Need subspace diagonalization with parallel

[pxlxingliang]

Background

Now, the subspace diagonalization of dav is by lapack with one core, while for large system, the dimension of this subspace may be hundreds, and can be effectively accelerated by parallel.

QE has the same function and can be used by setting value of nd in command: https://www.quantum-espresso.org/Doc/user_guide/node20.html

Describe the solution you'd like

I will implement a function to divide the H and S matrices into 2D blocks, and then call elpa or scalapack to do parallel diagonalization.

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.