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expit

Compute the standard logistic function.

The standard logistic function, also called the expit function, inverse logit, or sigmoid function, is defined as the logistic function with parameters (k = 1, x0 = 0, L = 1).

$$\begin{aligned}\mathop{\mathrm{expit}}(x) &= \frac{1}{1+e^{-x}} \\ &= \frac{e^{x}}{e^{x}+1} \\ &= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}$$

Installation

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

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

expit( x )

Computes the standard logistic function.

var v = expit( 0.0 );
// returns ~0.5

v = expit( 1.0 );
// returns ~0.731

v = expit( -1.0 );
// returns ~0.269

v = expit( Infinity );
// returns 1.0

v = expit( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var expit = require( '@stdlib/math-base-special-expit' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu();
    console.log( 'expit(%d) = %d', x, expit( x ) );
}

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C APIs

Usage

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

stdlib_base_expit( x )

Computes the standard logistic function.

double out = stdlib_base_expit( 0.0 );
// returns ~0.5

out = stdlib_base_expit( 1.0 );
// returns ~0.731

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_expit( const double x );

Examples

#include "stdlib/math/base/special/expit.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;
        v = stdlib_base_expit( x );
        printf( "expit(%lf) = %lf\n", x, v );
    }
}

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See Also

• @stdlib/math-base/special/exp: natural exponential function.
• @stdlib/math-base/special/logit: logit function.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.