npm package: @stdlib/math-strided-special-rsqrt
Description: Compute the reciprocal square root for each element in a strided array.
Author: The Stdlib Authors
Latest version: 0.2.3

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# rsqrt

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

> Compute the [reciprocal square root][@stdlib/math/base/special/rsqrt] for each element in a strided array.

<section class="intro">

The reciprocal of the principal [square root][@stdlib/math/base/special/rsqrt] is defined as

<!-- <equation class="equation" label="eq:reciprocal_square_root" align="center" raw="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->

<div class="equation" align="center" data-raw-text="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aef240872db6f1b5417518bfaa8248004af4ffba/lib/node_modules/@stdlib/math/strided/special/rsqrt/docs/img/equation_reciprocal_square_root.svg" alt="Reciprocal square root">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-strided-special-rsqrt
```

</section>

<section class="usage">

## Usage

```javascript
var rsqrt = require( '@stdlib/math-strided-special-rsqrt' );
```

#### rsqrt( N, dtypeX, x, strideX, dtypeY, y, strideY )

Computes the [reciprocal square root][@stdlib/math/base/special/rsqrt] for each element in a strided array `x` and assigns the results to elements in a strided array `y`.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 0.0, 4.0, 9.0, 12.0, 24.0 ] );

// Perform operation in-place:
rsqrt( x.length, 'float64', x, 1, 'float64', x, 1 );
// x => <Float64Array>[ Infinity, 0.5, ~0.333, ~0.289, ~0.204 ]
```

The function accepts the following arguments:

-   **N**: number of indexed elements.
-   **dtypeX**: [data type][@stdlib/strided/dtypes] for `x`.
-   **x**: input array-like object.
-   **strideX**: index increment for `x`.
-   **dtypeY**: [data type][@stdlib/strided/dtypes] for `y`.
-   **y**: output array-like object.
-   **strideY**: index increment for `y`.

The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to index every other value in `x` and the first `N` elements of `y` in reverse order,

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 0.0, 4.0, 9.0, 12.0, 24.0, 64.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

rsqrt( 3, 'float64', x, 2, 'float64', y, -1 );
// y => <Float64Array>[ ~0.204, ~0.333, Infinity, 0.0, 0.0, 0.0 ]
```

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

```javascript
var Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 4.0, 9.0, 12.0, 24.0, 64.0 ] );
var y0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

rsqrt( 3, 'float64', x1, -2, 'float64', y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 0.125, ~0.289, 0.5 ]
```

#### rsqrt.ndarray( N, dtypeX, x, strideX, offsetX, dtypeY, y, strideY, offsetY )

Computes the [reciprocal square root][@stdlib/math/base/special/rsqrt] for each element in a strided array `x` and assigns the results to elements in a strided array `y` using alternative indexing semantics.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 0.0, 4.0, 9.0, 12.0, 24.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0 ] );

rsqrt.ndarray( x.length, 'float64', x, 1, 0, 'float64', y, 1, 0 );
// y => <Float64Array>[ Infinity, 0.5, ~0.333, ~0.289, ~0.204 ]
```

The function accepts the following additional arguments:

-   **offsetX**: starting index for `x`.
-   **offsetY**: starting index for `y`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offsetX` and `offsetY` parameters support indexing semantics based on starting indices. For example, to index every other value in `x` starting from the second value and to index the last `N` elements in `y`,

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 0.0, 4.0, 9.0, 12.0, 24.0, 64.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

rsqrt.ndarray( 3, 'float64', x, 2, 1, 'float64', y, -1, y.length-1 );
// y => <Float64Array>[ 0.0, 0.0, 0.0, 0.125, ~0.289, 0.5 ]
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var uniform = require( '@stdlib/random-base-uniform' ).factory;
var filledarray = require( '@stdlib/array-filled' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var dtypes = require( '@stdlib/array-typed-real-float-dtypes' );
var rsqrt = require( '@stdlib/math-strided-special-rsqrt' );

var dt;
var x;
var y;
var i;

dt = dtypes();
for ( i = 0; i < dt.length; i++ ) {
    x = filledarrayBy( 10, dt[ i ], uniform( 0.0, 100.0 ) );
    console.log( x );

    y = filledarray( 0.0, x.length, 'generic' );
    console.log( y );

    rsqrt.ndarray( x.length, dt[ i ], x, 1, 0, 'generic', y, -1, y.length-1 );
    console.log( y );
    console.log( '' );
}
```

</section>

<!-- /.examples -->

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

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-strided/special/drsqrt`][@stdlib/math/strided/special/drsqrt]</span><span class="delimiter">: </span><span class="description">compute the reciprocal square root for each element in a double-precision floating-point strided array.</span>
-   <span class="package-name">[`@stdlib/math-strided/special/sqrt`][@stdlib/math/strided/special/sqrt]</span><span class="delimiter">: </span><span class="description">compute the principal square root for each element in a strided array.</span>
-   <span class="package-name">[`@stdlib/math-strided/special/srsqrt`][@stdlib/math/strided/special/srsqrt]</span><span class="delimiter">: </span><span class="description">compute the reciprocal square root for each element in a single-precision floating-point strided array.</span>

</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>

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[@stdlib/math/base/special/rsqrt]: https://www.npmjs.com/package/@stdlib/math-base-special-rsqrt

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