92 lines
2.2 KiB
JavaScript
92 lines
2.2 KiB
JavaScript
/**
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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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// MODULES //
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var incrmean = require( './../../../incr/mean' );
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// MAIN //
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/**
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* Returns an accumulator function which incrementally computes a harmonic mean.
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*
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* ## Method
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*
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* - The harmonic mean of positive real numbers \\(x_0, x_1, \ldots, x_{n-1}\\) is defined as
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*
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* ```tex
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* \begin{align*}
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* H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\
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* &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}}
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* \end{align*}
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* ```
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*
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* which may be expressed
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*
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* ```tex
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* H = \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}
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* ```
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*
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* - Accordingly, to compute the harmonic mean incrementally, we can simply compute the arithmetic mean of reciprocal values and then compute the reciprocal of the result.
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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 = incrhmean();
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*
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* var v = accumulator();
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* // returns null
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*
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* v = accumulator( 2.0 );
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* // returns 2.0
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*
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* v = accumulator( 5.0 );
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* // returns ~2.86
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*
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* v = accumulator();
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* // returns ~2.86
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*/
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function incrhmean() {
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var mean = incrmean();
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var v;
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return accumulator;
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/**
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* If provided a value, the accumulator function returns an updated harmonic mean. If not provided a value, the accumulator function returns the current harmonic 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)} harmonic mean 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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return ( v === void 0 ) ? null : v;
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}
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v = 1.0 / mean( 1.0/x );
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return v;
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}
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}
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// EXPORTS //
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module.exports = incrhmean;
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