feat: add lapack/base/dge-trans

[Pranavchiku]

Towards #2464.

Description

What is the purpose of this pull request?

This pull request exposes utility function dge_trans as lapack/base/dge-trans.

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NA

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@stdlib-js/reviewers

[kgryte]

@Pranavchiku Is there a reason to name the package as transpose rather than dge-trans? We'll need separate packages for single-precision and complex dtypes.

[Pranavchiku]

I see, I initially used snake case and it threw me lint error. Also, I am unable to understand sense of dge-*, can we not have dtrans?

[Pranavchiku]

Is it double precision general matrix transpose? If yes, then it makes sense.

[kgryte]

Is it double precision general matrix transpose? If yes, then it makes sense.

Yes, I believe so. Not sure why they didn't do dgetrans, but 🤷‍♂️ .

[kgryte]

Left some initial comments.

[kgryte]

LGTM. Thanks for working on this, @Pranavchiku.

Note that the tests were rather spartan. I would argue it is better to create tests which build on one another, rather than creating a single test which attempts to do all the things. By isolating one behavioral aspect at a time, we can better ensure that an implementation behaves as expected. For combining all the things into one, it can be harder to disentangle which aspect is causing a test to fail.

[kgryte]

In principle, we could implement matrix transposition using loop tiling. Loop tiling would only benefit when layout access patterns for A and out differ. E.g., if both A and out are the same (e.g., row-major), because we are taking the transpose, the access pattern for A will be column-major. In this instance, loop tiling can be beneficial. Otherwise, a naive nested loop is cache optimal. Regardless, I'll leave implementing loop tiling to a follow-up PR.