[SOLVED] LAPACKE_zheevx() failed to converge -- how to increase ABSTOL with 2*DLAMCH('S') in C++?

LAPACKE_zheevx() failed to converge -- how to increase ABSTOL with 2*DLAMCH('S') in C++?

This is a question about setting proper tolerance ("abstol") for convergence of eigenvalue calculation with LAPACKE_zheevx() function in C++.

When LAPACKE_zheev() fails to converge when calculating eigenvalues/eigenvectors with the default value of "abstol" (i.e. abstol=-1), the LAPACK manual says to set abstol=2*DLAMCH('S'). However, DLAMCH is Fortran function and I use C++ which does not recognize it as a valid C++ function. Could anyone please help me how to properly set "abstol=2*DLAMCH('S')" when using LAPACK with C++ (i.e. when using LAPACKE)?

Thanks very much in advance!!

Background: LAPACKE is C++ interface for LAPACK (Fortran library for numerical algebra). LAPACKE_zheevx() is LAPACKE's C++ interface for LAPACK's ZHEEVX() function.

Keywords: LAPACK, LAPACKE, C++, ABSTOL, DLAMCH, CONVERGENCE, EIGENVALUES, EIGENVECTORS

Solution

I don’t know anything about these libraries, but a bit of Googling reveals there is a corresponding LAPACKE_dlamch() function:

double LAPACKE_dlamch(char cmach)

So you should be able to just pass LAPACKE_dlamch('S') as the abstol (12th) parameter of LAPACKE_zheevx():

lapack_int LAPACKE_zheevx (
    int matrix_layout,
    char jobz,
    char range,
    char uplo,
    lapack_int n,
    lapack_complex_double *a,
    lapack_int lda,
    double vl,
    double vu,
    lapack_int il,
    lapack_int iu,
    double abstol,
//  ^^^^^^^^^^^^^
    lapack_int *m,
    double *w,
    lapack_complex_double *z,
    lapack_int ldz,
    lapack_int *ifail
)