main.js (3044B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2019 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 /** 22 * Returns an accumulator function which incrementally computes a weighted arithmetic mean. 23 * 24 * ## Method 25 * 26 * - The weighted arithmetic mean is defined as 27 * 28 * ```tex 29 * \mu = \frac{\sum_{i=0}^{n-1} w_i x_i}{\sum_{i=0}^{n-1} w_i} 30 * ``` 31 * 32 * where \\( w_i \\) are the weights. 33 * 34 * - The weighted arithmetic mean is equivalent to the simple arithmetic mean when all weights are equal. 35 * 36 * ```tex 37 * \begin{align*} 38 * \mu &= \frac{\sum_{i=0}^{n-1} w x_i}{\sum_{i=0}^{n-1} w} \\ 39 * &= \frac{w\sum_{i=0}^{n-1} x_i}{nw} \\ 40 * &= \frac{1}{n} \sum_{i=0}^{n-1} 41 * \end{align*} 42 * ``` 43 * 44 * - If the weights are different, then one can view weights either as sample frequencies or as a means to calculate probabilities where \\( p_i = w_i / \sum w_i \\). 45 * 46 * - To derive an incremental formula for computing a weighted arithmetic mean, let 47 * 48 * ```tex 49 * W_n = \sum_{i=1}^{n} w_i 50 * ``` 51 * 52 * - Accordingly, 53 * 54 * ```tex 55 * \begin{align*} 56 * \mu_n &= \frac{1}{W_n} \sum_{i=1}^{n} w_i x_i \\ 57 * &= \frac{1}{W_n} \biggl(w_n x_n + \sum_{i=1}^{n-1} w_i x_i \biggr) \\ 58 * &= \frac{1}{W_n} (w_n x_n + W_{n-1} \mu_{n-1}) \\ 59 * &= \frac{1}{W_n} (w_n x_n + (W_n - w_n) \mu_{n-1}) \\ 60 * &= \frac{1}{W_n} (W_n \mu_{n-1} + w_n x_n - w_n\mu_{n-1}) \\ 61 * &= \mu_{n-1} + \frac{w_n}{W_n} (x_n - \mu_{n-1}) 62 * \end{align*} 63 * ``` 64 * 65 * @returns {Function} accumulator function 66 * 67 * @example 68 * var accumulator = incrwmean(); 69 * 70 * var mu = accumulator(); 71 * // returns null 72 * 73 * mu = accumulator( 2.0, 1.0 ); 74 * // returns 2.0 75 * 76 * mu = accumulator( 2.0, 0.5 ); 77 * // returns 2.0 78 * 79 * mu = accumulator( 3.0, 1.5 ); 80 * // returns 2.5 81 * 82 * mu = accumulator(); 83 * // returns 2.5 84 */ 85 function incrwmean() { 86 var wsum; 87 var FLG; 88 var mu; 89 90 wsum = 0.0; 91 mu = 0.0; 92 93 return accumulator; 94 95 /** 96 * If provided arguments, the accumulator function returns an updated weighted mean. If not provided arguments, the accumulator function returns the current weighted mean. 97 * 98 * @private 99 * @param {number} [x] - value 100 * @param {number} [w] - weight 101 * @returns {(number|null)} weighted mean or null 102 */ 103 function accumulator( x, w ) { 104 if ( arguments.length === 0 ) { 105 if ( FLG === void 0 ) { 106 return null; 107 } 108 return mu; 109 } 110 FLG = true; 111 wsum += w; 112 mu += ( w/wsum ) * ( x-mu ); 113 return mu; 114 } 115 } 116 117 118 // EXPORTS // 119 120 module.exports = incrwmean;