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* @license Apache-2.0
*
* Copyright (c) 2020 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';
// MODULES //
var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Computes the arithmetic mean of a strided array using Welford's algorithm.
*
* ## Method
*
* - This implementation uses Welford's algorithm 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*}
* ```
*
* ## References
*
* - 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).
* - 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)
*
* @param {PositiveInteger} N - number of indexed elements
* @param {NumericArray} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} arithmetic mean
*
* @example
* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
*
* var v = meanwd( 4, x, 2, 1 );
* // returns 1.25
*/
function meanwd( N, x, strideX, offsetX ) {
var mu;
var ix;
var o;
var n;
var i;
if ( N <= 0 ) {
return NaN;
}
o = arraylike2object( x );
if ( o.accessorProtocol ) {
return accessors( N, o, strideX, offsetX );
}
if ( N === 1 || strideX === 0 ) {
return x[ offsetX ];
}
ix = offsetX;
mu = 0.0;
n = 0;
for ( i = 0; i < N; i++ ) {
n += 1;
mu += ( x[ix]-mu ) / n;
ix += strideX;
}
return mu;
}
// EXPORTS //
module.exports = meanwd;
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