README.md (5258B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2020 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 # gnrm2 22 23 > Calculate the L2-norm of a vector. 24 25 <section class="intro"> 26 27 The [L2-norm][l2-norm] is defined as 28 29 <!-- <equation class="equation" label="eq:l2_norm" align="center raw="\|\mathbf{x}\|_2 = \sqrt{x_0^2 + x_1^2 + \ldots + x_{N-1}^2}" alt="L2-norm definition."> --> 30 31 <div class="equation" align="center" data-raw-text="\|\mathbf{x}\|_2 = \sqrt{x_0^2 + x_1^2 + \ldots + x_{N-1}^2}" data-equation="eq:l2_norm"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f8997c489e47eb1a9d993ef4ab3a522a095331f5/lib/node_modules/@stdlib/blas/base/gnrm2/docs/img/equation_l2_norm.svg" alt="L2-norm definition."> 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 gnrm2 = require( '@stdlib/blas/base/gnrm2' ); 48 ``` 49 50 #### gnrm2( N, x, stride ) 51 52 Computes the [L2-norm][l2-norm] of a vector `x`. 53 54 ```javascript 55 var x = [ 1.0, -2.0, 2.0 ]; 56 57 var z = gnrm2( x.length, x, 1 ); 58 // returns 3.0 59 ``` 60 61 The function has the following parameters: 62 63 - **N**: number of indexed elements. 64 - **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. 65 - **stride**: index increment for `x`. 66 67 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [L2-norm][l2-norm] of every other element in `x`, 68 69 ```javascript 70 var floor = require( '@stdlib/math/base/special/floor' ); 71 72 var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ]; 73 var N = floor( x.length / 2 ); 74 75 var z = gnrm2( N, x, 2 ); 76 // returns 5.0 77 ``` 78 79 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 80 81 <!-- eslint-disable stdlib/capitalized-comments --> 82 83 ```javascript 84 var Float64Array = require( '@stdlib/array/float64' ); 85 var floor = require( '@stdlib/math/base/special/floor' ); 86 87 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 88 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 89 90 var N = floor( x0.length / 2 ); 91 92 var z = gnrm2( N, x1, 2 ); 93 // returns 5.0 94 ``` 95 96 If either `N` or `stride` is less than or equal to `0`, the function returns `0`. 97 98 #### gnrm2.ndarray( N, x, stride, offset ) 99 100 Computes the [L2-norm][l2-norm] of a vector using alternative indexing semantics. 101 102 ```javascript 103 var x = [ 1.0, -2.0, 2.0 ]; 104 105 var z = gnrm2.ndarray( x.length, x, 1, 0 ); 106 // returns 3.0 107 ``` 108 109 The function has the following additional parameters: 110 111 - **offset**: starting index for `x`. 112 113 While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [L2-norm][l2-norm] for every other value in `x` starting from the second value 114 115 ```javascript 116 var floor = require( '@stdlib/math/base/special/floor' ); 117 118 var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; 119 var N = floor( x.length / 2 ); 120 121 var z = gnrm2.ndarray( N, x, 2, 1 ); 122 // returns 5.0 123 ``` 124 125 </section> 126 127 <!-- /.usage --> 128 129 <section class="notes"> 130 131 ## Notes 132 133 - If `N <= 0`, both functions return `0.0`. 134 - `gnrm2()` corresponds to the [BLAS][blas] level 1 function [`dnrm2`][dnrm2] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dnrm2`][@stdlib/blas/base/dnrm2], [`snrm2`][@stdlib/blas/base/snrm2], etc.) are likely to be significantly more performant. 135 136 </section> 137 138 <!-- /.notes --> 139 140 <section class="examples"> 141 142 ## Examples 143 144 <!-- eslint no-undef: "error" --> 145 146 ```javascript 147 var randu = require( '@stdlib/random/base/randu' ); 148 var round = require( '@stdlib/math/base/special/round' ); 149 var Float64Array = require( '@stdlib/array/float64' ); 150 var gnrm2 = require( '@stdlib/blas/base/gnrm2' ); 151 152 var x; 153 var i; 154 155 x = new Float64Array( 10 ); 156 for ( i = 0; i < x.length; i++ ) { 157 x[ i ] = round( randu()*100.0 ); 158 } 159 console.log( x ); 160 161 var z = gnrm2( x.length, x, 1 ); 162 console.log( z ); 163 ``` 164 165 </section> 166 167 <!-- /.examples --> 168 169 <section class="links"> 170 171 [l2-norm]: https://en.wikipedia.org/wiki/Euclidean_distance 172 173 [blas]: http://www.netlib.org/blas 174 175 [dnrm2]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html 176 177 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array 178 179 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 180 181 [@stdlib/blas/base/dnrm2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/dnrm2 182 183 [@stdlib/blas/base/snrm2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/snrm2 184 185 </section> 186 187 <!-- /.links -->