gammasgn

Sign of the gamma function.

The sign of the gamma-function is defined as

The gamma function can be computed as the product of gammasgn(x) and exp(gammaln(x)).

Installation

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

Usage

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

gammasgn( x )

Returns the sign of the gamma function.

var v = gammasgn( 1.0 );
// returns 1.0

v = gammasgn( -2.5 );
// returns -1.0

v = gammasgn( 0.0 );
// returns 0.0

v = gammasgn( NaN );
// returns NaN

Notes

• The gamma function is not defined for negative integer values (i.e., gamma(x) === NaN when x is a negative integer). The natural logarithm of the gamma function is defined for negative integer values (i.e., gammaln(x) === Infinity when x is a negative integer). Accordingly, in order for the equality gamma(x) === gammasgn(x) * exp(gammaln(x)) to hold (i.e., return NaN), gammasgn needs to either return NaN or 0. By convention, this function returns 0.

Examples

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

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

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

C APIs

Usage

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

stdlib_base_gammasgn( x )

Returns the sign of the gamma-function.

double out = stdlib_base_gammasgn( 1.0 );
// returns 1.0

out = stdlib_base_gammasgn( -2.5 );
// returns -1.0

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_gammasgn( const double x );

Examples

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

int main( void ) {
    double x;
    double v;
    int i;
    
    for ( i = 0; i < 100; i++ ) {
        x = ( (double)rand() / (double)RAND_MAX ) * 100.0;
        v = stdlib_base_gammasgn( x );
        printf( "gammasgn%lf = %lf\n", x, v );
    }
}

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.