124 lines
3.0 KiB
Markdown
124 lines
3.0 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.
|
||
|
|
|
||
|
|
-->
|
||
|
|
|
||
|
|
# cis
|
||
|
|
|
||
|
|
> Compute the [cis][cis] function of a complex number.
|
||
|
|
|
||
|
|
<section class="intro">
|
||
|
|
|
||
|
|
The [cis][cis] function is defined as
|
||
|
|
|
||
|
|
<!-- <equation class="equation" label="eq:cis_function" align="center" raw="\operatorname{cis}(z) = e^{iz} = \cos(z) + i \sin(z)" alt="cis function"> -->
|
||
|
|
|
||
|
|
<div class="equation" align="center" data-raw-text="\operatorname{cis}(z) = e^{iz} = \cos(z) + i \sin(z)" data-equation="eq:cis_function">
|
||
|
|
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/ccis/docs/img/equation_cis_function.svg" alt="cis function">
|
||
|
|
<br>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- </equation> -->
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.intro -->
|
||
|
|
|
||
|
|
<section class="usage">
|
||
|
|
|
||
|
|
## Usage
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var cis = require( '@stdlib/math/base/special/ccis' );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### cis( \[out,] re, im )
|
||
|
|
|
||
|
|
Evaluates the [cis][cis] function with a `complex` argument comprised of a **real** component `re` and an **imaginary** component `im`.
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var v = cis( 0.0, 0.0 );
|
||
|
|
// returns [ 1.0, 0.0 ]
|
||
|
|
|
||
|
|
v = cis( 1.0, 0.0 );
|
||
|
|
// returns [ ~0.540, ~0.841 ]
|
||
|
|
```
|
||
|
|
|
||
|
|
By default, the function returns real and imaginary components as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var Float64Array = require( '@stdlib/array/float64' );
|
||
|
|
|
||
|
|
var out = new Float64Array( 2 );
|
||
|
|
|
||
|
|
var v = cis( out, 1.0, 0.0 );
|
||
|
|
// returns <Float64Array>[ ~0.540, ~0.841 ]
|
||
|
|
|
||
|
|
var bool = ( v === out );
|
||
|
|
// returns true
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.usage -->
|
||
|
|
|
||
|
|
<section class="examples">
|
||
|
|
|
||
|
|
## Examples
|
||
|
|
|
||
|
|
<!-- eslint no-undef: "error" -->
|
||
|
|
|
||
|
|
```javascript
|
||
|
|
var Complex128 = require( '@stdlib/complex/float64' );
|
||
|
|
var randu = require( '@stdlib/random/base/randu' );
|
||
|
|
var round = require( '@stdlib/math/base/special/round' );
|
||
|
|
var real = require( '@stdlib/complex/real' );
|
||
|
|
var imag = require( '@stdlib/complex/imag' );
|
||
|
|
var cis = require( '@stdlib/math/base/special/ccis' );
|
||
|
|
|
||
|
|
var re;
|
||
|
|
var im;
|
||
|
|
var z1;
|
||
|
|
var z2;
|
||
|
|
var o;
|
||
|
|
var i;
|
||
|
|
|
||
|
|
for ( i = 0; i < 100; i++ ) {
|
||
|
|
re = round( randu()*100.0 ) - 50.0;
|
||
|
|
im = round( randu()*100.0 ) - 50.0;
|
||
|
|
z1 = new Complex128( re, im );
|
||
|
|
|
||
|
|
o = cis( [ 0.0, 0.0 ], real(z1), imag(z1) );
|
||
|
|
z2 = new Complex128( o[ 0 ], o[ 1 ] );
|
||
|
|
|
||
|
|
console.log( 'cis(%s) = %s', z1.toString(), z2.toString() );
|
||
|
|
}
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.examples -->
|
||
|
|
|
||
|
|
<section class="links">
|
||
|
|
|
||
|
|
[cis]: https://en.wikipedia.org/wiki/Cis_%28mathematics%29
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.links -->
|