erfinv

Inverse error function.

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

$$\mathop{\mathrm{erf}}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}$$

where c_0 = 1 and

$$c_k=\sum_{m=0}^{k-1}\frac{c_m c_{k-1-m}}{(m+1)(2m+1)} = \left\{1,1,\frac{7}{6},\frac{127}{90},\frac{4369}{2520},\frac{34807}{16200},\ldots\right\}$$

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 uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var erfinv = require( '@stdlib/math/base/special/erfinv' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, -1.0, 1.0, opts );

logEachMap( 'x: %0.4f, erfinv(x): %0.4f', x, erfinv );

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C APIs

Usage

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

stdlib_base_erfinv( x )

Evaluates the inverse error function.

double out = stdlib_base_erfinv( 0.5 );
// returns ~0.4769

out = stdlib_base_erfinv( 0.8 );
// returns ~0.9062

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_erfinv( const double x );

Examples

#include "stdlib/math/base/special/erfinv.h"
#include <stdlib.h>
#include <stdio.h>

int main() {
    const double x[] = { -1.0, -0.78, -0.56, -0.33, -0.11, 0.11, 0.33, 0.56, 0.78, 1.0 };
    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_erfinv( x[ i ] );
        printf( "x: %lf, erfinv(x): %lf\n", x[ i ], v );
    }
}

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See Also

• @stdlib/math/base/special/erf: error function.
• @stdlib/math/base/special/erfc: complementary error function.
• @stdlib/math/base/special/erfcinv: inverse complementary error function.