Hello,

I'm trying to adapt the conjugate gradient method so that it can be use with a sparse matrix product:

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typedef Eigen::SparseMatrix<double, Eigen::ColMajor> MatrixType;
const MatrixType& A = getA(); // use a const reference
auto AA = A.transpose() * A; //  Eigen::SparseMatrixBase<Eigen::SparseSparseProduct<Eigen::SparseMatrix<double, 0, int>, Eigen::SparseMatrix<double, 0, int> const&> >


The objective is to eventually add some extra code in order to avoid determining the resulting matrix explicitly but instead do always the following product:

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A.transpose() * A * x


where x is a dense vector.

Therefore, for now, I'm trying to use the type MatrixMatrixType:

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typedef Eigen::TransposeImpl<const MatrixType, Eigen::Sparse> MatrixTType;
typedef Eigen::SparseSparseProduct<MatrixTType, const MatrixType&> MatrixMatrixType;


However inside my code I get the following error:
SparseProduct.h:47:84: error: invalid use of incomplete type ‘struct Eigen::internal::traits<Eigen::TransposeImpl<const Eigen::SparseMatrix<double, 0>, Eigen::Sparse> >’
typename traits<_RhsNested>::Index>::type Index;

So, just to have a complete example that triggers this issue:

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typedef double Scalar;
typedef Eigen::SparseMatrix<Scalar, Eigen::ColMajor> MatrixType;
typedef Eigen::TransposeImpl<const MatrixType, Eigen::Sparse> MatrixTType;
typedef Eigen::SparseSparseProduct<MatrixTType, const MatrixType&> MatrixMatrixType;

MatrixType A(100, 200);
   
MatrixMatrixType AA(A.transpose(), A); // <<<<<<<< Error!


Should I be using something else in the types of SparseSparseProduct?

I would be grateful for any help!
João Leal

P.S.- Edited in order to have a complete example with the issue.

You must use "Eigen::Transpose<const MatrixType>". However, this will result in (A^T * A) * x instead of A^T * (A * x). So that's probably not the right way to do so. It would be better to implement a true LSCG class properly support preconditioning.