LAPACK/ScaLAPACK Development

Hi,

I am using dgeevx routine in LAPACK to solve a system of ordinary differential equations (chemical kinetics reaction model). This routine returns the eigenvectors that are normalized to have Euclidean norm equal to 1 and largest component real. How do I fix the sign of each eigenvector so that I can obtain the time course of each chemical species? I know that the concentrations of all species should be positive at all times. Any suggestions or pointers are welcome.

Thanks,

mmgk

Can you please explain what you mean by the "sign of each eigenvector". Thanks,

Sven Hammarling.

"Sign of eigenvector" means +ve or -ve.

The concentration of each species in a chemical reaction scheme will be given by C(t) = Sigma_i a_i exp(-k_i t), where k_i are the eigenvalues and a_i are the eigenvectors obtained by solving the system of ordinary differential equations. Depending on the sign of eigenvectors whether it is +ve or -ve, C(t) can become +ve or -ve. I want to make sure that C(t) is +ve at all t. How do I do that?

mmgk

In general there is no guarantee that an eigenvector has elements of the same sign since, after all, it represents a direction. But I presume that there is something special about your matrices that means that the eigenvectors are real and do have elements of the same sign? (Forgive me, I am not familiar with your application.)

Since the eigenvectors represent a direction, you can scale them by any non-zero value, and in particular by -1.

Sven.