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My research is in electron spin resonance, where we deal with the time-independent stochastic Liouville equation and end up with the task of finding the eigenvectors and eigenvalues of complex symmetric matrices (size ~ 10000x10000, ~30% elements non-zero).

We have been using Lanczos algorithm with conjugate gradients/QMR, but lose orthogonality of the Lanczos vectors (and hence the eigenvectors).

Note: Here orthogonality between complex vectors $a$, $b$ means $a^{T}b=0$, not $a^\dagger b=0$.

Therefore, the next step seems to be increasing the precision from double to quadruple, along with implementing Lanczos algorithm with partial reorthogonalization for sparse, complex symmetric matrices.

I want a link to a FORTRAN package that implements Lanczos algorithm with partial reorthogonalization for large, sparse, complex symmetric matrices. My Google search seemed futile.

user3812405
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    Did you attempt going to the Netlib? –  Jul 12 '18 at 23:52
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    @Geronimo I'm not sure if you mean the same thing but it seems like the implementation in QMRPACK does not support reorthogonalization. – Algebraic Pavel Jul 13 '18 at 12:18
  • Geronimo, Pavel is right. Files at http://www.netlib.org/linalg/qmr/ don't have reorthogonalization. Not only that, the routines like cslal.f don't give eigenvectors. They just give out eigenvalues. – user3812405 Jul 18 '18 at 16:48

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