time-to-botec/js/node_modules/@stdlib/math/base/special/expit/README.md

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# expit
> 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="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 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 ) );
}
```
</section>
<!-- /.examples -->
<section class="links">
[logistic-function]: https://en.wikipedia.org/wiki/Logistic_function
</section>
<!-- /.links -->