Armadillo eigs_sym(A,k) for complex sparse matrix A

Question

To find the 10 smallest eigenvalue of a sparse matrix 'A', the minimal code below works well:

g++ -std=c++17  -o test_sparse.o -c test_sparse.cpp
g++ -std=c++17  -o myapp test_sparse.o -larmadillo -larpack

#include <armadillo>
#include <iostream>
int main(){
    arma::SpMat<double> A = arma::sprandu(100,100,0.1) ;
    A = A.t()*A ;
    arma::dvec e = arma::eigs_sym(A,10,"sm") ;
    std::cout << e ; 
    return 0 ;
}

But when I change A to a complex sparse matrix, like:

#include <armadillo>
#include <iostream>
#include <complex>
int main(){
    arma::SpMat<arma::cx_double> A = arma::sprandu<arma::SpMat<arma::cx_double>>(100,100,0.1) ;
    A = A.t()*A ;
    arma::dvec e = arma::eigs_sym(A,1,"sm") ;
    std::cout << e ; 
    return 0 ;
}

with the same compilation flags, I get the following no matching function error:

g++ -std=c++17  -o test_sparse.o -c test_sparse.cpp
test_sparse.cpp:8:43: error: no matching function for call to ‘eigs_sym(arma::SpMat<std::complex<double> >&, int, const char [3])’
    8 |     arma::dvec e = arma::eigs_sym(A,1,"sm") ;                    ^
make: *** [Makefile:47: test_sparse.o] Error 1

I know from http://arma.sourceforge.net/docs.html#config_hpp that

ARMA_USE_ARPACK Enable use of ARPACK, or a high-speed replacement for ARPACK. Armadillo requires ARPACK for the eigen decomposition of complex sparse matrices, ie. eigs_gen(), eigs_sym() and svds()

so I change the config.hpp file and here is the corresponding line in my config.hpp file:

#if !defined(ARMA_USE_NEWARP)
#define ARMA_USE_NEWARP
#endif
#if !defined(ARMA_USE_ARPACK)
#define ARMA_USE_ARPACK
#endif
#if !defined(ARMA_USE_SUPERLU)
#define ARMA_USE_SUPERLU
#endif

more info: I can run arpack from gfortran with no problem.

Any idea how to do the trick? Thank you for your help in advance.

Answer 1

It is an inherent limitation of the library. According to the documentation (emphasis mine):

eigs_sym limited number of eigenvalues & eigenvectors of sparse symmetric real matrix

eigs_gen limited number of eigenvalues & eigenvectors of sparse general square matrix

You should rather use eigs_gen which allows for complex matrices. Or you should convert the matrix to a dense one and use eig_sym.