89 lines
2.0 KiB
JavaScript
89 lines
2.0 KiB
JavaScript
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 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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/**
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* Returns an accumulator function which incrementally computes an arithmetic mean.
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*
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* ## Method
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*
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* - This implementation uses [Welford's method][algorithms-variance] 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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* [algorithms-variance]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
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*
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* @returns {Function} accumulator function
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*
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* @example
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* var accumulator = incrmean();
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*
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* var mu = accumulator();
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* // returns null
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*
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* mu = accumulator( 2.0 );
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* // returns 2.0
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*
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* mu = accumulator( -5.0 );
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* // returns -1.5
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*
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* mu = accumulator();
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* // returns -1.5
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*/
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function incrmean() {
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var mu;
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var N;
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mu = 0.0;
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N = 0;
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return accumulator;
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/**
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* If provided a value, the accumulator function returns an updated mean. If not provided a value, the accumulator function returns the current mean.
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*
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* @private
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* @param {number} [x] - new value
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* @returns {(number|null)} mean value or null
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*/
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function accumulator( x ) {
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if ( arguments.length === 0 ) {
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if ( N === 0 ) {
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return null;
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}
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return mu;
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}
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N += 1;
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mu += (x-mu) / N;
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return mu;
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}
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}
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// EXPORTS //
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module.exports = incrmean;
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