gcusumpw.js (1978B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2020 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var cusum = require( './ndarray.js' ); 24 25 26 // MAIN // 27 28 /** 29 * Computes the cumulative sum of strided array elements using pairwise summation. 30 * 31 * ## Method 32 * 33 * - This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`. 34 * 35 * ## References 36 * 37 * - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050). 38 * 39 * @param {PositiveInteger} N - number of indexed elements 40 * @param {number} sum - initial sum 41 * @param {NumericArray} x - input array 42 * @param {integer} strideX - `x` stride length 43 * @param {NumericArray} y - output array 44 * @param {integer} strideY - `y` stride length 45 * @returns {NumericArray} output array 46 * 47 * @example 48 * var x = [ 1.0, -2.0, 2.0 ]; 49 * var y = [ 0.0, 0.0, 0.0 ]; 50 * 51 * var v = gcusumpw( x.length, 0.0, x, 1, y, 1 ); 52 * // returns [ 1.0, -1.0, 1.0 ] 53 */ 54 function gcusumpw( N, sum, x, strideX, y, strideY ) { 55 var ix; 56 var iy; 57 58 if ( N <= 0 ) { 59 return y; 60 } 61 if ( strideX < 0 ) { 62 ix = (1-N) * strideX; 63 } else { 64 ix = 0; 65 } 66 if ( strideY < 0 ) { 67 iy = (1-N) * strideY; 68 } else { 69 iy = 0; 70 } 71 return cusum( N, sum, x, strideX, ix, y, strideY, iy ); 72 } 73 74 75 // EXPORTS // 76 77 module.exports = gcusumpw;