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https://github.com/stdlib-js/math-base-utils-relative-difference

Compute the relative difference of two real numbers.
https://github.com/stdlib-js/math-base-utils-relative-difference

abs diff difference dist distance error javascript math mathematics node node-js nodejs numbers relative stdlib

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Compute the relative difference of two real numbers.

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README 

        



  

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# Relative Difference



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



> Compute the [relative difference][relative-difference] of two real numbers.



The [relative difference][relative-difference] of two real `numbers` is defined as



```math

\Delta(x,y) = \frac{|x - y|}{|f(x,y)|} = \left|\frac{x - y}{f(x,y)}\right|

```



where `|x-y|` is the [absolute difference][@stdlib/math/base/utils/absolute-difference] and `f(x,y)` is a scale function. Common scale functions include



```math

\begin{align*}f(x,y) &= \max(|x|, |y|)\\f(x,y) &= \max(x,y)\\ f(x,y) &= \min(|x|,|y|)\\f(x,y) &= \min(x,y) \\f(x,y) &= \frac{|x|+|y|}{2} \\f(x,y) &= \frac{x + y}{2}\end{align*}

```



The choice of scale function depends on application context.



## Installation



```bash

npm install @stdlib/math-base-utils-relative-difference

```



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 reldiff = require( '@stdlib/math-base-utils-relative-difference' );

```



#### reldiff( x, y\[, scale] )



Computes the [relative difference][relative-difference] of two real numbers.



```javascript

var d = reldiff( 2.0, 5.0 ); // => 3/5

// returns 0.6



d = reldiff( -1.0, 3.14 ); // => 4.14/3.14

// returns ~1.318

```



The following `scale` functions are supported:



-   **max-abs**: maximum [absolute value][@stdlib/math/base/special/abs] of `x` and `y` (_default_).

-   **max**: maximum value of `x` and `y`.

-   **min-abs**: minimum [absolute value][@stdlib/math/base/special/abs] of `x` and `y`.

-   **min**: minimum value of `x` and `y`.

-   **mean-abs**: arithmetic mean of the [absolute values][@stdlib/math/base/special/abs] of `x` and `y`.

-   **mean**: arithmetic mean of `x` and `y`.

-   **x**: `x` (_noncommutative_).

-   **y**: `y` (_noncommutative_).



By default, the function scales the [absolute difference][@stdlib/math/base/utils/absolute-difference] by dividing the [absolute difference][@stdlib/math/base/utils/absolute-difference] by the maximum [absolute value][@stdlib/math/base/special/abs] of `x` and `y`. To scale by a different function, specify a scale function name.



```javascript

var d = reldiff( -2.0, 5.0 ); // => |-7/5|

// returns 1.4



d = reldiff( -2.0, 5.0, 'max-abs' ); // => |-7/5|

// returns 1.4



d = reldiff( -2.0, 5.0, 'max' ); // => |-7/5|

// returns 1.4



d = reldiff( -2.0, 5.0, 'min-abs' ); // => |-7/2|

// returns 3.5



d = reldiff( -2.0, 5.0, 'min' ); // => |-7/-2|

// returns 3.5



d = reldiff( -2.0, 5.0, 'mean-abs' ); // => |-7/3.5|

// returns 2.0



d = reldiff( -2.0, 5.0, 'mean' ); // => |-7/1.5|

// returns ~4.67



d = reldiff( -2.0, 5.0, 'x' ); // => |-7/-2|

// returns 3.5



d = reldiff( 5.0, -2.0, 'x' ); // => |7/5|

// returns 1.4



d = reldiff( -2.0, 5.0, 'y' ); // => |-7/5|

// returns 1.4



d = reldiff( 5.0, -2.0, 'y' ); // => |7/-2|

// returns 3.5

```



To use a custom scale `function`, provide a `function` which accepts two numeric arguments `x` and `y`.



```javascript

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

var EPS = require( '@stdlib/constants-float64-eps' );



function scale( x, y ) {

    var s;

    x = abs( x );

    y = abs( y );



    // Maximum absolute value:

    s = (x < y ) ? y : x;



    // Scale in units of epsilon:

    return s * EPS;

}



var d = reldiff( 12.15, 12.149999999999999, scale );

// returns ~0.658

```



## Notes



-   If the [absolute difference][@stdlib/math/base/utils/absolute-difference] of `x` and `y` is `0`, the relative difference is **always** `0`.



    ```javascript

    var d = reldiff( 0.0, 0.0 );

    // returns 0.0



    d = reldiff( 3.14, 3.14 );

    // returns 0.0

    ```



-   If `|x| = |y| = infinity`, the function returns `NaN`.



    ```javascript

    var d = reldiff( Infinity, Infinity );

    // returns NaN



    d = reldiff( -Infinity, -Infinity );

    // returns NaN

    ```



-   If `|x| = |-y| = infinity`, the relative difference is `+infinity`.



    ```javascript

    var d = reldiff( Infinity, -Infinity );

    // returns Infinity



    d = reldiff( -Infinity, Infinity );

    // returns Infinity

    ```



-   If a `scale` function returns `0`, the function returns `NaN`.



    ```javascript

    var d = reldiff( 0.0, 2.0, 'mean' ); // => |2/1|

    // returns 2.0



    d = reldiff( -1.0, 1.0, 'mean' ); // => |2/0|

    // returns NaN

    ```



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var reldiff = require( '@stdlib/math-base-utils-relative-difference' );



var scales = [ 'max-abs', 'max', 'min-abs', 'min', 'mean-abs', 'mean', 'x', 'y' ];

var x;

var y;

var d;

var i;

var j;



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

    x = ( randu()*1.0e4 ) - 5.0e3;

    y = ( randu()*1.0e4 ) - 5.0e3;

    for ( j = 0; j < scales.length; j++ ) {

        d = reldiff( x, y, scales[j] );

        console.log( 'x = %d. y = %d. d = %d. scale: %s.', x, y, d, scales[j] );

    }

}

```



* * *



## See Also



-   [`@stdlib/math-base/utils/absolute-difference`][@stdlib/math/base/utils/absolute-difference]: compute the absolute difference of two real numbers.

-   [`@stdlib/math-base/utils/float64-epsilon-difference`][@stdlib/math/base/utils/float64-epsilon-difference]: compute the relative difference of two real numbers in units of double-precision floating-point epsilon.



* * *



## 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-utils-relative-difference.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-utils-relative-difference



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

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



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

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-utils-relative-difference?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-utils-relative-difference/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-utils-relative-difference/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-utils-relative-difference/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-utils-relative-difference/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-utils-relative-difference/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-utils-relative-difference/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-utils-relative-difference/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-utils-relative-difference/main/LICENSE



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



[relative-difference]: https://en.wikipedia.org/wiki/Relative_change_and_difference



[@stdlib/math/base/utils/absolute-difference]: https://github.com/stdlib-js/math-base-utils-absolute-difference



[@stdlib/math/base/utils/float64-epsilon-difference]: https://github.com/stdlib-js/math-base-utils-float64-epsilon-difference