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https://github.com/stdlib-js/blas-base-csrot

Apply a plane rotation.
https://github.com/stdlib-js/blas-base-csrot

algebra array blas complex complex64 csrot javascript level-1 linear math mathematics ndarray node node-js nodejs rotation stdlib subroutines typed vector

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Apply a plane rotation.

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README 

          



  

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# csrot



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



> Applies a plane rotation.



## Installation



```bash

npm install @stdlib/blas-base-csrot

```



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 csrot = require( '@stdlib/blas-base-csrot' );

```



#### csrot( N, cx, strideX, cy, strideY, c, s )



Applies a plane rotation.



```javascript

var Complex64Array = require( '@stdlib/array-complex64' );

var realf = require( '@stdlib/complex-float32-real' );

var imagf = require( '@stdlib/complex-float32-imag' );



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 ] );



csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );



var z = cy.get( 0 );

// returns 



var re = realf( z );

// returns ~-0.6



var im = imagf( z );

// returns ~-1.2



z = cx.get( 0 );

// returns 



re = realf( z );

// returns ~0.8



im = imagf( z );

// returns ~1.6

```



The function has the following parameters:



-   **N**: number of indexed elements.

-   **cx**: first input [`Complex64Array`][@stdlib/array/complex64].

-   **strideX**: index increment for `cx`.

-   **cy**: second input [`Complex64Array`][@stdlib/array/complex64].

-   **strideY**: index increment 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 realf = require( '@stdlib/complex-float32-real' );

var imagf = require( '@stdlib/complex-float32-imag' );



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 ] );



csrot( 2, cx, 2, cy, 2, 0.8, 0.6 );



var z = cy.get( 0 );

// returns 



var re = realf( z );

// returns ~-0.6



var im = imagf( z );

// returns ~-1.2



z = cx.get( 0 );

// returns 



re = realf( z );

// returns ~0.8



im = imagf( z );

// returns ~1.6

```



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



```javascript

var Complex64Array = require( '@stdlib/array-complex64' );

var realf = require( '@stdlib/complex-float32-real' );

var imagf = require( '@stdlib/complex-float32-imag' );



// 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



csrot( 2, cx1, -2, cy1, 1, 0.8, 0.6 );



var z = cy0.get( 2 );

// returns 



var re = realf( z );

// returns ~-4.2



var im = imagf( z );

// returns ~-4.8



z = cx0.get( 3 );

// returns 



re = realf( z );

// returns ~5.6



im = imagf( z );

// returns ~6.4

```



#### csrot.ndarray( N, cx, strideX, offsetX, cy, strideY, offsetY, c, s )



Applies a plane rotation using alternative indexing semantics.



```javascript

var Complex64Array = require( '@stdlib/array-complex64' );

var realf = require( '@stdlib/complex-float32-real' );

var imagf = require( '@stdlib/complex-float32-imag' );



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 ] );



csrot.ndarray( cx.length, cx, 1, 0, cy, 1, 0, 0.8, 0.6 );



var z = cy.get( 0 );

// returns 



var re = realf( z );

// returns ~-0.6



var im = imagf( z );

// returns ~-1.2



z = cx.get( 0 );

// returns 



re = realf( z );

// returns ~0.8



im = imagf( z );

// returns ~1.6

```



The function has the following additional parameters:



-   **offsetX**: starting index for `cx`.

-   **offsetY**: 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 realf = require( '@stdlib/complex-float32-real' );

var imagf = require( '@stdlib/complex-float32-imag' );



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 ] );



csrot.ndarray( 2, cx, 2, 1, cy, 2, 1, 0.8, 0.6 );



var z = cy.get( 3 );

// returns 



var re = realf( z );

// returns ~-4.2



var im = imagf( z );

// returns ~-4.8



z = cx.get( 1 );

// returns 



re = realf( z );

// returns ~2.4



im = imagf( z );

// returns ~3.2

```



## Notes



-   If `N <= 0`, both functions leave `cx` and `cy` unchanged.

-   `csrot()` corresponds to the [BLAS][blas] level 1 function [`csrot`][csrot].



## Examples



```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 csrot = require( '@stdlib/blas-base-csrot' );



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 );



// Apply a plane rotation:

csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );



// Print the results:

logEach( '(%s,%s) => (%s,%s)', cxc, cyc, cx, cy );

```



* * *



## C APIs



### Usage



```c

#include "stdlib/blas/base/csrot.h"

```



#### c_csrot( N, \*X, strideX, \*Y, strideY, c, s )



Applies a plane rotation.



```c

float x[] = { 1.0f, 2.0f, 3.0f, 4.0f }; // interleaved real and imaginary components

float y[] = { 5.0f, 6.0f, 7.0f, 8.0f };



c_csrot( 2, (void *)x, 1, (void *)y, 1, 0.8f, 0.6f );

```



The function accepts the following arguments:



-   **N**: `[in] CBLAS_INT` number of indexed elements.

-   **CX**: `[inout] void*` first input array.

-   **strideX**: `[in] CBLAS_INT` index increment for `CX`.

-   **CY**: `[inout] void*` second input array.

-   **strideY**: `[in] CBLAS_INT` index increment for `CY`.

-   **c**: `[in] float` cosine of the angle of rotation.

-   **s**: `[in] float` sine of the angle of rotation.



```c

void c_csrot( const CBLAS_INT N, void *CX, const CBLAS_INT strideX, void *CY, const CBLAS_INT strideY, const float c, const float s );

```



#### c_csrot_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY, c, s )



Applies a plane rotation using alternative indexing semantics.



```c

float x[] = { 1.0f, 2.0f, 3.0f, 4.0f }; // interleaved real and imaginary components

float y[] = { 5.0f, 6.0f, 7.0f, 8.0f };



c_csrot_ndarray( 2, (void *)x, 1, 0, (void *)y, 1, 0, 0.8f, 0.6f );

```



The function accepts the following arguments:



-   **N**: `[in] CBLAS_INT` number of indexed elements.

-   **CX**: `[inout] void*` first input array.

-   **strideX**: `[in] CBLAS_INT` index increment for `CX`.

-   **offsetX**: `[in] CBLAS_INT` starting index for `CX`.

-   **CY**: `[inout] void*` second input array.

-   **strideY**: `[in] CBLAS_INT` index increment for `CY`.

-   **offsetY**: `[in] CBLAS_INT` starting index for `CY`.

-   **c**: `[in] float` cosine of the angle of rotation.

-   **s**: `[in] float` sine of the angle of rotation.



```c

void c_csrot_ndarray( const CBLAS_INT N, void *CX, const CBLAS_INT strideX, const CBLAS_INT offsetX, void *CY, const CBLAS_INT strideY, const CBLAS_INT offsetY, const float c, const float s );

```



### Examples



```c

#include "stdlib/blas/base/csrot.h"

#include 



int main( void ) {

    // Create strided arrays:

    float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

    float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };



    // Specify the number of elements:

    const int N = 4;



    // Specify stride lengths:

    const int strideX = 1;

    const int strideY = -1;



    // Copy elements:

    c_csrot( N, (void *)x, strideX, (void *)y, strideY, 0.8f, 0.6f );



    // Print the result:

    for ( int i = 0; i < N; i++ ) {

        printf( "x[ %i ] = %f + %fj\n", i, x[ i*2 ], x[ (i*2)+1 ] );

        printf( "y[ %i ] = %f + %fj\n", i, y[ i*2 ], y[ (i*2)+1 ] );

    }

}

```



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



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

[npm-url]: https://npmjs.org/package/@stdlib/blas-base-csrot



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

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



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

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



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[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/blas-base-csrot/tree/deno

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

[umd-url]: https://github.com/stdlib-js/blas-base-csrot/tree/umd

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

[esm-url]: https://github.com/stdlib-js/blas-base-csrot/tree/esm

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

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



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



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



[csrot]: http://www.netlib.org/lapack/explore-html/da/df6/group__complex__blas__level1.html



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



[@stdlib/array/complex64]: https://github.com/stdlib-js/array-complex64