erfinv

Inverse error function.

The inverse error function is defined in terms of the Maclaurin series

e r f Superscript negative 1 Baseline left-parenthesis z right-parenthesis equals sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction c Subscript k Baseline Over 2 k plus 1 EndFraction left-parenthesis StartFraction StartRoot pi EndRoot Over 2 EndFraction z right-parenthesis Superscript 2 k plus 1

where c_0 = 1 and

c Subscript k Baseline equals sigma-summation Underscript m equals 0 Overscript k minus 1 Endscripts StartFraction c Subscript m Baseline c Subscript k minus 1 minus m Baseline Over left-parenthesis m plus 1 right-parenthesis left-parenthesis 2 m plus 1 right-parenthesis EndFraction equals StartSet 1 comma 1 comma seven-sixths comma StartFraction 127 Over 90 EndFraction comma StartFraction 4369 Over 2520 EndFraction comma StartFraction 34807 Over 16200 EndFraction comma ellipsis EndSet

Usage

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

erfinv( x )

Evaluates the inverse error function.

var y = erfinv( 0.5 );
// returns ~0.4769

y = erfinv( 0.8 );
// returns ~0.9062

y = erfinv( -1.0 );
// returns -Infinity

y = erfinv( 1.0 );
// returns Infinity

The domain of x is restricted to [-1,1]. If |x| > 1, the function returns NaN.

var y = erfinv( -3.14 );
// returns NaN

If provided NaN, the function returns NaN.

var y = erfinv( NaN );
// returns NaN

The inverse error function is an odd function; i.e., erfinv(-x) = -erfinv(x). Thus, in accordance with the IEEE 754 standard, if provided -0, the function returns -0.

var y = erfinv( -0.0 );
// returns -0.0

Examples

var linspace = require( '@stdlib/math/utils/linspace' );
var erfinv = require( '@stdlib/math/base/special/erfinv' );

var x = linspace( -1.0, 1.0, 100 );
var y;
var i;

for ( i = 0; i < x.length; i++ ) {
    y = erfinv( x[ i ] );
    console.log( 'x: %d, erfinv(x): %d', x[ i ], y );
}