README.md (7224B)
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 # ssort2hp 22 23 > Simultaneously sort two single-precision floating-point strided arrays based on the sort order of the first array using heapsort. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var ssort2hp = require( '@stdlib/blas/ext/base/ssort2hp' ); 31 ``` 32 33 #### ssort2hp( N, order, x, strideX, y, strideY ) 34 35 Simultaneously sorts two single-precision floating-point strided arrays based on the sort order of the first array `x` using heapsort. 36 37 ```javascript 38 var Float32Array = require( '@stdlib/array/float32' ); 39 40 var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 41 var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 42 43 ssort2hp( x.length, 1.0, x, 1, y, 1 ); 44 45 console.log( x ); 46 // => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ] 47 48 console.log( y ); 49 // => <Float32Array>[ 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 [`Float32Array`][@stdlib/array/float32]. 57 - **strideX**: `x` index increment. 58 - **y**: second input [`Float32Array`][@stdlib/array/float32]. 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 Float32Array = require( '@stdlib/array/float32' ); 65 var floor = require( '@stdlib/math/base/special/floor' ); 66 67 var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 68 var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 69 var N = floor( x.length / 2 ); 70 71 ssort2hp( N, -1.0, x, 2, y, 2 ); 72 73 console.log( x ); 74 // => <Float32Array>[ 3.0, -2.0, 1.0, -4.0 ] 75 76 console.log( y ); 77 // => <Float32Array>[ 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 Float32Array = require( '@stdlib/array/float32' ); 84 var floor = require( '@stdlib/math/base/special/floor' ); 85 86 // Initial arrays... 87 var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] ); 88 var y0 = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 89 90 // Create offset views... 91 var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 92 var y1 = new Float32Array( 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 ssort2hp( N, -1.0, x1, 2, y1, 2 ); 97 98 console.log( x0 ); 99 // => <Float32Array>[ 1.0, 4.0, 3.0, 2.0 ] 100 101 console.log( y0 ); 102 // => <Float32Array>[ 0.0, 3.0, 2.0, 1.0 ] 103 ``` 104 105 #### ssort2hp.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY ) 106 107 Simultaneously sorts two single-precision floating-point strided arrays based on the sort order of the first array `x` using heapsort and alternative indexing semantics. 108 109 ```javascript 110 var Float32Array = require( '@stdlib/array/float32' ); 111 112 var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] ); 113 var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] ); 114 115 ssort2hp.ndarray( x.length, 1.0, x, 1, 0, y, 1, 0 ); 116 117 console.log( x ); 118 // => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ] 119 120 console.log( y ); 121 // => <Float32Array>[ 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 Float32Array = require( '@stdlib/array/float32' ); 133 134 var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] ); 135 var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] ); 136 137 ssort2hp.ndarray( 3, 1.0, x, 1, x.length-3, y, 1, y.length-3 ); 138 139 console.log( x ); 140 // => <Float32Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ] 141 142 console.log( y ); 143 // => <Float32Array>[ 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 time complexity `O(N log2 N)`. 158 - 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). 159 - The input strided arrays are sorted **in-place** (i.e., the input strided arrays are **mutated**). 160 161 </section> 162 163 <!-- /.notes --> 164 165 <section class="examples"> 166 167 ## Examples 168 169 <!-- eslint no-undef: "error" --> 170 171 ```javascript 172 var round = require( '@stdlib/math/base/special/round' ); 173 var randu = require( '@stdlib/random/base/randu' ); 174 var Float32Array = require( '@stdlib/array/float32' ); 175 var ssort2hp = require( '@stdlib/blas/ext/base/ssort2hp' ); 176 177 var rand; 178 var sign; 179 var x; 180 var y; 181 var i; 182 183 x = new Float32Array( 10 ); 184 y = new Float32Array( 10 ); // index array 185 for ( i = 0; i < x.length; i++ ) { 186 rand = round( randu()*100.0 ); 187 sign = randu(); 188 if ( sign < 0.5 ) { 189 sign = -1.0; 190 } else { 191 sign = 1.0; 192 } 193 x[ i ] = sign * rand; 194 y[ i ] = i; 195 } 196 console.log( x ); 197 console.log( y ); 198 199 ssort2hp( x.length, -1.0, x, -1, y, -1 ); 200 console.log( x ); 201 console.log( y ); 202 ``` 203 204 </section> 205 206 <!-- /.examples --> 207 208 * * * 209 210 <section class="references"> 211 212 ## References 213 214 - Williams, John William Joseph. 1964. "Algorithm 232: Heapsort." _Communications of the ACM_ 7 (6). New York, NY, USA: Association for Computing Machinery: 347–49. doi:[10.1145/512274.512284][@williams:1964a]. 215 - Floyd, Robert W. 1964. "Algorithm 245: Treesort." _Communications of the ACM_ 7 (12). New York, NY, USA: Association for Computing Machinery: 701. doi:[10.1145/355588.365103][@floyd:1964a]. 216 217 </section> 218 219 <!-- /.references --> 220 221 <section class="links"> 222 223 [@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32 224 225 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 226 227 [@williams:1964a]: https://doi.org/10.1145/512274.512284 228 229 [@floyd:1964a]: https://doi.org/10.1145/355588.365103 230 231 </section> 232 233 <!-- /.links -->