115 lines
2.6 KiB
Markdown
115 lines
2.6 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.
|
||
|
|
|
||
|
|
-->
|
||
|
|
|
||
|
|
# erf
|
||
|
|
|
||
|
|
> [Error function][error-function].
|
||
|
|
|
||
|
|
<section class="intro">
|
||
|
|
|
||
|
|
The [error function][error-function] is defined as
|
||
|
|
|
||
|
|
<!-- <equation class="equation" label="eq:error_function" align="center" raw="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" alt="Error function."> -->
|
||
|
|
|
||
|
|
<div class="equation" align="center" data-raw-text="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" data-equation="eq:error_function">
|
||
|
|
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/erf/docs/img/equation_error_function.svg" alt="Error function.">
|
||
|
|
<br>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- </equation> -->
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.intro -->
|
||
|
|
|
||
|
|
<section class="usage">
|
||
|
|
|
||
|
|
## Usage
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var erf = require( '@stdlib/math/base/special/erf' );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### erf( x )
|
||
|
|
|
||
|
|
Evaluates the [error function][error-function].
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var y = erf( 2.0 );
|
||
|
|
// returns ~0.9953
|
||
|
|
|
||
|
|
y = erf( -1.0 );
|
||
|
|
// returns ~-0.8427
|
||
|
|
```
|
||
|
|
|
||
|
|
If provided `NaN`, the function returns `NaN`.
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var y = erf( NaN );
|
||
|
|
// returns NaN
|
||
|
|
```
|
||
|
|
|
||
|
|
The [error function][error-function] is an [odd function][odd-function]; i.e., `erf(-x) = -erf(x)`. Thus, in accordance with the [IEEE 754][ieee754] standard, if provided `-0`, the function returns `-0`.
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var y = erf( -0.0 );
|
||
|
|
// returns -0.0
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.usage -->
|
||
|
|
|
||
|
|
<section class="examples">
|
||
|
|
|
||
|
|
## Examples
|
||
|
|
|
||
|
|
<!-- eslint no-undef: "error" -->
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var linspace = require( '@stdlib/array/linspace' );
|
||
|
|
var erf = require( '@stdlib/math/base/special/erf' );
|
||
|
|
|
||
|
|
var x = linspace( -10.0, 10.0, 100 );
|
||
|
|
var y;
|
||
|
|
var i;
|
||
|
|
|
||
|
|
for ( i = 0; i < x.length; i++ ) {
|
||
|
|
y = erf( x[ i ] );
|
||
|
|
console.log( 'x: %d, erf(x): %d', x[ i ], y );
|
||
|
|
}
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.examples -->
|
||
|
|
|
||
|
|
<section class="links">
|
||
|
|
|
||
|
|
[error-function]: https://en.wikipedia.org/wiki/Error_function
|
||
|
|
|
||
|
|
[odd-function]: https://en.wikipedia.org/wiki/Even_and_odd_functions
|
||
|
|
|
||
|
|
[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.links -->
|