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https://github.com/stdlib-js/math-base-special-cabs2

Compute the squared absolute value of a complex number.
https://github.com/stdlib-js/math-base-special-cabs2

abs2 absolute cabs2 cmplx complex distance javascript magnitude math mathematics node node-js nodejs number squared stdlib

Last synced: 3 months ago
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Compute the squared absolute value of a complex number.

Host: GitHub
URL: https://github.com/stdlib-js/math-base-special-cabs2
Owner: stdlib-js
License: apache-2.0
Created: 2021-06-08T13:46:10.000Z (over 3 years ago)
Default Branch: main
Last Pushed: 2024-10-01T09:59:50.000Z (3 months ago)
Last Synced: 2024-10-12T20:04:47.992Z (3 months ago)
Topics: abs2, absolute, cabs2, cmplx, complex, distance, javascript, magnitude, math, mathematics, node, node-js, nodejs, number, squared, stdlib
Language: Python
Homepage: https://github.com/stdlib-js/stdlib
Size: 525 KB
Stars: 1
Watchers: 3
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md

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README

        

  

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# cabs2

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

> Compute the squared [absolute value][absolute-value] of a double-precision [complex][@stdlib/complex/float64/ctor] floating-point number.

The [absolute value][absolute-value] of a [complex][@stdlib/complex/float64/ctor] number is defined as

```math

|a + bi| = \sqrt{a^2 + b^2}

```

which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.

## Installation

```bash

npm install @stdlib/math-base-special-cabs2

```

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 cabs2 = require( '@stdlib/math-base-special-cabs2' );

```

#### cabs2( z )

Computes the squared [absolute value][absolute-value] of a double-precision [complex][@stdlib/complex/float64/ctor] floating-point number.

```javascript

var Complex128 = require( '@stdlib/complex-float64-ctor' );

var y = cabs2( new Complex128( 5.0, 3.0 ) );

// returns 34.0

```

## Notes

-   Be careful to avoid overflow and underflow.

-   Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a [complex][@stdlib/complex/float64/ctor] number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].

## Examples

```javascript

var Complex128 = require( '@stdlib/complex-float64-ctor' );

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' ).factory;

var cabs2 = require( '@stdlib/math-base-special-cabs2' );

// Create a PRNG to generate uniformly distributed pseudorandom integers:

var rand = discreteUniform( -50, 50 );

// Compute the squared absolute value for a set of random numbers...

var z;

var i;

for ( i = 0; i < 100; i++ ) {

    z = new Complex128( rand(), rand() );

    console.log( 'cabs2(%s) = %d', z.toString(), cabs2( z ) );

}

```

* * *

## C APIs

### Usage

```c

#include "stdlib/math/base/special/cabs2.h"

```

#### stdlib_base_cabs2( z )

Computes the squared [absolute value][absolute-value] of a double-precision complex floating-point number.

```c

#include "stdlib/complex/float64/ctor.h"

stdlib_complex128_t z = stdlib_complex128( 5.0, 3.0 );

double y = stdlib_base_cabs2( z );

// returns 34.0

```

The function accepts the following arguments:

-   **z**: `[in] stdlib_complex128_t` input value.

```c

double stdlib_base_cabs2( const stdlib_complex128_t z );

```

### Examples

```c

#include "stdlib/math/base/special/cabs2.h"

#include "stdlib/complex/float64/ctor.h"

#include "stdlib/complex/float64/reim.h"

#include 

int main( void ) {

    const stdlib_complex128_t x[] = {

        stdlib_complex128( 3.14, 1.0 ),

        stdlib_complex128( -3.14, -1.0 ),

        stdlib_complex128( 0.0, 0.0 ),

        stdlib_complex128( 0.0/0.0, 0.0/0.0 )

    };

    stdlib_complex128_t v;

    double re;

    double im;

    double y;

    int i;

    for ( i = 0; i < 4; i++ ) {

        v = x[ i ];

        y = stdlib_base_cabs2( v );

        stdlib_complex128_reim( v, &re, &im );

        printf( "f(%lf + %lf) = %lf\n", re, im, y );

    }

}

```

* * *

## See Also

-   [`@stdlib/math-base/special/cabs`][@stdlib/math/base/special/cabs]: compute the absolute value of a double-precision complex floating-point number.

-   [`@stdlib/math-base/special/abs2`][@stdlib/math/base/special/abs2]: compute the squared absolute value of a double-precision floating-point number.

* * *

## 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/math-base-special-cabs2.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-cabs2

[test-image]: https://github.com/stdlib-js/math-base-special-cabs2/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-special-cabs2/actions/workflows/test.yml?query=branch:main

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-cabs2/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-cabs2?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/math-base-special-cabs2/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-special-cabs2/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-special-cabs2/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-special-cabs2/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-special-cabs2/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-special-cabs2/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-special-cabs2/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-cabs2/main/LICENSE

[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value

[@stdlib/math/base/special/cabs]: https://github.com/stdlib-js/math-base-special-cabs

[@stdlib/complex/float64/ctor]: https://github.com/stdlib-js/complex-float64-ctor

[@stdlib/math/base/special/abs2]: https://github.com/stdlib-js/math-base-special-abs2