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Need subspace diagonalization without scc #5615

@Cstandardlib

Description

@Cstandardlib

Background

#5463
When using DiagH_subspace in cg method, we construct an overlap matrix scc by default.
This can be a huge burden on memory.

Initial psi set is not orthogonal
Image

However, in cg we do orthogonalization, so that psi set becomes diagonal after a cg loop, and we will call DiagH_subspace to actually solve
a standard eigenproblem since scc is identity:
Image

Describe the solution you'd like

So we may need a wrapper of standard eigensolver.
Will it be faster?

Task list only for developers

  • Notice possible changes of behavior
  • Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

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Notice any changes of core modules (Reminder only for developers)

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Task list for Issue attackers (only for developers)

  • Review and understand the proposed feature and its importance.
  • Research on the existing solutions and relevant research articles/resources.
  • Discuss with the team to evaluate the feasibility of implementing the feature.
  • Create a design document outlining the proposed solution and implementation details.
  • Get feedback from the team on the design document.
  • Develop the feature following the agreed design.
  • Write unit tests and integration tests for the feature.
  • Update the documentation to include the new feature.
  • Perform code review and address any issues.
  • Merge the feature into the main branch.
  • Monitor for any issues or bugs reported by users after the feature is released.
  • Address any issues or bugs reported by users and continuously improve the feature.

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