Iterative eigensolvers for LCAO

[maki49]

Background

Iterative eigensolvers like CG, Davidson, etc. should be commonly used independent of basis type, but now they're not supported for LCAO.

Describe the solution you'd like

• support real-value (double) data type
• add hpsi and spsi
• deal with (or do not use) bands' parallelization

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

• HSolver (datatype double support)
• OperatorLCAO (hpsi and spsi interface)
• ESolver_KS_LCAO (call iterative HSolver)

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.