stdlib-js/math-base-special-erfinv

Inverse error function.

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

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

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

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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.

Community

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.