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# logit

> Compute the [logit][logit] function.

<section class="intro">

The [logit][logit] function is defined as the logarithm of the odds `p / (1-p)`; i.e.,

<!-- <equation class="equation" label="eq:logit_function" align="center" raw="\operatorname{logit}(p)=\log \left({\frac {p}{1-p}}\right)" alt="Logit function."> -->

<div class="equation" align="center" data-raw-text="\operatorname{logit}(p)=\log \left({\frac {p}{1-p}}\right)" data-equation="eq:logit_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/logit/docs/img/equation_logit_function.svg" alt="Logit function.">
    <br>
</div>

<!-- </equation> -->

The [logit][logit] function is the inverse of the [standard logistic][standard-logistic] function, sometimes also called the sigmoid function. 

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### logit( p )

Computes the [logit][logit] function.

```javascript
var v = logit( 0.2 );
// returns ~-1.386

v = logit( 0.9 );
// returns ~2.197
```

If `p < 0` or `p > 1`, the function returns `NaN`.

```javascript
var v = logit( 1.3 );
// returns NaN

v = logit( -0.2 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var logit = require( '@stdlib/math/base/special/logit' );

var p;
var i;

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

</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/logit.h"
```

#### stdlib_base_logit( p )

Computes the [logit][logit] function.

```c
double out = stdlib_base_logit( 0.2 );
// returns ~-1.386

out = stdlib_base_logit( 0.9 );
// returns ~2.197
```

The function accepts the following arguments:

-   **p**: `[in] double` input value.

```c
double stdlib_base_logit( const double p ); 
```

</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/logit.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_logit( x );
        printf( "logit(%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">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[logit]: https://en.wikipedia.org/wiki/Logit

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

</section>

<!-- /.links -->
