feat: add blas/ext/base/drss

[nakul-krishnakumar]

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• Adds blas/ext/base/drss .

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Coverage Report

Package	Statements	Branches	Functions	Lines
blas/ext/base/drss	$\color{red}422/439$ $color{green}+96.13%$	$\color{red}20/23$ $color{green}+86.96%$	$\color{green}4/4$ $color{green}+100.00%$	$\color{red}422/439$ $color{green}+96.13%$

The above coverage report was generated for the changes in this PR.

[kgryte]

@nakul-krishnakumar I am not sure this behaves quite as you expect. The implementation that you should be following is not exactly what we did for drrss, as that has different scaling properties. Instead, you should be following

• https://www.netlib.org/lapack/explore-html/d8/d76/group__lassq_gae8f40b0a34771b4f2d9c863de3af7be5.html#gae8f40b0a34771b4f2d9c863de3af7be5
• https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/lapack/base/dlassq

Notice that the underlying algorithm is similar, but not the same, and certainly not the same as simply undoing sqrt operations.

I suggest implementing the algorithm in dlassq and instead of returning a scale and a sum, doing what you do here and returning scale**2 * sumsq.

Additionally, as previously discussed, we'll also want different variants of drss based on the underlying summation algorithm (e.g., drsskbn, drsskbn2, drssli, drsslipw, drssors, drsspn, drsspw). As such, I recommend renaming this package to drssbl as this is based on Blue's algorithm for computing the Euclidean norm of a vector.

[nakul-krishnakumar]

Thank you for the review @kgryte.
Also does the renaming apply for drrss (square root of residual sum of squares) too? Current implementation of drrss depends on Blue's algorithm, so can it too have the different variants you mentioned above?

[kgryte]

We can deal with that later. For now, fine to leave as is, as we can use a different migration strategy for that package given that it has already been created.