time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

README.md (3207B)

      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 # Dirac Delta
     22 
     23 > Evaluate the [Dirac delta function][dirac-delta-function].
     24 
     25 <section class="intro">
     26 
     27 The [Dirac delta function][dirac-delta-function] may be loosely defined as
     28 
     29 <!-- <equation class="equation" label="eq:dirac_delta" align="center" raw="\delta = \begin{cases} \infty & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \neq 0\end{cases}" alt="Dirac delta function."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\delta = \begin{cases} \infty &amp; \textrm{if}\ x = 0 \\ 0 &amp; \textrm{if}\ x \neq 0\end{cases}" data-equation="eq:dirac_delta">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/dirac-delta/docs/img/equation_dirac_delta.svg" alt="Dirac delta function.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 and is constrained to satisfy the identity
     39 
     40 <!-- <equation class="equation" label="eq:dirac_delta_integral" align="center" raw="\int^{+\infty}_{-\infty} \delta(x)\ dx = 1" alt="Dirac delta function integral."> -->
     41 
     42 <div class="equation" align="center" data-raw-text="\int^{+\infty}_{-\infty} \delta(x)\ dx = 1" data-equation="eq:dirac_delta_integral">
     43     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/dirac-delta/docs/img/equation_dirac_delta_integral.svg" alt="Dirac delta function integral.">
     44     <br>
     45 </div>
     46 
     47 <!-- </equation> -->
     48 
     49 Note that the [Dirac delta function][dirac-delta-function] is **not** a function in the traditional sense, as any real-valued function which is zero everywhere except at a single point, must have an integral equal to `0`.
     50 
     51 </section>
     52 
     53 <!-- /.intro -->
     54 
     55 <section class="usage">
     56 
     57 ## Usage
     58 
     59 ```javascript
     60 var diracDelta = require( '@stdlib/math/base/special/dirac-delta' );
     61 ```
     62 
     63 #### diracDelta( x )
     64 
     65 Evaluates the [Dirac delta function][dirac-delta-function].
     66 
     67 ```javascript
     68 var v = diracDelta( 0.0 );
     69 // returns Infinity
     70 
     71 v = diracDelta( 3.14 );
     72 // returns 0.0
     73 
     74 v = diracDelta( NaN );
     75 // returns NaN
     76 ```
     77 
     78 </section>
     79 
     80 <!-- /.usage -->
     81 
     82 <section class="examples">
     83 
     84 ## Examples
     85 
     86 <!-- eslint no-undef: "error" -->
     87 
     88 ```javascript
     89 var linspace = require( '@stdlib/array/linspace' );
     90 var diracDelta = require( '@stdlib/math/base/special/dirac-delta' );
     91 
     92 var x = linspace( -1.0, 1.0, 101 );
     93 var i;
     94 
     95 for ( i = 0; i < x.length; i++ ) {
     96     console.log( 'dirac(%d) = %d', x[ i ], diracDelta( x[ i ] ) );
     97 }
     98 ```
     99 
    100 </section>
    101 
    102 <!-- /.examples -->
    103 
    104 <section class="links">
    105 
    106 [dirac-delta-function]: https://en.wikipedia.org/wiki/Dirac_delta_function
    107 
    108 </section>
    109 
    110 <!-- /.links -->