feat: add blas/base/zdotu

[gururaj1512]

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Resolves a part of #2039.

Description

What is the purpose of this pull request?

This pull request:

• Adds javascript implementation for blas/base/zdotu

Related Issues

Does this pull request have any related issues?

This pull request:

• Resolves a part of [RFC]: Add BLAS bindings and implementations for linear algebra (tracking issue) #2039.

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No.

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• Read, understood, and followed the contributing guidelines.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/base/zdotu	$\color{green}315/315$ $\color{green}+100.00\%$	$\color{green}14/14$ $\color{green}+100.00\%$	$\color{green}3/3$ $\color{green}+100.00\%$	$\color{green}315/315$ $\color{green}+100.00\%$

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

[ShabiShett07]

/stdlib merge

[kgryte]

/stdlib merge

[kgryte]

This isn't correct. We should not be using the accessors. We should reinterpret the complex input arrays as Float64Arrays of interleaved real and imaginary components. And then we should use muladd.strided. For reference, see

stdlib/lib/node_modules/@stdlib/blas/base/zaxpy/lib/ndarray.js

Line 79 in 0283804

muladd( re, im, viewX[ ix ], viewX[ ix+1 ], viewY[ iy ], viewY[ iy+1 ], viewY, 1, iy ); // eslint-disable-line max-len

.

[kgryte]

Instead of muladd.assign, you want to use muladd.strided: https://github.com/stdlib-js/stdlib/tree/02838049b98a8ae3c595714e397364aace06f7b9/lib/node_modules/%40stdlib/complex/float64/base/mul-add#muladdstrided-alpha-sa-oa-x-sx-ox-y-sy-oy-out-so-oo-

This allows you to have the output real and imaginary components stored in a Float64Array. To return a complex number, you then do new Complex128( out[ 0 ], out[ 1 ] ).

[kgryte]

The reason we shouldn't be using accessors and constantly materializing Complex128 instances is that all of this is happening in a hot loop. Instead, prefer to operate on the individual components directly.

[kgryte]

This PR needs a bit of clean-up still.

@ShabiShett07 Also, in addition to the main export and the ndarray method, we should add an assign method with the following signature:

zdotu.assign( N, x, strideX, offsetX, y, strideY, offsetY, out, offsetOut );

In this case, the real and imaginary components of the complex number output will be written to out which should be a Complex128Array at the index offsetOut.

The ndarray method can then wrap the assign API and you can use a preallocated Complex128Array workspace array which you then pass as input to assign. When returning from ndarray, you then do workspace.get( 0 ), which will materialize a new Complex128 value.

Similarly, the main export can also wrap the assign API.

Why are we doing this? Because in zgemm, you will want to use the assign API of zdotu, not the ndarray API. The assign API will allow you to avoid materializing complex number instances in hot loops.

[kgryte]

@ShabiShett07 Would you mind resolving the lint failures in this PR? Cheers!