Fix error in _soft_dtw, add test and add option compute_with_backend in soft_dtw and soft_dtw_alignment.

In the file tslearn/metrics/soft_dtw_fast.py, the functions _soft_dtw, _soft_dtw_batch, _soft_dtw_grad and _soft_dtw_grad_batch do not return a value, they modify directly the input value as a mutable object. An error was introduced in the PR #479 casting the input values to the selected backend with:

    D = be.array(D, dtype=be.float64)
    R = be.array(R, dtype=be.float64)
    gamma = be.array(gamma, dtype=be.float64)

Indeed, be.array cast the input values to the desired backend, but it creates a copy input values. Therefore the input values will not be modified as mutable objects. These lines are removed in this PR.

We add a test to make sure that this error will not be reproduced.

We also add the option compute_with_backend in the functions soft_dtw, soft_dtw_alignment, cdist_soft_dtw and cdist_soft_dtw_normalized. Before, the input data was cast to NumPy arrays to use Numba with the decorator @njit and the results were converted to the backend of the input data. We can now use PyTorch automatic differentiation with these functions.

Codecov Report

All modified lines are covered by tests :white_check_mark:

Comparison is base (e7a177c) 92.70% compared to head (74ef6c4) 93.32%.

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Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #481 +/- ## ========================================== + Coverage 92.70% 93.32% +0.61% ========================================== Files 67 67 Lines 5732 5725 -7 ========================================== + Hits 5314 5343 +29 + Misses 418 382 -36 ``` | [Files](https://app.codecov.io/gh/tslearn-team/tslearn/pull/481?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=tslearn-team) | Coverage Δ | | |---|---|---| | [tslearn/metrics/soft\_dtw\_fast.py](https://app.codecov.io/gh/tslearn-team/tslearn/pull/481?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=tslearn-team#diff-dHNsZWFybi9tZXRyaWNzL3NvZnRfZHR3X2Zhc3QucHk=) | `75.42% <ø> (+24.26%)` | :arrow_up: | | [tslearn/metrics/softdtw\_variants.py](https://app.codecov.io/gh/tslearn-team/tslearn/pull/481?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=tslearn-team#diff-dHNsZWFybi9tZXRyaWNzL3NvZnRkdHdfdmFyaWFudHMucHk=) | `94.58% <100.00%> (+0.49%)` | :arrow_up: | | [tslearn/tests/test\_metrics.py](https://app.codecov.io/gh/tslearn-team/tslearn/pull/481?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=tslearn-team#diff-dHNsZWFybi90ZXN0cy90ZXN0X21ldHJpY3MucHk=) | `99.22% <100.00%> (+<0.01%)` | :arrow_up: | ... and [1 file with indirect coverage changes](https://app.codecov.io/gh/tslearn-team/tslearn/pull/481/indirect-changes?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=tslearn-team)

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tslearn-team / tslearn

Fix error in _soft_dtw, add test and add option compute_with_backend in soft_dtw and soft_dtw_alignment. #481

Codecov Report