86 lines
2.4 KiB
JavaScript
86 lines
2.4 KiB
JavaScript
|
/**
|
|||
|
|
* @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';
|
|||
|
|
|
|||
|
|
// 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} stride - stride length
|
|||
|
|
* @param {NonNegativeInteger} offset - starting index
|
|||
|
|
* @returns {number} arithmetic mean
|
|||
|
|
*
|
|||
|
|
* @example
|
|||
|
|
* var floor = require( '@stdlib/math/base/special/floor' );
|
|||
|
|
*
|
|||
|
|
* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
|
|||
|
|
* var N = floor( x.length / 2 );
|
|||
|
|
*
|
|||
|
|
* var v = meanwd( N, x, 2, 1 );
|
|||
|
|
* // returns 1.25
|
|||
|
|
*/
|
|||
|
|
function meanwd( N, x, stride, offset ) {
|
|||
|
|
var mu;
|
|||
|
|
var ix;
|
|||
|
|
var n;
|
|||
|
|
var i;
|
|||
|
|
|
|||
|
|
if ( N <= 0 ) {
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
if ( N === 1 || stride === 0 ) {
|
|||
|
|
return x[ offset ];
|
|||
|
|
}
|
|||
|
|
ix = offset;
|
|||
|
|
mu = 0.0;
|
|||
|
|
n = 0;
|
|||
|
|
for ( i = 0; i < N; i++ ) {
|
|||
|
|
n += 1;
|
|||
|
|
mu += ( x[ix]-mu ) / n;
|
|||
|
|
ix += stride;
|
|||
|
|
}
|
|||
|
|
return mu;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// EXPORTS //
|
|||
|
|
|
|||
|
|
module.exports = meanwd;
|