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feat: add blas/base/zswap
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PR-URL: 	#2075
Closes: #2047
Ref: #2039
Ref: https://netlib.org/lapack/explore-html-3.6.1/d2/df9/group__complex16__blas__level1_ga13a187010a0cae1fef2820072404e857.html#ga13a187010a0cae1fef2820072404e857
Co-authored-by: Athan Reines <[email protected]>
Reviewed-by: Athan Reines <[email protected]> 
Signed-off-by: Athan Reines <[email protected]>
Co-authored-by: stdlib-bot <[email protected]>
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# zswap

> Interchange two complex double-precision floating-point vectors.
<section class="intro">

This BLAS level 1 routine interchanges complex double-precision floating-point vectors `x` and `y`. The operation is performed in-place, with `x` being overwritten with the values from `y`, and `y` being overwritten with the values from `x`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### zswap( N, x, strideX, y, strideY )

Interchange two complex double-precision floating-point vectors.

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

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zswap( x.length, x, 1, y, 1 );

var z = y.get( 0 );
// returns <Complex128>

var re = real( z );
// returns 1.0

var im = imag( z );
// returns 2.0

z = x.get( 0 );
// returns <Complex128>

re = real( z );
// returns 0.0

im = imag( z );
// returns 0.0
```

The function has the following parameters:

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

The `N` and stride parameters determine how values from `x` are interchanged with values from `y`. For example, to interchange in reverse order every other value in `x` into the first `N` elements of `y`,

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

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zswap( 2, x, -2, y, 1 );

var z = y.get( 0 );
// returns <Complex128>

var re = real( z );
// returns 5.0

var im = imag( z );
// returns 6.0

z = x.get( 0 );
// returns <Complex128>

re = real( z );
// returns 0.0

im = imag( z );
// returns 0.0
```

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/real' );
var imag = require( '@stdlib/complex/imag' );

// Initial arrays...
var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Interchange in reverse order every other value from `x1` into `y1`...
zswap( 2, x1, -2, y1, 1 );

var z = y0.get( 2 );
// returns <Complex128>

var re = real( z );
// returns 7.0

var im = imag( z );
// returns 8.0

z = x0.get( 1 );
// returns <Complex128>

re = real( z );
// returns 0.0

im = imag( z );
// returns 0.0
```

#### zswap.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )

Interchange two complex double-precision floating-point vectors using alternative indexing semantics.

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

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zswap.ndarray( x.length, x, 1, 0, y, 1, 0 );

var z = y.get( 0 );
// returns <Complex128>

var re = real( z );
// returns 1.0

var im = imag( z );
// returns 2.0

z = x.get( 0 );
// returns <Complex128>

re = real( z );
// returns 0.0

im = imag( z );
// returns 0.0
```

The function has the following additional parameters:

- **offsetX**: starting index for `x`.
- **offsetY**: starting index for `y`.

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 interchange every other value in `x` starting from the second value into the last `N` elements in `y` where `x[i] = y[n]`, `x[i+2] = y[n-1]`, and so on,

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

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zswap.ndarray( 2, x, 2, 1, y, -1, y.length-1 );

var z = y.get( y.length-1 );
// returns <Complex128>

var re = real( z );
// returns 3.0

var im = imag( z );
// returns 4.0

z = x.get( x.length-1 );
// returns <Complex128>

re = real( z );
// returns 0.0

im = imag( z );
// returns 0.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

- If `N <= 0`, both functions leave `x` and `y` unchanged.
- `zswap()` corresponds to the [BLAS][blas] level 1 function [`zswap`][zswap].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

var x = filledarrayBy( 10, 'complex128', rand );
console.log( x.get( 0 ).toString() );

var y = filledarrayBy( 10, 'complex128', rand );
console.log( y.get( 0 ).toString() );

// Swap elements in `x` into `y` starting from the end of `y`:
zswap( x.length, x, 1, y, -1 );
console.log( x.get( x.length-1 ).toString() );
console.log( y.get( y.length-1 ).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">

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

[zswap]: https://netlib.org/lapack/explore-html-3.6.1/d2/df9/group__complex16__blas__level1_ga13a187010a0cae1fef2820072404e857.html#ga13a187010a0cae1fef2820072404e857

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

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

</section>

<!-- /.links -->
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Coverage Report

Package Statements Branches Functions Lines
blas/base/zswap $\color{green}572/572$
$\color{green}+100.00\%$ 		$\color{green}31/31$
$\color{green}+100.00\%$ 		$\color{green}4/4$
$\color{green}+100.00\%$ 		$\color{green}572/572$
$\color{green}+100.00\%$

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

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