution might be as simple as taking Bill Greene's suggestion of using double's and int's instead of scalars and index – James Nov 19 '15 at 6:46

Eigen::SparseLU<Eigen::SparseMatrix<double> > solverA;
A.makeCompressed();
solverA.analyzePattern(A);
solverA.factorize(A);

if(solverA.info()!=Eigen::Success) {
std::cout << "Oh: Very bad" <<"\n";
}
else{
std::cout<<"okay computed"<<"\n";
}
Eigen::VectorXd solnew = solverA.solve(b);

You don't need to mention the COLAMDOrdering but if you want you can declare the solver as :

Eigen::SparseLU<Eigen::SparseMatrix<double>, Eigen::COLAMDOrdering<int> > solver;