Feature: Rename DAV_subspace as DAV and update the corresponding default parameters

[WHUweiqingzhou]

Background

New DAV_subspace method is much faster than old DAV method, we should use DAV_subspace as the default Davidson method.

Describe the solution you'd like

Please change it.

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)

No response

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

No response

Notice Possible Changes of Core Modules (Reminder only for developers)

No response

Additional Context

No response

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.

[Cstandardlib]

Will the old Davidson with orthogonalization be deprecated, or will it be renamed to some other names?

[WHUweiqingzhou]

Will the old Davidson with orthogonalization be deprecated, or will it be renamed to some other names?

I prefer to keep the old Davidson method, and rename it as dav_orth or something like that.

[kirk0830]

Will the old Davidson with orthogonalization be deprecated, or will it be renamed to some other names?

I prefer to keep the old Davidson method, and rename it as dav_orth or something like that.

I vote the dav_legacy