[eigen] Sparse Cholesky

[Brad Bell <bradbell@xxxxxxxxxx>]

I do am trying to get a copy of the lower triangular matrix 
corresponding to a sparse Cholesky factorization. It seems to me that, 
in the case of a 1 by 1 matrix, this should be a 1 by 1 matrix with 
entry equal to the square root of the original matrix. But the following 
program is printing 1 instead of 2 for its result. What am I doing wrong ?

# include <iostream>
# include <Eigen/Sparse>
int main(void)
{   typedef Eigen::SparseMatrix<double, Eigen::ColMajor> 
sparse_matrix;
    typedef Eigen::SimplicialLDLT<sparse_matrix, Eigen::Lower> 
sparse_cholesky;
    typedef sparse_matrix::InnerIterator                       column_itr;
    //
    int n = 1;
    sparse_matrix H(n, n);
    H.insert(0, 0) = 4.0;
    //
    sparse_cholesky C;
    C.compute( H );
    sparse_matrix L = C.matrixL();
    //
    for(int j = 0; j < L.outerSize(); j++)
    {   for(column_itr itr(L, j); itr; ++itr)
        {   std::cout << "L(" << itr.row() << "," << itr.col() << ") = ";
            std::cout << itr.value() << "\n";
        }
    }
    return 0;
}