ties fix with unit test

[6DammK9]

As discussed.
Added comments and unit test, meanwhile eliminated all loops (syntax trick only).
vmap is only for batched processing. Data type was messed.
Yet it is a merge with O(N) space complexity.

[ljleb]

thanks for the contribution, generally I'm fine with annotating with pseudo code from paper for more clarity. I primarily like functions to fit on my screen, but here I think you're right that matching the paper implementation is more important.

Let me know if you're okay with me pushing to this branch, I can tackle the comments I left in this case.

I'll close #23 in favor of this.

[ljleb]

I made some changes to the format, pycharm was not happy with triple quotes (giving warnings) so I replaced with comments. Let me know if this doesn't work with the vscode extension, in which case I'll change my formatting settings for this project I guess.

[6DammK9]

Native VSCode don't have LaTeX stuffs. I think upmath.me / Jupyter notebook / github are all not compatable each other.
Especially github, it is in single $ without space e.g. $\alpha$ for $\alpha$
Usually I need to edit again copying them across platforms.
It will be fine when they can be formatted in any one platform. It is fine for me.
Just pick one and keep it consistent.