Guidelines

Here we give guidelines on how to setup the eigensolver in Pescan. As indicated in pescan.input, the eigensolver is set by imthd (in line 5 of pescan.input) and the following algorithms are currently available:
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imthd algorithm parameters in line #6 of pescan.input
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1 (H-Eref)^2 CG niter, nline, iprec, idump
2 (H-Eref) CG; Eref=0 niter, nline, iprec, idump
3 (H-Eref)^2 LOBPCG niter, iprec, ideflt, iblock
4 (H-Eref)^2 PARPACK niter, ncv
5 (H-Eref) PARPACK niter, ncv
6 (H-Eref)^2 PRIMME method, ncv_min, ncv_max, nmatvec
7 (H-Eref) PRIMME method, ncv_min, ncv_max, nmatvec
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** The system example-14Cd.13Se provided in the Pescan download tar file contains input files that exercise all the possible values of imthd, together with the corresponding output files. The user can modify the pescan.input starting from the input files in that directory. **

For the systems we have studied:

Recommendations:
Based on the systems we have studied and the number os eigenstates we have computed, we recommend the default PRIMME MIN_MATVECS, with the restart size close to the number of required eigestates, and a basis size equal to 2 or 3 times the restart size. Also, for large systems, it is important to set tol to a smaller value that would be normally set for PCG or LOBPCG.

Important considerations about the tolerance (in line 4 of pescan.input):

A pair (E,w) is declared an eigenpair of H when r(E,w)=|| Hw-E*w || <= tol. However, this criterion raises a potential issue when using the folded spectrum approach. While in practice one cares about the (final) residual r(E,w) being small with respect to H, in some software packages the convergence criterion may be actually based on the operator (H-E_ref*I)2. This is the case of PRIMME, which means that currently PRIMME may have to do some more work for some systems, i.e. it may require a tighter tol. However, it is important to note that even with a smaller tol PRIMME showed to outperform the other eigensolvers. If there is a good guess for the norm of H then it can be used for a more realistic setting of tol.