Inv: bug fix and implementation for UniTensor

[manuschneider]

-fixed a bug in Inv, where the clipping was applied to the value instead of the absolute part of it for real valued Tensors. -implemented Inv for UniTensor

[codecov[bot]]

Codecov Report

:x: Patch coverage is 55.31915% with 42 lines in your changes missing coverage. Please review. :white_check_mark: Project coverage is 32.16%. Comparing base (be1cfcf) to head (e839fa8). :warning: Report is 66 commits behind head on master.

Files with missing lines	Patch %	Lines
...ckend/linalg_internal_cpu/Inv_inplace_internal.cpp	25.00%	16 Missing and 2 partials :warning:
include/UniTensor.hpp	38.46%	0 Missing and 8 partials :warning:
src/linalg/Inv.cpp	61.53%	3 Missing and 2 partials :warning:
src/linalg/Inv_.cpp	50.00%	4 Missing and 1 partial :warning:
src/linalg/Pow.cpp	60.00%	1 Missing and 1 partial :warning:
src/linalg/Pow_.cpp	60.00%	1 Missing and 1 partial :warning:
src/linalg/Gesvd_truncate.cpp	90.00%	1 Missing :warning:
src/linalg/Svd_truncate.cpp	90.00%	1 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #680      +/-   ##
==========================================
+ Coverage   32.07%   32.16%   +0.08%     
==========================================
  Files         215      215              
  Lines       36242    36316      +74     
  Branches    14543    14583      +40     
==========================================
+ Hits        11626    11680      +54     
- Misses      22692    22700       +8     
- Partials     1924     1936      +12     

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[manuschneider]

I revised Inv and Pow. Both is available in cytnx::linalg and as methods of UniTensor. I updated the comments and wrote tests. These two functions can be taken as blueprints to implement the other elementwise linalg functions for UniTensor, as suggested in https://github.com/Cytnx-dev/Cytnx/issues/681 Breaking changes: The condition $\sqrt{Re^2 + Im^2} \le \mathrm{clip}$ is used for the pseudo-inverse. This way, real and complex numbers are treated similarly. The implementation is fast.

The changes can be reviewed and merged now.

[manuschneider]

The TDVP check fails. It seems that the Lanczos does not converge. However, the algorithm should not be affected by any of the changes in this branch. Could it be that TDVP is sensitive to the random seed? On my machine the TDVP check works fine (Linux). Any suggestions?

[hunghaoti]

The TDVP check fails. It seems that the Lanczos does not converge. However, the algorithm should not be affected by any of the changes in this branch. Could it be that TDVP is sensitive to the random seed? On my machine the TDVP check works fine (Linux). Any suggestions?

I will check.

[manuschneider]

#690 is still open, I would like to fix it before merging, since some breaking changes are introduced here.