105 lines
2.6 KiB
Markdown
105 lines
2.6 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2019 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# expit
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> Compute the [standard logistic][logistic-function] function.
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<section class="intro">
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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`).
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<!-- <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."> -->
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<div class="equation" align="center" data-raw-text="\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}" data-equation="eq:expit_function">
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<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.">
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<br>
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</div>
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var expit = require( '@stdlib/math/base/special/expit' );
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```
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#### expit( x )
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Computes the [standard logistic][logistic-function] function.
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```javascript
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var v = expit( 0.0 );
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// returns ~0.5
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v = expit( 1.0 );
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// returns ~0.731
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v = expit( -1.0 );
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// returns ~0.269
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v = expit( Infinity );
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// returns 1.0
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v = expit( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var expit = require( '@stdlib/math/base/special/expit' );
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var x;
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var i;
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for ( i = 0; i < 100; i++ ) {
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x = randu();
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console.log( 'expit(%d) = %d', x, expit( x ) );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[logistic-function]: https://en.wikipedia.org/wiki/Logistic_function
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</section>
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<!-- /.links -->
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