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.

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Copyright

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