Bath compression

[kbidzhiev]

In this PR, I introduce a new method for packing Hermitian objects of the shape (χ, m , χ), specifically energy baths.

The main idea is to avoid storing the full Hermitian matrix. Instead, we store only the lower triangular part, including the main diagonal. The upper triangular part can then be reconstructed from the lower triangular entries using complex conjugation. Lower triangular columns are stacked to m vectors of length $$\chi(\chi+1)/2$$

This reduces the memory footprint of an $$\chi \times \chi$$ matrix from $$\chi^2$$ to $$\chi(\chi+1)/2$$.

The PR closes #95
(I've tried decompositions like SVD, eigh, cholesky. No compression, baths are ~full rank tensors)

the following part contains results for 5x5 quench_performance_gpu from our benchmark suit.
Memory measurement is done with get_max_rss in emu_base/utils.py, which is using torch.cuda.max_memory_allocated(...). In the following I'm going to tests the new code with .memory_allocated(...) vs .max_memory_allocated(...)

Results

torch.cuda.memory_allocated(...):
Returns the current GPU memory occupied by tensors in bytes for a given device.

Before

After

torch.cuda.max_memory_allocated(...): <- MAX allocation:
Return the maximum GPU memory occupied by tensors in bytes for a given device. By default, this returns the peak allocated memory since the beginning of this program.

Before

After

NB on performance.

every Hermitean bath tensor is validated on hermiticity. That can be weakened

Outcome

The real GPU memory occupation is reduced asymptotically by factor 2, though the peak memory occupation is still high and is not addressed here. The peak memory is hidden in operator application in Krylov routines

[kbidzhiev]

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