Feature: a promising angle mixing method for non-colinear calculations

[WHUweiqingzhou]

Linked Issue

Fix #3336. As is mentioned in Issue #3336, If one is not interested in the energies of a given magnetic configuration but wants to determine the ground state by relaxing the magnetic moments’ directions, one cannot rely on the standard Broyden mixing algorithm.
To enhance ABACUS's ability to find correct magnetic configuration for non-colinear calculations, I implement a promising mixing method proposed by J. Phys. Soc. Jpn. 82 (2013) 114706.
b.t.w, in this PR, I only realize a special case with angle mixing parameter is 1 NOW.

What's changed?

1. add a new parameter mixing_angle to control if this method is used.
2. new angle mixing method is actually implemented in mix_rho_real() and mix_rho_recip_new().
3. add resize_tmp in Kerker and inner_product to corporate with new angle mixing method.
4. delete Charge_Mixing::Kerker_screen_real_test().
5. add corresponding docs of angle mixing method.

Notice that:

1. After test, new angle mixing can give exactly same result with old broyden mixing when old method can find the correct magnectic configuration.
2. Old broyden mixing sometimes fails to find the correct magnectic configuration. At that time, you can try new method with mixing_angle 1
3. In new angle mixing, you should set mixing_beta_mag >> mixing_beta, and mixing_beta_mag is around 1.

[dyzheng]

Thanks for your contribution, mixing method for noncollinear spin will be improved with this PR.

[dyzheng]

Please update the description in https://abacus.deepmodeling.com/en/latest/advanced/scf/converge.html#charge-mixing for new mixing parameters.

[dyzheng]

Users often set "lspinorb=1" or "noncolin=1" rather than "nspin=4".

[dyzheng]

Please add unit-test for this mixing_angle parameter.

[dyzheng]

I hope you can replace the use of "GlobalV" with local variables or class members in Charge_Mixing code.