All files / stats/strided/dsmeanwd/lib ndarray.js

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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';
 
// MAIN //
 
/**
* Computes the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm with extended accumulation and returning an extended precision result.
*
* ## 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 {Float32Array} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} arithmetic mean
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
*
* var v = dsmeanwd( 4, x, 2, 1 );
* // returns 1.25
*/
function dsmeanwd( N, x, strideX, offsetX ) {
	var mu;
	var ix;
	var n;
	var i;
 
	if ( N <= 0 ) {
		return NaN;
	}
	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 = dsmeanwd;