implemented Trace for GPU

[manuschneider]

Currently, Tensor.Trace corresponds to creating a UniTensor and contracting it with a (diagonal) identity UniTensor;
removed Nomp argument in internal Trace functions;

This fixes #735

[codecov]

Codecov Report

❌ Patch coverage is 30.00000% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 35.53%. Comparing base (7aa7862) to head (f02a7a8).
⚠️ Report is 12 commits behind head on master.

Files with missing lines	Patch %	Lines
src/linalg/Trace.cpp	22.22%	6 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #749   +/-   ##
=======================================
  Coverage   35.53%   35.53%           
=======================================
  Files         214      214           
  Lines       33016    33018    +2     
  Branches    13133    13133           
=======================================
+ Hits        11731    11732    +1     
- Misses      19361    19362    +1     
  Partials     1924     1924           

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[IvanaGyro]

Is this less efficient than the original implementation?

[ianmccul]

@codex review

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[chatgpt-codex-connector]

Handle rectangular matrix trace on GPU

Tensor::Trace computes Ndiag = min(dim[axisA], dim[axisB]), so rectangular traces are expected to work, but this GPU path now contracts eye(Ndiag) against the full 2D tensor. For inputs like shape (m,n) with m != n, one contracted label has size Ndiag while the tensor bond still has size max(m,n), so Contract sees mismatched bond dimensions and raises instead of returning the diagonal sum (CPU still handles this case).

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[manuschneider]

I do not think that tracing over indices with different dimensions is an essential feature that we need to support at the moment.
For now, I added error messages when the user tries this, but the backend does not support it.

In the long term, it would be good to implement more efficient ways to calculate the trace on both CPU and GPU without multiplying by the identity. Then, we can also decide whether to allow traces over indices of different lengths. This is not a high priority currently, though.

[ianmccul]

I think there is no reason to ever allow trace over a non-square tensor. By definition that means that the left right indices represent different spaces, so the trace is meaningless. In the special case where one space is a diagonal projection $P$ of the other space, it might make sense to calculate something like $\text{Tr} PM$ and optimize that if necessary.

[manuschneider]

An error message is now thrown in all cases where the index dimensions of the traced indices do not match.