README.md (4952B)
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 # gapxsumkbn2 22 23 > Add a constant to each strided array element and compute the sum using a second-order iterative Kahan–Babuška algorithm. 24 25 <section class="intro"> 26 27 </section> 28 29 <!-- /.intro --> 30 31 <section class="usage"> 32 33 ## Usage 34 35 ```javascript 36 var gapxsumkbn2 = require( '@stdlib/blas/ext/base/gapxsumkbn2' ); 37 ``` 38 39 #### gapxsumkbn2( N, alpha, x, stride ) 40 41 Adds a constant to each strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm. 42 43 ```javascript 44 var x = [ 1.0, -2.0, 2.0 ]; 45 var N = x.length; 46 47 var v = gapxsumkbn2( N, 5.0, x, 1 ); 48 // returns 16.0 49 ``` 50 51 The function has the following parameters: 52 53 - **N**: number of indexed elements. 54 - **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. 55 - **stride**: index increment for `x`. 56 57 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to access every other element in `x`, 58 59 ```javascript 60 var floor = require( '@stdlib/math/base/special/floor' ); 61 62 var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ]; 63 var N = floor( x.length / 2 ); 64 65 var v = gapxsumkbn2( N, 5.0, x, 2 ); 66 // returns 25.0 67 ``` 68 69 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 70 71 <!-- eslint-disable stdlib/capitalized-comments --> 72 73 ```javascript 74 var Float64Array = require( '@stdlib/array/float64' ); 75 var floor = require( '@stdlib/math/base/special/floor' ); 76 77 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 78 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 79 80 var N = floor( x0.length / 2 ); 81 82 var v = gapxsumkbn2( N, 5.0, x1, 2 ); 83 // returns 25.0 84 ``` 85 86 #### gapxsumkbn2.ndarray( N, alpha, x, stride, offset ) 87 88 Adds a constant to each strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics. 89 90 ```javascript 91 var x = [ 1.0, -2.0, 2.0 ]; 92 var N = x.length; 93 94 var v = gapxsumkbn2.ndarray( N, 5.0, x, 1, 0 ); 95 // returns 16.0 96 ``` 97 98 The function has the following additional parameters: 99 100 - **offset**: starting index for `x`. 101 102 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 access every other value in `x` starting from the second value 103 104 ```javascript 105 var floor = require( '@stdlib/math/base/special/floor' ); 106 107 var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; 108 var N = floor( x.length / 2 ); 109 110 var v = gapxsumkbn2.ndarray( N, 5.0, x, 2, 1 ); 111 // returns 25.0 112 ``` 113 114 </section> 115 116 <!-- /.usage --> 117 118 <section class="notes"> 119 120 ## Notes 121 122 - If `N <= 0`, both functions return `0.0`. 123 - Depending on the environment, the typed versions ([`dapxsumkbn2`][@stdlib/blas/ext/base/dapxsumkbn2], [`sapxsumkbn2`][@stdlib/blas/ext/base/sapxsumkbn2], etc.) are likely to be significantly more performant. 124 125 </section> 126 127 <!-- /.notes --> 128 129 <section class="examples"> 130 131 ## Examples 132 133 <!-- eslint no-undef: "error" --> 134 135 ```javascript 136 var randu = require( '@stdlib/random/base/randu' ); 137 var round = require( '@stdlib/math/base/special/round' ); 138 var Float64Array = require( '@stdlib/array/float64' ); 139 var gapxsumkbn2 = require( '@stdlib/blas/ext/base/gapxsumkbn2' ); 140 141 var x; 142 var i; 143 144 x = new Float64Array( 10 ); 145 for ( i = 0; i < x.length; i++ ) { 146 x[ i ] = round( randu()*100.0 ); 147 } 148 console.log( x ); 149 150 var v = gapxsumkbn2( x.length, 5.0, x, 1 ); 151 console.log( v ); 152 ``` 153 154 </section> 155 156 <!-- /.examples --> 157 158 * * * 159 160 <section class="references"> 161 162 ## References 163 164 - Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a]. 165 166 </section> 167 168 <!-- /.references --> 169 170 <section class="links"> 171 172 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array 173 174 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 175 176 [@stdlib/blas/ext/base/dapxsumkbn2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/dapxsumkbn2 177 178 [@stdlib/blas/ext/base/sapxsumkbn2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/sapxsumkbn2 179 180 [@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x 181 182 </section> 183 184 <!-- /.links -->