npm package: @stdlib/math-base-special-expit
Description: Standard logistic function.
Author: The Stdlib Authors
Latest version: 0.2.4

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# expit

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the [standard logistic][logistic-function] function.

<section class="intro">

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

<!-- <equation class="equation" label="eq:expit_function" align="center" raw="\begin{aligned}\operatorname{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}" alt="Standard logistic function."> -->

<div class="equation" align="center" data-raw-text="\begin{aligned}\operatorname{expit}(x) &amp;= \frac{1}{1+e^{-x}} \\ &amp;= \frac{e^{x}}{e^{x}+1} \\ &amp;= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}" data-equation="eq:expit_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@011d8b8e35ceb466ad31f5484e176ccaeaa087a2/lib/node_modules/@stdlib/math/base/special/expit/docs/img/equation_expit_function.svg" alt="Standard logistic function.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### expit( x )

Computes the [standard logistic][logistic-function] function.

```javascript
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
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var expit = require( '@stdlib/math-base-special-expit' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, 0.0, 1.0, opts );

logEachMap( 'expit(%0.4f) = %0.4f', x, expit );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_expit( x )

Computes the [standard logistic][logistic-function] function.

```c
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.

```c
double stdlib_base_expit( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#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 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/exp`][@stdlib/math/base/special/exp]</span><span class="delimiter">: </span><span class="description">natural exponential function.</span>
-   <span class="package-name">[`@stdlib/math-base/special/logit`][@stdlib/math/base/special/logit]</span><span class="delimiter">: </span><span class="description">logit function.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-expit/main/LICENSE

[logistic-function]: https://en.wikipedia.org/wiki/Logistic_function

<!-- <related-links> -->

[@stdlib/math/base/special/exp]: https://www.npmjs.com/package/@stdlib/math-base-special-exp

[@stdlib/math/base/special/logit]: https://www.npmjs.com/package/@stdlib/math-base-special-logit

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</section>

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