npm package: @stdlib/blas-base-wasm-csrot
Description: Apply a plane rotation.
Author: The Stdlib Authors
Latest version: 0.1.1

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# csrot

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

> Apply a plane rotation.

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-base-wasm-csrot
```

</section>

<section class="usage">

## Usage

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

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

Applies a plane rotation.

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

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.main( cx.length, cx, 1, cy, 1, 0.8, 0.6 );
// cx => <Complex64Array>[ ~0.8, ~1.6, ~2.4, ~3.2, 4.0, ~4.8, ~5.6, ~6.4 ]
// cy => <Complex64Array>[ ~-0.6, ~-1.2, ~-1.8, ~-2.4, -3.0, ~-3.6, ~-4.2, ~-4.8 ]
```

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`.
-   **c**: cosine of the angle of rotation.
-   **s**: sine of the angle of rotation.

The `N` and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a plane rotation to every other element,

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

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.main( 2, cx, 2, cy, 2, 0.8, 0.6 );
// cx => <Complex64Array>[ ~0.8, ~1.6, 3.0, 4.0, 4.0, ~4.8, 7.0, 8.0 ]
// cy => <Complex64Array>[ ~-0.6, ~-1.2,  0.0, 0.0, -3.0, ~-3.6,  0.0, 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 Complex64Array = require( '@stdlib/array-complex64' );

// 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.main( 2, cx1, -2, cy1, 1, 0.8, 0.6 );
// cx0 => <Complex64Array>[ 1.0, 2.0, ~2.4, ~3.2, 5.0, 6.0, ~5.6, ~6.4 ]
// cy0 => <Complex64Array>[ 0.0, 0.0,  0.0, 0.0, ~-4.2, ~-4.8, ~-1.8, ~-2.4 ]
```

#### 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 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 );
// cx => <Complex64Array>[ ~0.8, ~1.6, ~2.4, ~3.2, 4.0, ~4.8 ]
// cy => <Complex64Array>[ ~-0.6, ~-1.2, ~-1.8, ~-2.4, -3.0, ~-3.6 ]
```

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 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 );
// cx => <Complex64Array>[ 1.0, 2.0, ~2.4, ~3.2, 5.0, 6.0, ~5.6, ~6.4 ]
// cy => <Complex64Array>[ 0.0, 0.0, ~-1.8, ~-2.4, 0.0, 0.0, ~-4.2, ~-4.8 ]
```

* * *

### Module

#### csrot.Module( memory )

Returns a new WebAssembly [module wrapper][@stdlib/wasm/module-wrapper] instance which uses the provided WebAssembly [memory][@stdlib/wasm/memory] instance as its underlying memory.

<!-- eslint-disable node/no-sync -->

```javascript
var Memory = require( '@stdlib/wasm-memory' );

// Create a new memory instance with an initial size of 10 pages (640KiB) and a maximum size of 100 pages (6.4MiB):
var mem = new Memory({
    'initial': 10,
    'maximum': 100
});

// Create a BLAS routine:
var mod = new csrot.Module( mem );
// returns <Module>

// Initialize the routine:
mod.initializeSync();
```

#### csrot.Module.prototype.main( N, cxp, sx, cyp, sy, c, s )

Applies a plane rotation.

<!-- eslint-disable node/no-sync -->

```javascript
var Memory = require( '@stdlib/wasm-memory' );
var oneTo = require( '@stdlib/array-one-to' );
var ones = require( '@stdlib/array-ones' );
var zeros = require( '@stdlib/array-zeros' );
var bytesPerElement = require( '@stdlib/ndarray-base-bytes-per-element' );
var Complex64Array = require( '@stdlib/array-complex64' );
var reinterpretComplex64 = require( '@stdlib/strided-base-reinterpret-complex64' );
var csrot = require( '@stdlib/blas-base-wasm-csrot' );

// Create a new memory instance with an initial size of 10 pages (320KiB) and a maximum size of 100 pages (6.4MiB):
var mem = new Memory({
    'initial': 10,
    'maximum': 100
});

// Create a BLAS routine:
var mod = new csrot.Module( mem );
// returns <Module>

// Initialize the routine:
mod.initializeSync();

// Define a vector data type:
var dtype = 'complex64';

// Specify a vector length:
var N = 5;

// Define pointers (i.e., byte offsets) for storing the input vectors:
var cxptr = 0;
var cyptr = N * bytesPerElement( dtype );

// Write vector values to module memory:
var xbuf = oneTo( N*2, 'float32' );
var cx = new Complex64Array( xbuf.buffer );
mod.write( cxptr, cx );

var ybuf = ones( N*2, 'float32' );
var cy = new Complex64Array( ybuf.buffer );
mod.write( cyptr, cy );

// Perform computation:
mod.main( N, cxptr, 1, cyptr, 1, 0.8, 0.6 );

// Read out the results:
var viewX = zeros( N, dtype );
var viewY = zeros( N, dtype );
mod.read( cxptr, viewX );
mod.read( cyptr, viewY );

console.log( reinterpretComplex64( viewX, 0 ) );
// => <Float32Array>[ ~1.4, ~2.2, 3.0, ~3.8, ~4.6, ~5.4, ~6.2, 7.0, ~7.8, ~8.6 ]

console.log( reinterpretComplex64( viewY, 0 ) );
// => <Float32Array>[ ~0.2, ~-0.4, -1.0, ~-1.6, ~-2.2, ~-2.8, ~-3.4, -4.0, ~-4.6, ~-5.2 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **cxp**: first input [`Complex64Array`][@stdlib/array/complex64] pointer (i.e., byte offset).
-   **sx**: index increment for `cx`.
-   **cyp**: second input [`Complex64Array`][@stdlib/array/complex64] pointer (i.e., byte offset).
-   **sy**: index increment for `cy`.
-   **c**: cosine of the angle of rotation.
-   **s**: sine of the angle of rotation.

#### csrot.Module.prototype.ndarray( N, cxp, sx, ox, cyp, sy, oy, c, s )

Applies a plane rotation using alternative indexing semantics.

<!-- eslint-disable node/no-sync -->

```javascript
var Memory = require( '@stdlib/wasm-memory' );
var oneTo = require( '@stdlib/array-one-to' );
var ones = require( '@stdlib/array-ones' );
var zeros = require( '@stdlib/array-zeros' );
var bytesPerElement = require( '@stdlib/ndarray-base-bytes-per-element' );
var Complex64Array = require( '@stdlib/array-complex64' );
var reinterpretComplex64 = require( '@stdlib/strided-base-reinterpret-complex64' );
var csrot = require( '@stdlib/blas-base-wasm-csrot' );

// Create a new memory instance with an initial size of 10 pages (320KiB) and a maximum size of 100 pages (6.4MiB):
var mem = new Memory({
    'initial': 10,
    'maximum': 100
});

// Create a BLAS routine:
var mod = new csrot.Module( mem );
// returns <Module>

// Initialize the routine:
mod.initializeSync();

// Define a vector data type:
var dtype = 'complex64';

// Specify a vector length:
var N = 5;

// Define pointers (i.e., byte offsets) for storing input vectors:
var cxptr = 0;
var cyptr = N * bytesPerElement( dtype );

// Write vector values to module memory:
var xbuf = oneTo( N*2, 'float32' );
var cx = new Complex64Array( xbuf.buffer );
mod.write( cxptr, cx );

var ybuf = ones( N*2, 'float32' );
var cy = new Complex64Array( ybuf.buffer );
mod.write( cyptr, cy );

// Perform computation:
mod.ndarray( N, cxptr, 1, 0, cyptr, 1, 0, 0.8, 0.6 );

// Read out the results:
var viewX = zeros( N, dtype );
var viewY = zeros( N, dtype );
mod.read( cxptr, viewX );
mod.read( cyptr, viewY );

console.log( reinterpretComplex64( viewX, 0 ) );
// => <Float32Array>[ ~1.4, ~2.2, 3.0, ~3.8, ~4.6, ~5.4, ~6.2, 7.0, ~7.8, ~8.6 ]

console.log( reinterpretComplex64( viewY, 0 ) );
// => <Float32Array>[ ~0.2, ~-0.4, -1.0, ~-1.6, ~-2.2, ~-2.8, ~-3.4, -4.0, ~-4.6, ~-5.2 ]
```

The function has the following additional parameters:

-   **ox**: starting index for `cx`.
-   **oy**: starting index for `cy`.

</section>

<!-- /.usage -->

<section class="notes">

* * *

## Notes

-   If `N <= 0`, `cx` and `cy` are left unchanged.
-   This package implements routines using WebAssembly. When provided arrays which are not allocated on a `csrot` module memory instance, data must be explicitly copied to module memory prior to computation. Data movement may entail a performance cost, and, thus, if you are using arrays external to module memory, you should prefer using [`@stdlib/blas-base/csrot`][@stdlib/blas/base/csrot]. However, if working with arrays which are allocated and explicitly managed on module memory, you can achieve better performance when compared to the pure JavaScript implementations found in [`@stdlib/blas/base/csrot`][@stdlib/blas/base/csrot]. Beware that such performance gains may come at the cost of additional complexity when having to perform manual memory management. Choosing between implementations depends heavily on the particular needs and constraints of your application, with no one choice universally better than the other.
-   `csrot()` corresponds to the [BLAS][blas] level 1 function [`csrot`][csrot].

</section>

<!-- /.notes -->

<section class="examples">

* * *

## Examples

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

```javascript
var oneTo = require( '@stdlib/array-one-to' );
var ones = require( '@stdlib/array-ones' );
var zeros = require( '@stdlib/array-zeros' );
var Complex64Array = require( '@stdlib/array-complex64' );
var reinterpretComplex64 = require( '@stdlib/strided-base-reinterpret-complex64' );
var csrot = require( '@stdlib/blas-base-wasm-csrot' );

// Specify a vector length:
var N = 5;

var xbuf = oneTo( N*2, 'float32' );
var cx = new Complex64Array( xbuf.buffer );

var ybuf = ones( N*2, 'float32' );
var cy = new Complex64Array( ybuf.buffer );

// Perform computation:
csrot.ndarray( N, cx, 1, 0, cy, 1, 0, 0.8, 0.6 );

// Print the results:
console.log( reinterpretComplex64( cx, 0 ) );
// => <Float32Array>[ ~1.4, ~2.2, 3.0, ~3.8, ~4.6, ~5.4, ~6.2, 7.0, ~7.8, ~8.6 ]

console.log( reinterpretComplex64( cy, 0 ) );
// => <Float32Array>[ ~0.2, ~-0.4, -1.0, ~-1.6, ~-2.2, ~-2.8, ~-3.4, -4.0, ~-4.6, ~-5.2 ]
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

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

</section>

<!-- /.stdlib -->

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-wasm-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://www.npmjs.com/package/@stdlib/array-complex64

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