README.md (4884B)
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 # dapxsumkbn 22 23 > Add a constant to each double-precision floating-point strided array element and compute the sum using an improved 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 dapxsumkbn = require( '@stdlib/blas/ext/base/dapxsumkbn' ); 37 ``` 38 39 #### dapxsumkbn( N, alpha, x, stride ) 40 41 Adds a constant to each double-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm. 42 43 ```javascript 44 var Float64Array = require( '@stdlib/array/float64' ); 45 46 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); 47 var N = x.length; 48 49 var v = dapxsumkbn( N, 5.0, x, 1 ); 50 // returns 16.0 51 ``` 52 53 The function has the following parameters: 54 55 - **N**: number of indexed elements. 56 - **x**: input [`Float64Array`][@stdlib/array/float64]. 57 - **stride**: index increment for `x`. 58 59 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to access every other element in `x`, 60 61 ```javascript 62 var Float64Array = require( '@stdlib/array/float64' ); 63 var floor = require( '@stdlib/math/base/special/floor' ); 64 65 var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] ); 66 var N = floor( x.length / 2 ); 67 68 var v = dapxsumkbn( N, 5.0, x, 2 ); 69 // returns 25.0 70 ``` 71 72 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 73 74 <!-- eslint-disable stdlib/capitalized-comments --> 75 76 ```javascript 77 var Float64Array = require( '@stdlib/array/float64' ); 78 var floor = require( '@stdlib/math/base/special/floor' ); 79 80 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 81 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 82 83 var N = floor( x0.length / 2 ); 84 85 var v = dapxsumkbn( N, 5.0, x1, 2 ); 86 // returns 25.0 87 ``` 88 89 #### dapxsumkbn.ndarray( N, alpha, x, stride, offset ) 90 91 Adds a constant to each double-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm and alternative indexing semantics. 92 93 ```javascript 94 var Float64Array = require( '@stdlib/array/float64' ); 95 96 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); 97 var N = x.length; 98 99 var v = dapxsumkbn.ndarray( N, 5.0, x, 1, 0 ); 100 // returns 16.0 101 ``` 102 103 The function has the following additional parameters: 104 105 - **offset**: starting index for `x`. 106 107 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 108 109 ```javascript 110 var Float64Array = require( '@stdlib/array/float64' ); 111 var floor = require( '@stdlib/math/base/special/floor' ); 112 113 var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 114 var N = floor( x.length / 2 ); 115 116 var v = dapxsumkbn.ndarray( N, 5.0, x, 2, 1 ); 117 // returns 25.0 118 ``` 119 120 </section> 121 122 <!-- /.usage --> 123 124 <section class="notes"> 125 126 ## Notes 127 128 - If `N <= 0`, both functions return `0.0`. 129 130 </section> 131 132 <!-- /.notes --> 133 134 <section class="examples"> 135 136 ## Examples 137 138 <!-- eslint no-undef: "error" --> 139 140 ```javascript 141 var randu = require( '@stdlib/random/base/randu' ); 142 var round = require( '@stdlib/math/base/special/round' ); 143 var Float64Array = require( '@stdlib/array/float64' ); 144 var dapxsumkbn = require( '@stdlib/blas/ext/base/dapxsumkbn' ); 145 146 var x; 147 var i; 148 149 x = new Float64Array( 10 ); 150 for ( i = 0; i < x.length; i++ ) { 151 x[ i ] = round( randu()*100.0 ); 152 } 153 console.log( x ); 154 155 var v = dapxsumkbn( x.length, 5.0, x, 1 ); 156 console.log( v ); 157 ``` 158 159 </section> 160 161 <!-- /.examples --> 162 163 * * * 164 165 <section class="references"> 166 167 ## References 168 169 - Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a]. 170 171 </section> 172 173 <!-- /.references --> 174 175 <section class="links"> 176 177 [@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64 178 179 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 180 181 [@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106 182 183 </section> 184 185 <!-- /.links -->