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feat: add lapack/base/zrot
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PR-URL: stdlib-js#4772
Ref: stdlib-js#2464
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com> 
Co-authored-by: stdlib-bot <82920195+stdlib-bot@users.noreply.github.com>
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299 changes: 299 additions & 0 deletions lib/node_modules/@stdlib/lapack/base/zrot/README.md
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# zrot

> Apply a plane rotation with real cosine and complex sine to a pair of complex vectors.
<section class="usage">

## Usage

```javascript
var zrot = require( '@stdlib/lapack/base/zrot' );
```

#### zrot( N, zx, strideX, zy, strideY, c, s )

Applies a plane rotation with real cosine and complex sine.

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
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( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex128( 0.0, 0.75 );

zrot( zx.length, zx, 1, zy, 1, 1.25, s );

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

var re = real( z );
// returns ~-1.5

var im = imag( z );
// returns ~0.75

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

re = real( z );
// returns ~1.25

im = imag( z );
// returns ~2.5
```

The function has the following parameters:

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

The `N` and stride parameters determine how values from `zx` and `zy` are accessed at runtime. For example, to apply a plane rotation to every other element,

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
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( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex128( 0.0, 0.75 );

zrot( 2, zx, 2, zy, 2, 1.25, s );

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

var re = real( z );
// returns ~-1.5

var im = imag( z );
// returns ~0.75

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

re = real( z );
// returns ~1.25

im = imag( z );
// returns ~2.5
```

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 Complex128 = require( '@stdlib/complex/float64/ctor' );
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, 7.0, 8.0 ] );
var zy0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// 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 3rd element

var s = new Complex128( 0.0, 0.75 );

zrot( 2, zx1, -2, zy1, 1, 1.25, s );

var z = zy0.get( 2 );
// returns <Complex128>

var re = real( z );
// returns ~-6

var im = imag( z );
// returns ~5.25

z = zx0.get( 3 );
// returns <Complex128>

re = real( z );
// returns ~8.75

im = imag( z );
// returns ~10
```

#### zrot.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY, c, s )

Applies a plane rotation with real cosine and complex sine using alternative indexing semantics.

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
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 ] );
var zy = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex128( 0.0, 0.75 );

zrot.ndarray( zx.length, zx, 1, 0, zy, 1, 0, 1.25, s );

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

var re = real( z );
// returns ~-1.5

var im = imag( z );
// returns ~0.75

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

re = real( z );
// returns ~1.25

im = imag( z );
// returns ~2.5
```

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 apply a plane rotation to every other element starting from the second element,

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
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( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex128( 0.0, 0.75 );

zrot.ndarray( 2, zx, 2, 1, zy, 2, 1, 1.25, s );

var z = zy.get( 3 );
// returns <Complex128>

var re = real( z );
// returns ~-6.0

var im = imag( z );
// returns ~5.25

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

re = real( z );
// returns ~3.75

im = imag( z );
// returns ~5.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

- If `N <= 0`, both functions leave `zx` and `zy` unchanged.
- `zrot()` corresponds to the [LAPACK][lapack] routine [`zrot`][zrot].

</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/ctor' );
var zcopy = require( '@stdlib/blas/base/zcopy' );
var zeros = require( '@stdlib/array/zeros' );
var logEach = require( '@stdlib/console/log-each' );
var zrot = require( '@stdlib/lapack/base/zrot' );

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

// Generate random input arrays:
var zx = filledarrayBy( 10, 'complex128', rand );
var zxc = zcopy( zx.length, zx, 1, zeros( zx.length, 'complex128' ), 1 );

var zy = filledarrayBy( 10, 'complex128', rand );
var zyc = zcopy( zy.length, zy, 1, zeros( zy.length, 'complex128' ), 1 );

var s = new Complex128( 0.0, 0.75 );

// Apply a plane rotation:
zrot( zx.length, zx, 1, zy, 1, 1.25, s );

// Print the results:
logEach( '(%s,%s) => (%s,%s)', zxc, zyc, zx, zy );
```

</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">

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

[zrot]: https://netlib.org/lapack/explore-html/d1/d45/group__rot_gaac9d54e7408105ad6f4c810902e75b7a.html#gaac9d54e7408105ad6f4c810902e75b7a

[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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