Unify numerical type template in PW calculation

[denghuilu]

Background

The usage of template parameters in ABACUS is relatively confusing. Here are a few examples:

• complex<FPTYPE> is used uniformly in PW code, that is, FPYTPE cannot take complex<double>;

• There is complex<T> in the DiagoBPCG written by @denghuilu, so T here cannot be complex<double> too;

• However: T in HamiltonLCAO<T> can be complex<double>;

• And In the new ESolver_LR module, FPTYPE can also be complex<double>...

Describe the solution you'd like

In the PW calculation, we employ a unified numerical type template represented by 'T' instead of 'FPTYPE' to denote the calculation's numerical type. This 'T' template is designed to accommodate various data types, including 'std::complex' and others.

Additional Context

No response

Task list for Issue attackers

• 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.

[maki49]

What's the problem from my point of view

The usage of std::complex<T> everywhere in PW classes restricts the value of T in base classes to float/double , then both std::complex<T> ops and T opsd appears in base class Hamilt, so my new added ESolver_LR(for #2460 )fails to unify 2 types of operators as long as I use a Hamilt* pointer.

What we will do

• @denghuilu will unify std::complex<T> into T in base and PW classes
• I will unify opsd and psid into ops and psi in base and LCAO classes