Translationally-invariant computation for position-related matrix elements

[sjhong6230]

The main differences of this pull request are

• Implementation of translationally-invariant formulas for position-related matrix elements

For the implementation, one should change the order of Wigner-Seitz minimal distance method and the Fourier transforms. This was done with the help of the following PR: #339.

Another related problem exists. Since the summation over the b vector is performed at the last stage, the number of Fourier transforms needed is multiplied by the number of b vectors, resulting in a large computational time. I resolved this issue by parallelizing the Fourier transform subroutines.

There is also a b vector sorting issue which was present in #498. To resolve this, the kmesh_sort subroutine is also called in postw90, and the b vector order for some checkpoint files was changed.

Corresponding documentation and tutorials were added.

[sjhong6230]

I don't understand why the tests fails for this remote repository. It passed in my local repository. Does anyone know the reason of this discrepancy?

[JeromeCCP9]

Hi Seung-Ju! I will check this myself and report back.

[jryates]

testpostw90_pt_ksliceshc

`At line 297 of file ../postw90/postw90.F90
Fortran runtime error: Index '1' of dimension 2 of array 'kpt_latt' outside of expected range (139771434723376:140730228691344)

Error termination. Backtrace:
#0 0x7f1f12eecd11 in ???
#1 0x7f1f12eed859 in ???
#2 0x7f1f12eeded6 in ???
#3 0x55f24d34cbf1 in postw90
at ../postw90/postw90.F90:297
#4 0x55f24d34de67 in main
at ../postw90/postw90.F90:23`

[JeromeCCP9]

Hi again!

The cause of the failure is an error whose message is this:

transl_inv_full=T not implemented for shc_method=qiao

Do you recognise this condition? Probably you know whether this should be changed?

This error was not visible to you because I had failed to update postw90.x after a change to the error handler.

I've made PR into develop for the error handler change.

I've pushed the merge of these changes into your work into this repository:

https://github.com/JeromeCCP9/wannier90/tree/wigner-seitz

and I think this will allow you update your PR so that it will merge, but I have not solved the underlying problem (the test above) that causes the tests to fail.

Yours, Jerome

[sjhong6230]

The cause of the failure is an error whose message is this:
transl_inv_full=T not implemented for shc_method=qiao
Do you recognise this condition? Probably you know whether this should be changed?

This was weird to me since the failed tests does not use full translation invariance. However, I got the clue from the above comment.

The fix is in line https://github.com/sjhong6230/wannier90_transl_inv/blob/213a9d1af5808e53728d6209a3cd29cf71ab5136/src/postw90/postw90_readwrite.F90#L1008. I added the initialization of local transl_inv_full variable in the subroutine.

Since this variable was not initialized, it showed different behaviors for my local tests and the remote tests. (My local repository was compiled with intel fortran, but the CI was compiled with gfortran.)

Now, the serial tests are good, but the parallel tests are suffering from memory issues.

Edited: The memory issue was resolved by allocating **_q_b arrays also for the non-root processes.

[JeromeCCP9]

Dear Seung-Ju, I'm so sorry that you had to fix my bugs! I've been using -finit to set variables to nan, which normally shows up these problems, but I missed this uninitialised one.

Thank you so much for your work resolving this issue!

[JeromeCCP9]

Clearly implemented and minimal set of changes to provide the translationally-invariant functionality. The changes fit the new code structure and the work includes important bug fixes (initialised variable and parallel allocation issues).

Examples and documentation are also provided.