time-to-botec

Benchmark sampling in different programming languages
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README.md (3217B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
     10 
     11    http://www.apache.org/licenses/LICENSE-2.0
     12 
     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
     18 
     19 -->
     20 
     21 # exp
     22 
     23 > Compute the [exponential][exponential-function] function of a complex number.
     24 
     25 <section class="intro"> 
     26 
     27 The [exponential][exponential-function] function of a complex number is defined as
     28 
     29 <!-- <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"> -->
     30 
     31 <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">
     32     <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">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 </section>
     39 
     40 <!-- /.intro -->
     41 
     42 <section class="usage">
     43 
     44 ## Usage
     45 
     46 ```javascript
     47 var cexp = require( '@stdlib/math/base/special/cexp' );
     48 ```
     49 
     50 #### cexp( \[out,] re, im )
     51 
     52 Evaluates the [exponential][exponential-function] function with a `complex` argument comprised of a **real** component `re` and an **imaginary** component `im`.
     53 
     54 ```javascript
     55 var v = cexp( 0.0, 0.0 );
     56 // returns [ 1.0, 0.0 ]
     57 
     58 v = cexp( 0.0, 1.0 );
     59 // returns [ ~0.540, ~0.841 ]
     60 ```
     61 
     62 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.
     63 
     64 ```javascript
     65 var Float64Array = require( '@stdlib/array/float64' );
     66 
     67 var out = new Float64Array( 2 );
     68 
     69 var v = cexp( out, 0.0, 1.0 );
     70 // returns <Float64Array>[ ~0.540, ~0.841 ]
     71 
     72 var bool = ( v === out );
     73 // returns true
     74 ```
     75 
     76 </section>
     77 
     78 <!-- /.usage -->
     79 
     80 <section class="examples">
     81 
     82 ## Examples
     83 
     84 <!-- eslint no-undef: "error" -->
     85 
     86 ```javascript
     87 var Complex128 = require( '@stdlib/complex/float64' );
     88 var randu = require( '@stdlib/random/base/randu' );
     89 var round = require( '@stdlib/math/base/special/round' );
     90 var real = require( '@stdlib/complex/real' );
     91 var imag = require( '@stdlib/complex/imag' );
     92 var cexp = require( '@stdlib/math/base/special/cexp' );
     93 
     94 var re;
     95 var im;
     96 var z1;
     97 var z2;
     98 var o;
     99 var i;
    100 
    101 for ( i = 0; i < 100; i++ ) {
    102     re = round( randu()*100.0 ) - 50.0;
    103     im = round( randu()*100.0 ) - 50.0;
    104     z1 = new Complex128( re, im );
    105 
    106     o = cexp( real(z1), imag(z1) );
    107     z2 = new Complex128( o[ 0 ], o[ 1 ] );
    108 
    109     console.log( 'cexp(%s) = %s', z1.toString(), z2.toString() );
    110 }
    111 ```
    112 
    113 </section>
    114 
    115 <!-- /.examples -->
    116 
    117 <section class="links">
    118 
    119 [exponential-function]: https://en.wikipedia.org/wiki/Exponential_function
    120 
    121 </section>
    122 
    123 <!-- /.links -->