[Fix] Gradient scaling in Partial GW solver

[yikun-baio]

Types of changes

I modify the code ot.partial.partial_gromov_wasserstein

Motivation and context / Related issue

There seems to be an inconsistency between ot.partial.partial_gromov_wasserstein and the line search section in the paper [29]. I fixed this section. In addition, I have made minor change to the initial guess in the partial-GW solver since the original initial guess is np.out(p,q), which might not be suitable for unbalanced case, i.e. |p|\neq |q|.

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How has this been tested (if it applies)

PR checklist

• I have read the CONTRIBUTING document.
• The documentation is up-to-date with the changes I made (check build artifacts).
• All tests passed, and additional code has been covered with new tests.
• I have added the PR and Issue fix to the RELEASES.md file.

[rflamary]

Hello @yikun-baio and thanks for the PR.

You should not propose anew file but instead implement directly your fix in th existing files. This is important because we have many tests that checks that nothing else breaks and we can compare easily your modification with the old implementation. We will do a code review with @lchapel when this is done.

[yikun-baio]

Hello @rflamary,

Thank you for your feedback. I apologize for not implementing the fix directly in the existing file and instead proposing a new file. This is my first time to contribute to a public project via a pull request.

I just realized that my email settings were inadvertently blocking emails from GitHub, which caused me to delay seeing your message.

Not sure if it's still needed, but I'll implement the fix as suggested and make sure it's done in an existing file for @lchapel's direct code review. Thank you very much for your guidance and I look forward to contributing more effectively in the future.

Thank you for your understanding and patience.

Sincerest regards,
Yikun

[rflamary]

Hello @yikun-baio this is a friendly reminder to implement your fix directly in the code if possible. I used a rocket emoji in your previous question to say that we are interested but maybe you did not receive a notfication.

[codecov]

Codecov Report

Merging #602 (a1ba2d6) into master (ab12dd6) will decrease coverage by 0.07%.
The diff coverage is 82.08%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #602      +/-   ##
==========================================
- Coverage   96.79%   96.73%   -0.07%     
==========================================
  Files          77       78       +1     
  Lines       16086    16153      +67     
==========================================
+ Hits        15570    15625      +55     
- Misses        516      528      +12