time-to-botec

Benchmark sampling in different programming languages
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README.md (4035B)

      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 # inv
     22 
     23 > Compute the inverse of a complex number.
     24 
     25 <section class="intro">
     26 
     27 The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined as
     28 
     29 <!-- <equation class="equation" label="eq:complex_inverse" align="center" raw="{\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i." alt="Complex Inverse" > -->
     30 
     31 <div class="equation" align="center" data-raw-text="{\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i." data-equation="eq:complex_inverse">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@026bc0ee34051ddb44f3222f620bc7a300b9799e/lib/node_modules/@stdlib/math/base/special/cinv/docs/img/equation_complex_inverse.svg" alt="Complex Inverse">
     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 cinv = require( '@stdlib/math/base/special/cinv' );
     48 ```
     49 
     50 #### cinv( \[out,] re1, im1 )
     51 
     52 Computes the inverse of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`.
     53 
     54 ```javascript
     55 var v = cinv( 2.0, 4.0 );
     56 // returns [ 0.1, -0.2 ]
     57 ```
     58 
     59 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.
     60 
     61 ```javascript
     62 var Float64Array = require( '@stdlib/array/float64' );
     63 
     64 var out = new Float64Array( 2 );
     65 
     66 var v = cinv( out, 2.0, 4.0 );
     67 // returns <Float64Array>[ 0.1, -0.2 ]
     68 
     69 var bool = ( v === out );
     70 // returns true
     71 ```
     72 
     73 </section>
     74 
     75 <!-- /.usage -->
     76 
     77 <section class="examples">
     78 
     79 ## Examples
     80 
     81 <!-- eslint no-undef: "error" -->
     82 
     83 ```javascript
     84 var Complex128 = require( '@stdlib/complex/float64' );
     85 var randu = require( '@stdlib/random/base/randu' );
     86 var round = require( '@stdlib/math/base/special/round' );
     87 var real = require( '@stdlib/complex/real' );
     88 var imag = require( '@stdlib/complex/imag' );
     89 var cinv = require( '@stdlib/math/base/special/cinv' );
     90 
     91 var re;
     92 var im;
     93 var z1;
     94 var z2;
     95 var o;
     96 var i;
     97 
     98 for ( i = 0; i < 100; i++ ) {
     99     re = round( randu()*100.0 ) - 50.0;
    100     im = round( randu()*100.0 ) - 50.0;
    101     z1 = new Complex128( re, im );
    102 
    103     o = cinv( real(z1), imag(z1) );
    104     z2 = new Complex128( o[ 0 ], o[ 1 ] );
    105 
    106     console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() );
    107 }
    108 ```
    109 
    110 </section>
    111 
    112 <!-- /.examples -->
    113 
    114 * * *
    115 
    116 <section class="references">
    117 
    118 ## References
    119 
    120 -   Smith, Robert L. 1962. "Algorithm 116: Complex Division." _Commun. ACM_ 5 (8). New York, NY, USA: ACM: 435. doi:[10.1145/368637.368661][@smith:1962a].
    121 -   Stewart, G. W. 1985. "A Note on Complex Division." _ACM Trans. Math. Softw._ 11 (3). New York, NY, USA: ACM: 238–41. doi:[10.1145/214408.214414][@stewart:1985a].
    122 -   Priest, Douglas M. 2004. "Efficient Scaling for Complex Division." _ACM Trans. Math. Softw._ 30 (4). New York, NY, USA: ACM: 389–401. doi:[10.1145/1039813.1039814][@priest:2004a].
    123 -   Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS] (October): 1–25. [&lt;https://arxiv.org/abs/1210.4539>][@baudin:2012a].
    124 
    125 </section>
    126 
    127 <!-- /.references -->
    128 
    129 <section class="links">
    130 
    131 [@smith:1962a]: https://doi.org/10.1145/368637.368661
    132 
    133 [@stewart:1985a]: https://doi.org/10.1145/214408.214414
    134 
    135 [@priest:2004a]: https://doi.org/10.1145/1039813.1039814
    136 
    137 [@baudin:2012a]: https://arxiv.org/abs/1210.4539
    138 
    139 </section>
    140 
    141 <!-- /.links -->