Eigen value and generalized eigen value of a Super Big Size Real Matrix(160000*160000) , Help!

[Shelton-hub]

Hello, I need to get the most 1 smallest algrebraic eigen value of a big size symmetric matrix G with a level about 160000*160000 to see if G is positive definite . I try the solver SymEigsSolver but the result shows me failed. Here is the code fragment.

SparseGenMatProd<double> op(G);
// Construct eigen solver object, requesting the largest three eigenvalues
SymEigsSolver<SparseGenMatProd<double>> eigs(op, 4, 6);
// Initialize and compute
eigs.init();
int nconv = eigs.compute(SortRule::SmallestAlge);

And If G is positve definete , I have another symmetric matrix C (but may be singular ) with the same size as G, I need to solve the largest k algebraic generalized eigen value $\lambda$ for the problem $Cx = \lambda Gx$. Without validtation the property of G , I have try to use SymGEigsSolver (Cholesky mode and RegularInverse), SymGEigsShiftSolver, but all failed or too long to be waited. Here are the code fragments, I wanna if there are something wrong. Since the size of the matrix is too large, I really want to konw how to improve the calculation speed, thanks for answering!

string path = "../data/matrix1/CSC_C.txt";
Eigen::SparseMatrix<double> C = readfrom_csc(path);
path = "../data/matrix1/CSC_G.txt";
Eigen::SparseMatrix<double> G = readfrom_csc(path);

//Cholesky mode
SparseSymMatProd<double> op(C);
SparseCholesky<double>  Bop(G);
SymGEigsSolver<SparseSymMatProd<double>, SparseCholesky<double>, GEigsMode::Cholesky> geigs(op, Bop, 3, 6);
geigs.init();
int nconv = geigs.compute(SortRule::LargestAlge); 

//RegularInverse mode
SparseSymMatProd<double> op(C);
SparseRegularInverse<double> Bop(G);
SymGEigsSolver<SparseSymMatProd<double>, SparseRegularInverse<double>, GEigsMode::RegularInverse> geigs(op, Bop, 3, 6);
geigs.init();
int nconv = geigs.compute(SortRule::LargestAlge);


//SymGEigsShiftSolver
using OpType = SymShiftInvert<double, Eigen::Sparse, Eigen::Sparse>;
using BOpType = SparseSymMatProd<double>;
OpType op(C, G);
BOpType Bop(G);
SymGEigsShiftSolver<OpType, BOpType, GEigsMode::ShiftInvert> geigs(op, Bop, 3, 6, 1.0);
geigs.init();
int nconv = geigs.compute(SortRule::LargestMagn);