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rsqrt

Compute the reciprocal square root for each element in a strided array.

The reciprocal of the principal square root is defined as

$$\mathop{\mathrm{rsqrt}}(x)=\frac{1}{\sqrt{x}}$$

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

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

Computes the reciprocal square root for each element in a strided array x and assigns the results to elements in a strided array y.

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 for x.
• x: input array-like object.
• strideX: index increment for x.
• dtypeY: data type 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,

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 views.

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 for each element in a strided array x and assigns the results to elements in a strided array y using alternative indexing semantics.

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 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,

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 ]

Examples

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( '' );
}

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See Also

• @stdlib/math-strided/special/drsqrt: compute the reciprocal square root for each element in a double-precision floating-point strided array.
• @stdlib/math-strided/special/sqrt: compute the principal square root for each element in a strided array.
• @stdlib/math-strided/special/srsqrt: compute the reciprocal square root for each element in a single-precision floating-point strided array.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.