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https://github.com/stdlib-js/lapack-base-zrot

LAPACK auxiliary routine to apply a plane rotation with real cosine and complex sine.
https://github.com/stdlib-js/lapack-base-zrot

algebra array blas complex complex128 javascript lapack linear math mathematics ndarray node node-js nodejs rotation stdlib subroutines typed vector zrot

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LAPACK auxiliary routine to apply a plane rotation with real cosine and complex sine.

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README 

        



  

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# zrot



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



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



## Installation



```bash

npm install @stdlib/lapack-base-zrot

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## 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 



var re = real( z );

// returns ~-1.5



var im = imag( z );

// returns ~0.75



z = zx.get( 0 );

// returns 



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 



var re = real( z );

// returns ~-1.5



var im = imag( z );

// returns ~0.75



z = zx.get( 0 );

// returns 



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.



```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 



var re = real( z );

// returns ~-6



var im = imag( z );

// returns ~5.25



z = zx0.get( 3 );

// returns 



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 



var re = real( z );

// returns ~-1.5



var im = imag( z );

// returns ~0.75



z = zx.get( 0 );

// returns 



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 



var re = real( z );

// returns ~-6.0



var im = imag( z );

// returns ~5.25



z = zx.get( 1 );

// returns 



re = real( z );

// returns ~3.75



im = imag( z );

// returns ~5.0

```



## Notes



-   If `N <= 0`, both functions leave `zx` and `zy` unchanged.

-   `zrot()` corresponds to the [LAPACK][lapack] routine [`zrot`][zrot].



## Examples



```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 );

```



* * *



## 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].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/lapack-base-zrot.svg

[npm-url]: https://npmjs.org/package/@stdlib/lapack-base-zrot



[test-image]: https://github.com/stdlib-js/lapack-base-zrot/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/lapack-base-zrot/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/lapack-base-zrot/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/lapack-base-zrot?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/lapack-base-zrot/tree/deno

[deno-readme]: https://github.com/stdlib-js/lapack-base-zrot/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/lapack-base-zrot/tree/umd

[umd-readme]: https://github.com/stdlib-js/lapack-base-zrot/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/lapack-base-zrot/tree/esm

[esm-readme]: https://github.com/stdlib-js/lapack-base-zrot/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/lapack-base-zrot/blob/main/branches.md



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



[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/array-complex128