Improve sparse diagonalization routine #100
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… for Orbitals.compute
…heck their validity
timcallow
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DanielKotik
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Nov 22, 2021
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This PR is a fix for issue #98.
scipy's sparse eigenvalue solver works better (both faster and more reliable) when fewer eigenvalues are requested, so this PR gives a better estimate for the lowest eigenvalue (for a given spin and quantum numberl), when previously it was just 0 (creating problems for very low lying core states).The routines to find the eigenvalues now include a "guess" option which performs a full diagonalization of the Hamiltonian (finding all eigenvalues), on a much smaller number of grid points to obtain an initial estimate for the eigenvalues. The lowest eigenvalues are then fed into the sparse matrix diagonalization routine, making we can reduce significantly the number of eigenvalues requested (since before we were finding lots of eigenvalues with energies >0 which were mostly discarded). The full diagonalization is only performed for the first 3 SCF iterations, since after that the estimates should be accurate enough for the rest of the cycle.
Attached are some output files to demonstrate examples of when the old code failed compared to now when it works, and an example of a speed increase.
Al_new_no_error.txt
Al_new_faster.txt
Al_old_error.txt
Al_old_slow.txt