Take-2 of polar-decomposition

[metric-space]

Code inspired by this PR/thread: #656

Main person behind this is @LucasCampos

This PR implements matrix polar decomposition

[sebcrozet]

Thanks! I took the liberty of making a few small changes:

• I renamed Matrix::polar to Matrix::try_polar and added Matrix::polar which returns the result instead of Option (similar to the other methods, e.g., Matrix::svd and Matrix::try_svd).
• I made your test use proptest instead of DMatrix::new_random. This will cover more cases.

The new proptest test is failing right now. I haven’t investigated in details yet to determine if this is a bug, or if the test are just failing because we used an epsilon that is too restrictive.

[metric-space]

@sebcrozet Thank you for the review and the additions. Not sure if you plan to look into it further but I will take look into the bug with the prop test and return back with a fix/solution

[metric-space]

I zeroed in on the causes.

1. The orthogonal test is a proxy for a unitary/semi-unitary check. It's a unitary check for square matrices and supposed to be a semi-unitary check for rectangular matrices which is a bit more involved because it tests whether either the rows are orthogonal or the columns are orthogonal. It depends on the dimensions of the rectangular matrix

2. In the main test, the test svd generated is ordered while the method based polar calls the unordered SVD for further processing, which gives different decompositions

Fixes applied and tests pass locally
Ball's back in your court @sebcrozet

[sebcrozet]

Perfect, thanks!

[metric-space]

Thank you