erfc

Complementary error function.

The complementary error function is defined as

The complementary error function can also be expressed using Craig's formula

Installation

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

Usage

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

erfc( x )

Evaluates the complementary error function.

var y = erfc( 2.0 );
// returns ~0.0047

y = erfc( -1.0 );
// returns ~1.8427

y = erfc( Infinity );
// returns 0.0

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

If provided NaN, the function returns NaN.

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

Examples

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

var x = linspace( -10.0, 10.0, 100 );

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

C APIs

Usage

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

stdlib_base_erfc( x )

Evaluates the complementary error function.

double out = stdlib_base_erfc( 2.0 );
// returns ~0.0047

out = stdlib_base_erfc( -1.0 );
// returns ~1.8427

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_erfc( const double x );

Examples

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

int main( void ) {
    const double x[] = { -10.0, -7.78, -5.56, -3.33, -1.11, 1.11, 3.33, 5.56, 7.78, 10.0 };
    
    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_erfc( x[ i ] );
        printf( "x: %lf, erfc(x): %lf\n", x[ i ], v );
    }
}

See Also

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