Function Stress_Func<FPTYPE, Device>::stress_nl need refactoring to balence memory and performance

[dyzheng]

Details

https://dptechnology.feishu.cn/wiki/XuLvwPqiCickS8kPZ8Bcxik7nyd?from=from_copylink

The key target of this refactoring is separate the functions get_vnl, get_vnl1 and get_vnl2, which have formulas as

code would be:

for(int ik=0;ik<nks;ik++)//loop k points
{
    for(int it=0;it<ntype;it++)//element types
    {
        // prepare the variables to calculate vkb，vkb1，vkb2
        // prepare vq and vq', size  nq * npwx 
        std::vector<double> vq = cal_vq(it);
        std::vector<double> vq_deri = cal_vq_deri(it);
        int lmax = ppcell.lmaxkb;
        //prepare ylm，size (lmax+1)^2 * npwx
        std::vector<double> ylm = cal_ylm(lmax);
        //prepare ylm'，size  3 * (lmax+1)^2 * npwx，for x, y, z axis
        std::vector<double> ylm_deri = cal_ylm_deri(lmax);
        // prepare（-i）^l, size  nh
        std::vector<complex<double>> pref = cal_pref(it);
        for(int ia=0;ia<na;ia++)
        {
            // pointer to access SK, no memory cost here
            complex<double>* sk = get_sk(it, ia);
            // 1. calculate becp
            // 1.a calculate vkb
            cal_vkb(it, ia, vq, ylm, pref, sk, ppcell_vkb);
            // 2.b calculate becp = vkb * psi
            gemm...
            //calculate stress（00，01，02，11，12，22）
            for(int ipol=0;ipol<3;ipol++)
            {
                for(int jpol=ipol;jpol<3;jpol++)
                {
                    // 2. calculate dbecp：
                    // 2.a. calculate dbecp_noevc, reuse the memory of ppcell.vkb
                    cal_dbecp_noevc(it, ia, 
                                    vq, vq_deri, 
                                    ylm, ylm_deri, 
                                    pref, sk, 
                                    ppcell.vkb);
                    // 2.b calculate dbecp = dbecp_noevc * psi
                    gemm...
                    // 3. calculate stress(ipol, jpol) += \sum becp * dbecp
                    cal_stress_nl_op(becp, dbecp...);
                }//jpol
            }//ipol
        }//ia
    }//it
}//ik

Task list for Issue attackers (only for developers)

• Reproduce the performance issue on a similar system or environment.
• Identify the specific section of the code causing the performance issue.
• Investigate the issue and determine the root cause.
• Research best practices and potential solutions for the identified performance issue.
• Implement the chosen solution to address the performance issue.
• Test the implemented solution to ensure it improves performance without introducing new issues.
• Optimize the solution if necessary, considering trade-offs between performance and other factors (e.g., code complexity, readability, maintainability).
• Review and incorporate any relevant feedback from users or developers.
• Merge the improved solution into the main codebase and notify the issue reporter.

[dyzheng]

This issue aim to solve #3714