Improve docstrings and test coverage

[ghiggi]

Prework

• [x] I understand and agree to this repository's code of conduct.
• [x] I understand and agree to this repository's contributing guidelines.
• [ ] I have already submitted an issue or discussion thread to discuss my idea with the maintainers.

What kind of change does this PR introduce? (check at least one)

• [x] Bugfix
• [x] Feature
• [x] Documentation
• [x] Tutorial
• [x] Code style update
• [x] Refactor
• [ ] Build-related changes
• [ ] Other, please describe:

Does this PR introduce a breaking change? (check one)

• [ ] Yes
• [x] No

If yes, please describe the impact and communicate accordingly:

The PR fulfills these requirements:

• [x] It's submitted to the branch named as follow:
  • Fix a bug: bugfix-<some_key>-<word>
  • Improve the doc: doc-<some_key>-<word>
  • Improve a tutorial tutorial-<some_key>-<word>
  • Add a new feature: feature-<some_key>-<word>
  • Refactor some code: refactor-<some_key>-<word>
  • Optimize some code: optimize-<some_key>-<word>
• [ ] When resolving a specific issue, it's referenced in the PR's title (e.g. fix #xxx[,#xxx], where "xxx" is the issue number)
• [ ] Don't forget to link PR to issue if you are solving one.
• [x] All tests are passing.
• [x] New/updated tests are included

Summary

This PR adds:

• improve the documentation
• improves internal functions and test units