110 lines
2.4 KiB
Markdown
110 lines
2.4 KiB
Markdown
|
<!--
|
||
|
|
|
||
|
|
@license Apache-2.0
|
||
|
|
|
||
|
|
Copyright (c) 2018 The Stdlib Authors.
|
||
|
|
|
||
|
|
Licensed under the Apache License, Version 2.0 (the "License");
|
||
|
|
you may not use this file except in compliance with the License.
|
||
|
|
You may obtain a copy of the License at
|
||
|
|
|
||
|
|
http://www.apache.org/licenses/LICENSE-2.0
|
||
|
|
|
||
|
|
Unless required by applicable law or agreed to in writing, software
|
||
|
|
distributed under the License is distributed on an "AS IS" BASIS,
|
||
|
|
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||
|
|
See the License for the specific language governing permissions and
|
||
|
|
limitations under the License.
|
||
|
|
|
||
|
|
-->
|
||
|
|
|
||
|
|
# 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 -->
|
||
|
|
|
||
|
|
<section class="links">
|
||
|
|
|
||
|
|
[logit]: https://en.wikipedia.org/wiki/Logit
|
||
|
|
|
||
|
|
[standard-logistic]: https://en.wikipedia.org/wiki/Logistic_function
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.links -->
|