erfinv

Inverse error function.

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

where c_0 = 1 and

Installation

npm install @stdlib/math-base-special-erfinv

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

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

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

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 );
    }
}

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.

Notice

This package is part of 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, see the main project repository.

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Copyright

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