Relative Difference
Compute 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.
Usage
var reldiff = require( '@stdlib/math/base/utils/relative-difference' );
reldiff( x, y[, scale] )
Computes the relative difference of two real numbers.
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 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 = 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
.
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 of
x
andy
is0
, the relative difference is always0
.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 returnsNaN
.var d = reldiff( Infinity, Infinity ); // returns NaN d = reldiff( -Infinity, -Infinity ); // returns NaN
If
|x| = |-y| = infinity
, the relative difference is+infinity
.var d = reldiff( Infinity, -Infinity ); // returns Infinity d = reldiff( -Infinity, Infinity ); // returns Infinity
If a
scale
function returns0
, the function returnsNaN
.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
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] );
}
}