Hi
Short question: how do the execution time of FEAST scale with the subspace size M0?
I am trying to add support for the eigensolver FEAST to a large atomic structure program package, GRASP2K, and it seems to work just fine for small and medium sized problems (up to matrix sizes about 3-4000, 100 000 non-zero elements and M0~200-300). For larger problems (N~200 000, NZ~50-60 000 000, M0~1000) the solution, or rather the execution time, depends a lot on the initial guess for emin and emax. I have an older approxiamte solver that can calculate approximate values for emin and emax but with large error bars. If I use these values and use FEAST to estimate the number of eigenvalues (fmp(14=2)) I always get a very large number recommended for M0 (~20 000). I know from the physics involved that it always is the Neig (a number comming from the way the Hamiltonian is constructed, ~2-300) lowest eigenvalues that I am interseted in.
I can either set emin and emax so that I am sure to bracket the eigenvalues I am interested in and accept a large value for M0 and only use the first few eigenvaules returned, or I can iterate and test lower and lower values for emax until M0 returned by fmp(14)=2 comes close to Neig*1.5. It is not cheap to call FEAST many times to find a good energy range as the solution is iterated over many times improving the basis set in an outer loop. I could just test the two cases but the resources I have at hand during development are a bit underpowered and each test run takes about a week so any hint would be welcome.
/Per Andersson