feat: add blas/ext/base/dcartesian-square

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Resolves stdlib-js/metr-issue-tracker#172.

Description

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This pull request:

• add blas/ext/base/dcartesian-square

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This pull request has the following related issues:

• Resloves [RFC]: add blas/ext/base/dcartesian-square metr-issue-tracker#172

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Coverage Report

Package	Statements	Branches	Functions	Lines
blas/ext/base/dcartesian-square	$\color{green}415/415$ $\color{green}+100.00%$	$\color{green}25/25$ $\color{green}+100.00%$	$\color{green}4/4$ $\color{green}+100.00%$	$\color{green}415/415$ $\color{green}+100.00%$

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

[kgryte]

I am realizing now why this looks odd to me. Namely, I led you astray with the original API design. For the non-ndarray API, it should be

dcartesianSquare( N, x, strideX, out, LDO )

where LDO is the stride of the leading dimension and the stride of the trailing dimension is assumed to be 1. This follows BLAS conventions. See https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/dsyr for an example.

This change should be made here and in the other Cartesian PRs.

[kgryte]

This is the wrong interpretation. strideOut* parameters don't have anything to do with the end-user experience of the output data. They refer to the storage layout of the provided array. You need to think about this from the end-user POV for an ndarray. The end-user should always see the results in the same orientation (e.g., rows of pairs); otherwise, the orientation is purely an artifact of the ndarray's underlying storage arrangement, which is clearly undesirable, as then an end-user needs to know the layout in order to interpret returned results and index into the array accordingly.

There is a reason why I said in the OP that the implementation needs to be cache-aware. And the reason is that the results need to be returned in a stable manner. Your implementation is currently unstable and needs to be refactored accordingly.

I suggest always returning results such that pairs are arranged along the first dimension (i.e., rows) and elements within the pair are arranged along the second dimension (i.e., columns).

Accordingly, your implementation needs to be fixed and should incorporate loop interchange. The algorithm for row-major and for column-major should be different.

This thinking is going to apply to all your other Cartesian PRs.

[kgryte]

Left initial comments.