CODEWITHSUNDEEP
c++armadillo
Bociek
Bociek

Reputation: 1265

Eigenvalue decomposition fails with armadillo eigs_sym() for too large matrices

I have recently installed armadillo and tried eigenvalue problem for sparse matrices. Unfortunately, decomposition fails is the parameter 'N' (code below) is too large e.q. 1000. I wonder what is going on here. Matrix is not very complicated - it has diagonal structure.

UPDATE

Mathematica also have problems with this matrix. It tells me that Arnoldi algorithm does not converge. Maybe I need to manually specify some parameters in arnoldi arpack routines to ensure convergence?

Here is my code:

#include <armadillo>

int main ()
{
    double N = 1000.0;

    // create matrix
    int kmin = 0;
    int kmax = static_cast<int>( std::floor( N/2.0 ) );
    int dim = (kmax - kmin) + 1;

    // locations and values in sparse matrices
    arma::umat hc_locations (2, 3*dim-2);
    arma::vec hc_values (3*dim-2);

    // diagonal part
    for (int k=0; k<dim; k++)
    {
        hc_locations (0,k) = k;
        hc_locations (1,k) = k;
        hc_values (k) = 2.0/N*static_cast<double>(kmin + k)*( 2.0*( N-2.0*static_cast<double>(k + kmin) ) - 1.0 );

    }
    // upper and lower diagonal
    for (int k=0; k<dim-1; k++)
    {
        hc_locations (0,k+dim) = k;
        hc_locations (1,k+dim) = k+1;
        hc_values (k+dim) = 2.0/N*std::sqrt( ( static_cast<double>(k+1+kmin) ) *
                                             ( static_cast<double>(k+1+kmin) ) *
                                             ( N - static_cast<double>(2*(k+1+kmin)) + 1.0 ) * 
                                             ( N - static_cast<double>(2*(k+1+kmin)) + 2.0 ) );

        hc_locations (0, k+2*dim-1) = k+1;
        hc_locations (1, k+2*dim-1) = k;
        hc_values (k+2*dim-1) = 2.0/N*std::sqrt ( ( static_cast<double>(k+1+kmin) ) * 
                                                   ( static_cast<double>(k+1+kmin) ) *
                                                   ( N - static_cast<double>(2*(k+kmin)) ) *
                                                   ( N - static_cast<double>(2*(k+kmin)) - 1.0 ) );
    }

    arma::sp_mat Ham(hc_locations, hc_values);

    // eigenvalue problem
    arma::vec eigval;
    arma::mat eigvec;

    arma::eigs_sym( eigval, eigvec, Ham, 3, "sa");

}

Upvotes: 2

Views: 1289

Answers (1)

anuragm
anuragm

Reputation: 11

For small matrices of size 2000 or so, it is often time easier to find all the eigenvalues and eigenvectors, as those methods are less susceptible to near singular matrices.

I replaced your code 

arma::eigs_sym( eigval, eigvec, Ham, 3, "sa");

with

arma::mat fullMat = arma::mat(Ham);
arma::eig_sym( eigval, eigvec, fullMat);

and the compiled program takes less than a second to solve on my late 2015 Macbook Pro.

Upvotes: 1

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