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* @license Apache-2.0
*
* Copyright (c) 2025 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 variance of a strided array using a one-pass algorithm proposed by Youngs and Cramer.
*
* ## Method
*
* - This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
*
* ## References
*
* - Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826](https://doi.org/10.1080/00401706.1971.10488826).
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {number} correction - degrees of freedom adjustment
* @param {Object} x - input array object
* @param {Collection} x.data - input array data
* @param {Array<Function>} x.accessors - array element accessors
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} variance
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var x = toAccessorArray( [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ] );
*
* var v = varianceyc( x.length, 1.0, arraylike2object( x ), 1, 0 );
* // returns 10.7
*/
function varianceyc( N, correction, x, strideX, offsetX ) {
var xbuf;
var xget;
var sum;
var ix;
var S;
var v;
var d;
var n;
var i;
n = N - correction;
// Cache a reference to array data:
xbuf = x.data;
// Cache a reference to an element accessor:
xget = x.accessors[ 0 ];
sum = xget( xbuf, offsetX );
ix = offsetX + strideX;
S = 0.0;
for ( i = 2; i <= N; i++ ) {
v = xget( xbuf, ix );
sum += v;
d = (i*v) - sum;
S += (1.0/(i*(i-1))) * d * d;
ix += strideX;
}
return S / n;
}
// EXPORTS //
module.exports = varianceyc;
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