feat: add lapack/base/dsptrf

[iampratik13]

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Resolves none.

Description

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This pull request:

• feat: add lapack/base/dsptrf

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Coverage Report

Package	Statements	Branches	Functions	Lines
lapack/base/dsptrf	$\\color{green}688/688$ $\\color{green}+100.00\\%$	$\\color{green}88/88$ $\\color{green}+100.00\\%$	$\\color{green}7/7$ $\\color{green}+100.00\\%$	$\\color{green}688/688$ $\\color{green}+100.00\\%$

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

[kgryte]

This sort of formatting is not particularly helpful. The purpose of A is to provide an easy visual representation of the matrix. This sort of layout puts the onus of visual reconstruction on the reader.

[kgryte]

You can avoid needing to create a closure by simply making pos( oa, sa, idx ) and passing in oa and sa explicitly at the call sites below. That is preferable due to how optimizing compilers work.

[kgryte]

Suggested change

	// Interchange rows and columns `kk` and `kp` in the leading submatrix `A(0:k-1,0:k-1)`...

Is it actually 1:k or is that one-based indexing? If the latter, make sure docs reflect zero-based indexing; otherwise, that is going to be misleading for people reading the code.

[kgryte]

Same comments. Are the indices in these comments all using one-based indexing? It is not clear.

[kgryte]

Use temporary variables here and below. These indexing expressions are repetitive and make the expressions hard to read.

[kgryte]

You have a lot of repeated calculations here. Figure out a way to simplify and clean-up.

[kgryte]

Left initial comments.