README.md (6190B)
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 # dsortsh 22 23 > Sort a double-precision floating-point strided array using Shellsort. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var dsortsh = require( '@stdlib/blas/ext/base/dsortsh' ); 31 ``` 32 33 #### dsortsh( N, order, x, stride ) 34 35 Sorts a double-precision floating-point strided array `x` using Shellsort. 36 37 ```javascript 38 var Float64Array = require( '@stdlib/array/float64' ); 39 40 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 41 42 dsortsh( x.length, 1.0, x, 1 ); 43 // x => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ] 44 ``` 45 46 The function has the following parameters: 47 48 - **N**: number of indexed elements. 49 - **order**: sort order. If `order < 0.0`, the input strided array is sorted in **decreasing** order. If `order > 0.0`, the input strided array is sorted in **increasing** order. If `order == 0.0`, the input strided array is left unchanged. 50 - **x**: input [`Float64Array`][@stdlib/array/float64]. 51 - **stride**: index increment. 52 53 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to sort every other element 54 55 ```javascript 56 var Float64Array = require( '@stdlib/array/float64' ); 57 var floor = require( '@stdlib/math/base/special/floor' ); 58 59 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 60 var N = floor( x.length / 2 ); 61 62 dsortsh( N, -1.0, x, 2 ); 63 // x => <Float64Array>[ 3.0, -2.0, 1.0, -4.0 ] 64 ``` 65 66 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 67 68 ```javascript 69 var Float64Array = require( '@stdlib/array/float64' ); 70 var floor = require( '@stdlib/math/base/special/floor' ); 71 72 // Initial array... 73 var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); 74 75 // Create an offset view... 76 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 77 var N = floor( x0.length/2 ); 78 79 // Sort every other element... 80 dsortsh( N, -1.0, x1, 2 ); 81 // x0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ] 82 ``` 83 84 #### dsortsh.ndarray( N, order, x, stride, offset ) 85 86 Sorts a double-precision floating-point strided array `x` using Shellsort and alternative indexing semantics. 87 88 ```javascript 89 var Float64Array = require( '@stdlib/array/float64' ); 90 91 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 92 93 dsortsh.ndarray( x.length, 1.0, x, 1, 0 ); 94 // x => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ] 95 ``` 96 97 The function has the following additional parameters: 98 99 - **offset**: starting index. 100 101 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 only the last three elements of `x` 102 103 ```javascript 104 var Float64Array = require( '@stdlib/array/float64' ); 105 106 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] ); 107 108 dsortsh.ndarray( 3, 1.0, x, 1, x.length-3 ); 109 // x => <Float64Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ] 110 ``` 111 112 </section> 113 114 <!-- /.usage --> 115 116 <section class="notes"> 117 118 ## Notes 119 120 - If `N <= 0` or `order == 0.0`, both functions return `x` unchanged. 121 - The algorithm distinguishes between `-0` and `+0`. When sorted in increasing order, `-0` is sorted before `+0`. When sorted in decreasing order, `-0` is sorted after `+0`. 122 - The algorithm sorts `NaN` values to the end. When sorted in increasing order, `NaN` values are sorted last. When sorted in decreasing order, `NaN` values are sorted first. 123 - The algorithm has space complexity `O(1)` and worst case time complexity `O(N^(4/3))`. 124 - The algorithm is efficient for **shorter** strided arrays (typically `N <= 50`). 125 - The algorithm is **unstable**, meaning that the algorithm may change the order of strided array elements which are equal or equivalent (e.g., `NaN` values). 126 - The input strided array is sorted **in-place** (i.e., the input strided array is **mutated**). 127 128 </section> 129 130 <!-- /.notes --> 131 132 <section class="examples"> 133 134 ## Examples 135 136 <!-- eslint no-undef: "error" --> 137 138 ```javascript 139 var round = require( '@stdlib/math/base/special/round' ); 140 var randu = require( '@stdlib/random/base/randu' ); 141 var Float64Array = require( '@stdlib/array/float64' ); 142 var dsortsh = require( '@stdlib/blas/ext/base/dsortsh' ); 143 144 var rand; 145 var sign; 146 var x; 147 var i; 148 149 x = new Float64Array( 10 ); 150 for ( i = 0; i < x.length; i++ ) { 151 rand = round( randu()*100.0 ); 152 sign = randu(); 153 if ( sign < 0.5 ) { 154 sign = -1.0; 155 } else { 156 sign = 1.0; 157 } 158 x[ i ] = sign * rand; 159 } 160 console.log( x ); 161 162 dsortsh( x.length, -1.0, x, -1 ); 163 console.log( x ); 164 ``` 165 166 </section> 167 168 <!-- /.examples --> 169 170 * * * 171 172 <section class="references"> 173 174 ## References 175 176 - Shell, Donald L. 1959. "A High-Speed Sorting Procedure." _Communications of the ACM_ 2 (7). Association for Computing Machinery: 30–32. doi:[10.1145/368370.368387][@shell:1959a]. 177 - Sedgewick, Robert. 1986. "A new upper bound for Shellsort." _Journal of Algorithms_ 7 (2): 159–73. doi:[10.1016/0196-6774(86)90001-5][@sedgewick:1986a]. 178 - Ciura, Marcin. 2001. "Best Increments for the Average Case of Shellsort." In _Fundamentals of Computation Theory_, 106–17. Springer Berlin Heidelberg. doi:[10.1007/3-540-44669-9_12][@ciura:2001a]. 179 180 </section> 181 182 <!-- /.references --> 183 184 <section class="links"> 185 186 [@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64 187 188 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 189 190 [@shell:1959a]: https://doi.org/10.1145/368370.368387 191 192 [@sedgewick:1986a]: https://doi.org/10.1016/0196-6774(86)90001-5 193 194 [@ciura:2001a]: https://doi.org/10.1007/3-540-44669-9_12 195 196 </section> 197 198 <!-- /.links -->