Thin SVD

Start by reading lax/src/svd.rs, especially the SvdWork implementation and the documented LAPACK operation table, then compare the entry point in lax/src/lib.rs with the SVD trait in ndarray-linalg/src/svd.rs. Determine how the gesvdx-based thin or economy SVD should fit the existing API; done means the capability is implemented and its supported operation documentation is updated.

I was studying PICARD (a faster version of ICA than "FastICA") and saw some mention of various types of SVD, which I'm already familiar with. One of the variants was "thin" SVD. I can see that there are other libs that save computation by only computing this "thin" variant and I was wondering if maybe ndarray-linalg could too.

I did a search of the code earlier and saw no mention of it, I'm curious if it'd be worth developing.

My understanding is that there are separate LAPACK functions/instructions you'd use for 'economy'/'thin' SVD, gesvdx being the relevant one

• Intel docs on gesvdkx https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-c/2023-0/gesvdx.html

  • note the x part is what differs from the others already implemented, i.e. what makes it 'thin'

For reference I am interested in its use in whitening in this crate

• svd function: https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/lib.rs#L422-L437
• SvdWork struct: https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/svd.rs#L15
• SVD trait: https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/ndarray-linalg/src/svd.rs#L8-L19

So two things I see there are that

1. there's this line saying it is unimplemented

https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/svd.rs#L63-L67

2. there's this comment making v clear which LAPACK instructions are supported

https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/svd.rs#L6-L8

and (from right to left in that table)

https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/svd.rs#L180-L181

https://github.com/rust-ndarray/ndarray-linalg/blob/49e964be06c830a04442e48e0f9a89d2000bbbd1/lax/src/svd.rs#L313-L314

I'd be interested in this but for now just pointing out where the relevant parts of code are, have not dug deeper! 👍