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Fix orthgonality loss in Davidson using Gram-Schmidt reorthogonalisation #191

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The Davidson solver occasionally lost subspace orthogonality, sometimes leading to linear dependence within the subspace, resulting in instant solver convergence towards zero eigenpairs.

This change fixes the subspace orhogonality loss using a conventional Gram-Schmidt reorthogonalisation in case this is needed, i.e., whenever the vector to be added to the subspace has non-negligible overlap with the previous subspace vectors. This comes at the expense of, at least, computing n_ss_vec addtional scalar products in each step, which in small systems may amount up to 5% of the total computational time spent for the Davidson solver. The overhead scales $N^4$, that is, for larger systems, the relative penalty can be expected to be negligible.

…ation in

  case orthogonality loss is detected.
AdrianLDempwolff and others added 2 commits February 26, 2025 16:02
  procedure. In cases where n_guesses > n_states, this may lead to a decrease
  in the number of matrix applies needed till convergence.
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3 participants