Relative Difference
Computes the relative difference of two real numbers.
The relative difference of two real numbers
is defined as
where |x-y|
is the absolute difference and f(x,y)
is a scale function. Common scale functions include
The choice of scale function depends on application context.
Installation
$ npm install math-relative-difference
Usage
var diff = ;
diff( x, y[, scale] )
Computes the relative difference of two real numbers.
var d = ;// returns 3/5 = 0.6d = ;// returns 4.14/3.14 = ~1.318
The following scale
functions are supported:
- max-abs: maximum absolute value of
x
andy
(default). - max: maximum value of
x
andy
. - min-abs: minimum absolute value of
x
andy
. - min: minimum value of
x
andy
. - mean-abs: arithmetic mean of the absolute values of
x
andy
. - mean: arithmetic mean of
x
andy
. - x:
x
(noncommutative). - y:
y
(noncommutative).
By default, the function
scales the absolute difference by dividing the absolute difference by the maximum absolute value of x
and y
. To scale by a different function
, specify a scale function name.
var d = ;// returns |-7/5| = 1.4d = ;// returns |-7/5| = 1.4d =// returns |-7/5| = 1.4d = ;// returns |-7/2| = 3.5d = ;// returns |-7/-2| = 3.5d = ;// returns |-7/3.5| = 2d = ;// returns |-7/1.5| = ~4.67d = ;// returns |-7/-2| = 3.5d = ;// returns |7/5| = 1.4d = ;// returns |-7/5| = 1.4d = ;// returns |7/-2| = 3.5
To use a custom scale function
, provide a function
which accepts two numeric arguments x
and y
.
var abs = ;var EPS = ;{var s;x = ;y = ;// Maximum absolute value:s = x < y ? y : x;// Scale in units of epsilon:return s * EPS;}var d = ;// returns ~0.658
Notes
-
If the absolute difference of
x
andy
is0
, the relative difference is always0
.var d = ;// returns 0d = ;// returns 0 -
If
|x| = |y| = infinity
, the function returnsNaN
.var PINF = NumberPOSITIVE_INFINITY;var NINF = NumberNEGATIVE_INFINITY;var d = ;// returns NaNd = ;// returns NaN -
If
|x| = |-y| = infinity
, the relative difference is+infinity
.var PINF = NumberPOSITIVE_INFINITY;var NINF = NumberNEGATIVE_INFINITY;var d = ;// returns +infinityd = ;// returns +infinity -
If a
scale
function returns0
, the function returnsNaN
.var d = ;// returns |2/1| = 2d = ;// returns NaN => |2/0|
Examples
var diff = ;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 = Math*1e4 - 5e3;y = Math*1e4 - 5e3;for j = 0; j < scaleslength; j++d = ;console;
To run the example code from the top-level application directory,
$ node ./examples/index.js
Tests
Unit
This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
Test Coverage
This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:
$ make test-cov
Istanbul creates a ./reports/coverage
directory. To access an HTML version of the report,
$ make view-cov
Browser Support
This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:
$ make test-browsers
To view the tests in a local web browser,
$ make view-browser-tests
License
Copyright
Copyright © 2016. The Compute.io Authors.