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feat: add blas/base/zdotu #4630

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251 changes: 251 additions & 0 deletions lib/node_modules/@stdlib/blas/base/zdotu/README.md
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<!--

@license Apache-2.0

Copyright (c) 2025 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# zdotu

> Calculate the dot product of two double-precision complex floating-point vectors.

<section class="intro">

The [dot product][dot-product] (or scalar product) is defined as

<!-- <equation class="equation" label="eq:dot_product" align="center" raw="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" alt="Dot product definition."> -->

```math
\mathbf{zx}\cdot\mathbf{zy} = \sum_{i=0}^{N-1} zx_i zy_i = zx_0 zy_0 + zx_1 zy_1 + \ldots + zx_{N-1} zy_{N-1}
```

<!-- <div class="equation" align="center" data-raw-text="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" data-equation="eq:dot_product">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@929657146427564b61e3e6bdda76949ebe2ce923/lib/node_modules/@stdlib/blas/base/ddot/docs/img/equation_dot_product.svg" alt="Dot product definition.">
<br>
</div> -->

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var zdotu = require( '@stdlib/blas/base/zdotu' );
```

#### zdotu( N, zx, strideX, zy, strideY )

Calculates the dot product of vectors `zx` and `zy`.

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

var zx = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );

var z = zdotu( 3, zx, 1, zy, 1 );
// returns <Complex128>

var re = real( z );
// returns -52.0

var im = imag( z );
// returns 82.0
```

The function has the following parameters:

- **N**: number of indexed elements.
- **zx**: input [`Complex128Array`][@stdlib/array/complex128].
- **strideX**: index increment for `zx`.
- **zy**: input [`Complex128Array`][@stdlib/array/complex128].
- **strideY**: index increment for `zy`.

The `N` and strides parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the dot product of every other value in `zx` and the first `N` elements of `zy` in reverse order,

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var z = zdotu( 2, zx, 2, zy, -1 );
// returns <Complex128>

var re = real( z );
// returns -2.0

var im = imag( z );
// returns 14.0
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

<!-- eslint-disable stdlib/capitalized-comments -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

// Initial arrays...
var zx0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var zy0 = new Complex128Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var zx1 = new Complex128Array( zx0.buffer, zx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var zy1 = new Complex128Array( zy0.buffer, zy0.BYTES_PER_ELEMENT*2 ); // start at 3th element

var z = zdotu( 1, zx1, 1, zy1, 1 );
// returns <Complex128>

var re = real( z );
// returns -15.0

var im = imag( z );
// returns 80.0
```

#### zdotu.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY )

Calculates the dot product of `zx` and `zy` using alternative indexing semantics.

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

var zx = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );

var z = zdotu.ndarray( zx.length, zx, 1, 0, zy, 1, 0 );
// returns <Complex128>

var re = real( z );
// returns -52.0

var im = imag( z );
// returns 82.0
```

The function has the following additional parameters:

- **offsetX**: starting index for `zx`.
- **offsetY**: starting index for `zy`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the dot product of every other value in `zx` starting from the second value with the last 2 elements in `zy` in reverse order

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy = new Complex128Array( [ 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] ); // eslint-disable-line max-len

var z = zdotu.ndarray( 2, zx, 2, 1, zy, -1, zy.length-1 );
// returns <Complex128>

var re = real( z );
// returns -40.0

var im = imag( z );
// returns 310.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

- If `N <= 0`, both functions return `0.0 + 0.0i`.
- `zdotu()` corresponds to the [BLAS][blas] level 1 function [`zdotu`][zdotu].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var zdotu = require( '@stdlib/blas/base/zdotu' );

function rand() {
return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var zx = filledarrayBy( 10, 'complex128', rand );
console.log( zx.toString() );

var zy = filledarrayBy( 10, 'complex128', rand );
console.log( zy.toString() );

var out = zdotu.ndarray( zx.length, zx, 1, 0, zy, -1, zy.length-1 );
console.log( out.toString() );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[dot-product]: https://en.wikipedia.org/wiki/Dot_product

[blas]: http://www.netlib.org/blas

[zdotu]: https://www.netlib.org/lapack/explore-html/d1/dcc/group__dot_ga6b0b69474b384d45fc4c7b1f7ec5959f.html#ga6b0b69474b384d45fc4c7b1f7ec5959f

[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

<!-- <related-links> -->

<!-- </related-links> -->

</section>

<!-- /.links -->
107 changes: 107 additions & 0 deletions lib/node_modules/@stdlib/blas/base/zdotu/benchmark/benchmark.js
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/**
* @license Apache-2.0
*
* Copyright (c) 2024 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var bench = require( '@stdlib/bench' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pow = require( '@stdlib/math/base/special/pow' );
var Complex128Array = require( '@stdlib/array/complex128' );
var pkg = require( './../package.json' ).name;
var zdotu = require( './../lib/zdotu.js' );


// VARIABLES //

var options = {
'dtype': 'float64'
};


// FUNCTIONS //

/**
* Creates a benchmark function.
*
* @private
* @param {PositiveInteger} len - array length
* @returns {Function} benchmark function
*/
function createBenchmark( len ) {
var zx;
var zy;

zx = new Complex128Array( uniform( len*2, -100.0, 100.0, options ) );
zy = new Complex128Array( uniform( len*2, -100.0, 100.0, options ) );
return benchmark;

/**
* Benchmark function.
*
* @private
* @param {Benchmark} b - benchmark instance
*/
function benchmark( b ) {
var d;
var i;

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
d = zdotu( zx.length, zx, 1, zy, 1 );
if ( isnan( d ) ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( isnan( d ) ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
}
}


// MAIN //

/**
* Main execution sequence.
*
* @private
*/
function main() {
var len;
var min;
var max;
var f;
var i;

min = 1; // 10^min
max = 5; // 10^max

for ( i = min; i <= max; i++ ) {
len = pow( 10, i );
f = createBenchmark( len );
bench( pkg+':len='+len, f );
}
}

main();
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