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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
/**
* Returns an accumulator function which incrementally computes an arithmetic mean.
*
* ## Method
*
* - This implementation uses [Welford's method][algorithms-variance] for efficient computation, which can be derived as follows
*
* ```tex
* \begin{align*}
* \mu_n &= \frac{1}{n} \sum_{i=0}^{n-1} x_i \\
* &= \frac{1}{n} \biggl(x_{n-1} + \sum_{i=0}^{n-2} x_i \biggr) \\
* &= \frac{1}{n} (x_{n-1} + (n-1)\mu_{n-1}) \\
* &= \mu_{n-1} + \frac{1}{n} (x_{n-1} - \mu_{n-1})
* \end{align*}
* ```
*
* [algorithms-variance]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
*
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrmean();
*
* var mu = accumulator();
* // returns null
*
* mu = accumulator( 2.0 );
* // returns 2.0
*
* mu = accumulator( -5.0 );
* // returns -1.5
*
* mu = accumulator();
* // returns -1.5
*/
function incrmean() {
var mu;
var N;
mu = 0.0;
N = 0;
return accumulator;
/**
* If provided a value, the accumulator function returns an updated mean. If not provided a value, the accumulator function returns the current mean.
*
* @private
* @param {number} [x] - new value
* @returns {(number|null)} mean value or null
*/
function accumulator( x ) {
if ( arguments.length === 0 ) {
if ( N === 0 ) {
return null;
}
return mu;
}
N += 1;
mu += (x-mu) / N;
return mu;
}
}
// EXPORTS //
module.exports = incrmean;
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