/// return the extremal eigenvalues of Ax=cBx
std::pair<double, double>
generalized_extreme_eigenvalues(const Eigen::SparseMatrix<double> &Ain,
const Eigen::SparseMatrix<double> &Bin) {
assert(Ain.rows() == Ain.cols());
assert(Ain.rows() == Ain.cols());
assert(Ain.rows() == Bin.rows());
assert(Ain.isCompressed());
assert(Bin.isCompressed());
const int N = static_cast<int>(Ain.rows());
/* mkl_sparse_d_gv input parameters */
char which =
'S'; /* Which eigenvalues to calculate. ('L' - largest (algebraic)
eigenvalues, 'S' - smallest (algebraic) eigenvalues) */
int pm[128]; /* This array is used to pass various parameters to Extended
Eigensolver Extensions routines. */
int k0 = 1; /* Desired number of max/min eigenvalues */
/* mkl_sparse_d_gv output parameters */
int k; /* Number of eigenvalues found (might be less than k0). */
double E_small[3]; /* Eigenvalues */
double E_large[3]; /* Eigenvalues */
double X[3]; /* Eigenvectors */
double res[3]; /* Residual */
/* Local variables */
int compute_vectors = 0; /* Flag to compute eigenvectors */
int tol = 7; /* Tolerance */
/* Sparse BLAS IE variables */
sparse_status_t status;
ConvertToMklResult A = to_mkl(Ain, status); // TODO: check A.status;
ConvertToMklResult B = to_mkl(Bin, status); // TODO: check B.status;
/* Step 2. Call mkl_sparse_ee_init to define default input values */
mkl_sparse_ee_init(pm);
pm[1] = tol; /* Set tolerance */
pm[6] = compute_vectors;
/* Step 3. Solve the standard Ax = ex eigenvalue problem. */
which = 'S';
const int infoS = mkl_sparse_d_gv(&which, pm, A.matrix, A.descr, B.matrix,
B.descr, k0, &k, E_small, X, res);
assert(infoS == 0);
which = 'L';
const int infoL = mkl_sparse_d_gv(&which, pm, A.matrix, A.descr, B.matrix,
B.descr, k0, &k, E_large, X, res);
assert(infoL == 0);
mkl_sparse_destroy(A.matrix);
mkl_sparse_destroy(B.matrix);
return {E_small[0], E_large[0]}; // todo: return the right thing
}
ColCompressedMatrix convert_from_Eigen(const Eigen::SparseMatrix<double> &m)
{
assert(m.rows() == m.cols());
assert(m.isCompressed());
return ColCompressedMatrix(m.rows, m.nonZeros(),
m.valuePtr(), m.outerIndexPtr(), m.innerIndexPtr());
}
