124 lines
3.1 KiB
Markdown
124 lines
3.1 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2018 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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# exp
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> Compute the [exponential][exponential-function] function of a complex number.
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<section class="intro">
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The [exponential][exponential-function] function of a complex number is defined as
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<!-- <equation class="equation" label="eq:cexp_function" align="center" raw="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" alt="Complex exponential function"> -->
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<div class="equation" align="center" data-raw-text="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" data-equation="eq:cexp_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/cexp/docs/img/equation_cexp_function.svg" alt="Complex exponential 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 cexp = require( '@stdlib/math/base/special/cexp' );
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```
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#### cexp( \[out,] re, im )
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Evaluates the [exponential][exponential-function] function with a `complex` argument comprised of a **real** component `re` and an **imaginary** component `im`.
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```javascript
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var v = cexp( 0.0, 0.0 );
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// returns [ 1.0, 0.0 ]
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v = cexp( 0.0, 1.0 );
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// returns [ ~0.540, ~0.841 ]
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```
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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.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var out = new Float64Array( 2 );
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var v = cexp( out, 0.0, 1.0 );
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// returns <Float64Array>[ ~0.540, ~0.841 ]
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var bool = ( v === out );
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// returns true
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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 Complex128 = require( '@stdlib/complex/float64' );
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var real = require( '@stdlib/complex/real' );
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var imag = require( '@stdlib/complex/imag' );
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var cexp = require( '@stdlib/math/base/special/cexp' );
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var re;
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var im;
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var z1;
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var z2;
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var o;
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var i;
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for ( i = 0; i < 100; i++ ) {
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re = round( randu()*100.0 ) - 50.0;
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im = round( randu()*100.0 ) - 50.0;
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z1 = new Complex128( re, im );
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o = cexp( real(z1), imag(z1) );
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z2 = new Complex128( o[ 0 ], o[ 1 ] );
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console.log( 'cexp(%s) = %s', z1.toString(), z2.toString() );
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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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[exponential-function]: https://en.wikipedia.org/wiki/Exponential_function
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</section>
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<!-- /.links -->
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