npm package: @stdlib/lapack-base-crot
Description: LAPACK auxiliary routine to apply a plane rotation with real cosine and complex sine.
Author: The Stdlib Authors
Latest version: 0.1.1

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# crot

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> Apply a plane rotation with real cosine and complex sine to a pair of single-precision complex floating-point vectors.

<section class="installation">

## Installation

```bash
npm install @stdlib/lapack-base-crot
```

</section>

<section class="usage">

## Usage

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

#### crot( N, cx, strideCX, cy, strideCY, c, s )

Applies a plane rotation with real cosine and complex sine.

```javascript
var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex64( 0.0, 0.75 );

crot( cx.length, cx, 1, cy, 1, 1.25, s );

var z = cy.get( 0 );
// returns <Complex64>[ ~-1.5, ~0.75 ]

z = cx.get( 0 );
// returns <Complex64>[ ~1.25, ~2.5 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **cx**: first input [`Complex64Array`][@stdlib/array/complex64].
-   **strideCX**: stride length for `cx`.
-   **cy**: second input [`Complex64Array`][@stdlib/array/complex64].
-   **strideCY**: stride length for `cy`.

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

```javascript
var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex64( 0.0, 0.75 );

crot( 2, cx, 2, cy, 2, 1.25, s );

var z = cy.get( 0 );
// returns <Complex64>[ ~-1.5, ~0.75 ]

z = cx.get( 0 );
// returns <Complex64>[ ~1.25, ~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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

// Initial arrays...
var cx0 = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy0 = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var cx1 = new Complex64Array( cx0.buffer, cx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var cy1 = new Complex64Array( cy0.buffer, cy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var s = new Complex64( 0.0, 0.75 );

crot( 2, cx1, -2, cy1, 1, 1.25, s );

var z = cy0.get( 2 );
// returns <Complex64>[ ~-6.0, ~5.25 ]

z = cx0.get( 3 );
// returns <Complex64>[ ~8.75, ~10.0 ]
```

#### crot.ndarray( N, cx, strideCX, offsetCX, cy, strideCY, offsetCY, c, s )

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

```javascript
var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex64( 0.0, 0.75 );

crot.ndarray( cx.length, cx, 1, 0, cy, 1, 0, 1.25, s );

var z = cy.get( 0 );
// returns <Complex64>[ ~-1.5, ~0.75 ]

z = cx.get( 0 );
// returns <Complex64>[ ~1.25, ~2.5 ]
```

The function has the following additional parameters:

-   **offsetCX**: starting index for `cx`.
-   **offsetCY**: starting index for `cy`.

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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
var s = new Complex64( 0.0, 0.75 );

crot.ndarray( 2, cx, 2, 1, cy, 2, 1, 1.25, s );

var z = cy.get( 3 );
// returns <Complex64>[ ~-6.0, ~5.25 ]

z = cx.get( 1 );
// returns <Complex64>[ ~3.75, ~5.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</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 Complex64 = require( '@stdlib/complex-float32-ctor' );
var ccopy = require( '@stdlib/blas-base-ccopy' );
var zeros = require( '@stdlib/array-zeros' );
var logEach = require( '@stdlib/console-log-each' );
var crot = require( '@stdlib/lapack-base-crot' );

function rand() {
    return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

// Generate random input arrays:
var cx = filledarrayBy( 10, 'complex64', rand );
var cxc = ccopy( cx.length, cx, 1, zeros( cx.length, 'complex64' ), 1 );

var cy = filledarrayBy( 10, 'complex64', rand );
var cyc = ccopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 );

var s = new Complex64( 0.0, 0.75 );

// Apply a plane rotation:
crot( cx.length, cx, 1, cy, 1, 1.25, s );

// Print the results:
logEach( '(%s,%s) => (%s,%s)', cxc, cyc, cx, cy );
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

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* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/lapack-base-crot/main/LICENSE

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

[crot]: https://netlib.org/lapack/explore-html/d1/d45/group__rot_ga25544801d45dcabdec7b24d863ebea9c.html#ga25544801d45dcabdec7b24d863ebea9c

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