README.md (7526B)
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 # dsort2sh 22 23 > Simultaneously sort two double-precision floating-point strided arrays based on the sort order of the first array using Shellsort. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var dsort2sh = require( '@stdlib/blas/ext/base/dsort2sh' ); 31 ``` 32 33 #### dsort2sh( N, order, x, strideX, y, strideY ) 34 35 Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first 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 var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 42 43 dsort2sh( x.length, 1.0, x, 1, y, 1 ); 44 45 console.log( x ); 46 // => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ] 47 48 console.log( y ); 49 // => <Float64Array>[ 3.0, 1.0, 0.0, 2.0 ] 50 ``` 51 52 The function has the following parameters: 53 54 - **N**: number of indexed elements. 55 - **order**: sort order. If `order < 0.0`, the input strided array `x` is sorted in **decreasing** order. If `order > 0.0`, the input strided array `x` is sorted in **increasing** order. If `order == 0.0`, the input strided arrays are left unchanged. 56 - **x**: first input [`Float64Array`][@stdlib/array/float64]. 57 - **strideX**: `x` index increment. 58 - **y**: second input [`Float64Array`][@stdlib/array/float64]. 59 - **strideY**: `y` index increment. 60 61 The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to sort every other element 62 63 ```javascript 64 var Float64Array = require( '@stdlib/array/float64' ); 65 var floor = require( '@stdlib/math/base/special/floor' ); 66 67 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 68 var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 69 var N = floor( x.length / 2 ); 70 71 dsort2sh( N, -1.0, x, 2, y, 2 ); 72 73 console.log( x ); 74 // => <Float64Array>[ 3.0, -2.0, 1.0, -4.0 ] 75 76 console.log( y ); 77 // => <Float64Array>[ 2.0, 1.0, 0.0, 3.0 ] 78 ``` 79 80 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 81 82 ```javascript 83 var Float64Array = require( '@stdlib/array/float64' ); 84 var floor = require( '@stdlib/math/base/special/floor' ); 85 86 // Initial arrays... 87 var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); 88 var y0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 89 90 // Create offset views... 91 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 92 var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 93 var N = floor( x0.length/2 ); 94 95 // Sort every other element... 96 dsort2sh( N, -1.0, x1, 2, y1, 2 ); 97 98 console.log( x0 ); 99 // => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ] 100 101 console.log( y0 ); 102 // => <Float64Array>[ 0.0, 3.0, 2.0, 1.0 ] 103 ``` 104 105 #### dsort2sh.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY ) 106 107 Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first array `x` using Shellsort and alternative indexing semantics. 108 109 ```javascript 110 var Float64Array = require( '@stdlib/array/float64' ); 111 112 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 113 var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 114 115 dsort2sh.ndarray( x.length, 1.0, x, 1, 0, y, 1, 0 ); 116 117 console.log( x ); 118 // => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ] 119 120 console.log( y ); 121 // => <Float64Array>[ 3.0, 1.0, 0.0, 2.0 ] 122 ``` 123 124 The function has the following additional parameters: 125 126 - **offsetX**: `x` starting index. 127 - **offsetY**: `y` starting index. 128 129 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` 130 131 ```javascript 132 var Float64Array = require( '@stdlib/array/float64' ); 133 134 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] ); 135 var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] ); 136 137 dsort2sh.ndarray( 3, 1.0, x, 1, x.length-3, y, 1, y.length-3 ); 138 139 console.log( x ); 140 // => <Float64Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ] 141 142 console.log( y ); 143 // => <Float64Array>[ 0.0, 1.0, 2.0, 5.0, 3.0, 4.0 ] 144 ``` 145 146 </section> 147 148 <!-- /.usage --> 149 150 <section class="notes"> 151 152 ## Notes 153 154 - If `N <= 0` or `order == 0.0`, both functions leave `x` and `y` unchanged. 155 - 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`. 156 - 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. 157 - The algorithm has space complexity `O(1)` and worst case time complexity `O(N^(4/3))`. 158 - The algorithm is efficient for **shorter** strided arrays (typically `N <= 50`). 159 - 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). 160 - The input strided arrays are sorted **in-place** (i.e., the input strided arrays are **mutated**). 161 162 </section> 163 164 <!-- /.notes --> 165 166 <section class="examples"> 167 168 ## Examples 169 170 <!-- eslint no-undef: "error" --> 171 172 ```javascript 173 var round = require( '@stdlib/math/base/special/round' ); 174 var randu = require( '@stdlib/random/base/randu' ); 175 var Float64Array = require( '@stdlib/array/float64' ); 176 var dsort2sh = require( '@stdlib/blas/ext/base/dsort2sh' ); 177 178 var rand; 179 var sign; 180 var x; 181 var y; 182 var i; 183 184 x = new Float64Array( 10 ); 185 y = new Float64Array( 10 ); // index array 186 for ( i = 0; i < x.length; i++ ) { 187 rand = round( randu()*100.0 ); 188 sign = randu(); 189 if ( sign < 0.5 ) { 190 sign = -1.0; 191 } else { 192 sign = 1.0; 193 } 194 x[ i ] = sign * rand; 195 y[ i ] = i; 196 } 197 console.log( x ); 198 console.log( y ); 199 200 dsort2sh( x.length, -1.0, x, -1, y, -1 ); 201 console.log( x ); 202 console.log( y ); 203 ``` 204 205 </section> 206 207 <!-- /.examples --> 208 209 * * * 210 211 <section class="references"> 212 213 ## References 214 215 - 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]. 216 - 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]. 217 - 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]. 218 219 </section> 220 221 <!-- /.references --> 222 223 <section class="links"> 224 225 [@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64 226 227 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 228 229 [@shell:1959a]: https://doi.org/10.1145/368370.368387 230 231 [@sedgewick:1986a]: https://doi.org/10.1016/0196-6774(86)90001-5 232 233 [@ciura:2001a]: https://doi.org/10.1007/3-540-44669-9_12 234 235 </section> 236 237 <!-- /.links -->