87 lines
2.2 KiB
JavaScript
87 lines
2.2 KiB
JavaScript
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MAIN //
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/**
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* Computes the arithmetic mean of a strided array using Welford's algorithm.
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*
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* ## Method
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*
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* - This implementation uses Welford's algorithm for efficient computation, which can be derived as follows
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*
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* ```tex
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* \begin{align*}
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* \mu_n &= \frac{1}{n} \sum_{i=0}^{n-1} x_i \\
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* &= \frac{1}{n} \biggl(x_{n-1} + \sum_{i=0}^{n-2} x_i \biggr) \\
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* &= \frac{1}{n} (x_{n-1} + (n-1)\mu_{n-1}) \\
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* &= \mu_{n-1} + \frac{1}{n} (x_{n-1} - \mu_{n-1})
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* \end{align*}
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* ```
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*
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* ## References
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*
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* - Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022](https://doi.org/10.1080/00401706.1962.10490022).
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* - van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961](https://doi.org/10.1145/362929.362961).
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*
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* @param {PositiveInteger} N - number of indexed elements
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* @param {NumericArray} x - input array
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* @param {integer} stride - stride length
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* @returns {number} arithmetic mean
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*
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* @example
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* var x = [ 1.0, -2.0, 2.0 ];
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* var N = x.length;
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*
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* var v = meanwd( N, x, 1 );
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* // returns ~0.3333
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*/
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function meanwd( N, x, stride ) {
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var mu;
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var ix;
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var n;
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var i;
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if ( N <= 0 ) {
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return NaN;
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}
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if ( N === 1 || stride === 0 ) {
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return x[ 0 ];
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}
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if ( stride < 0 ) {
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ix = (1-N) * stride;
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} else {
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ix = 0;
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}
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mu = 0.0;
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n = 0;
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for ( i = 0; i < N; i++ ) {
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n += 1;
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mu += ( x[ix]-mu ) / n;
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ix += stride;
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}
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return mu;
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}
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// EXPORTS //
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module.exports = meanwd;
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