@stdlib/math-base-special-erfcinv

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!

erfcinv

Inverse complementary error function.

The inverse complementary error function is defined as

where erf^{-1}(z) is the inverse error function.

Installation

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

Usage

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

erfcinv( x )

Evaluates the inverse complementary error function.

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

y = erfcinv( 0.8 );
// returns ~0.1791

y = erfcinv( 0.0 );
// returns Infinity

y = erfcinv( 2.0 );
// returns -Infinity

The domain of x is restricted to [0,2]. If x is outside this interval, the function returns NaN.

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

If provided NaN, the function returns NaN.

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

Examples

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

var x = linspace( 0.0, 2.0, 100 );

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

---

C APIs

Usage

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

stdlib_base_erfcinv( x )

Evaluates the inverse complementary error function.

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

out = stdlib_base_erfcinv( 0.8 );
// returns ~0.1791

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_erfcinv( const double x );

Examples

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

int main( void ) {
    const double x[] = { 0.0, 0.22, 0.44, 0.67, 0.89, 1.11, 1.33, 1.56, 1.78, 2.0 };
    
    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_erfcinv( x[ i ] );
        printf( "x: %lf, erfcinv(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/erfinv: inverse error function.
• @stdlib/math-base/special/erfcx: scaled 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.