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* @license Apache-2.0
*
* Copyright (c) 2026 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';
var isnan = require( '@stdlib/math/base/assert/is-nan' );
/**
* Returns an accumulator function which incrementally computes a weighted variance.
*
* ## Method
*
* - The weighted variance is defined as
*
* ```tex
* \sigma_w^2 = \frac{\sum_{i=1}^{n} w_i (x_i - \mu_w)^2}{\sum_{i=1}^{n} w_i}
* ```
*
* where \\( \mu_w \\) is the weighted arithmetic mean.
*
* - Define the total weight
*
* ```tex
* W_n = \sum_{i=1}^{n} w_i
* ```
*
* - Define the unnormalized second central moment
*
* ```tex
* S_n = \sum_{i=1}^{n} w_i (x_i - \mu_n)^2
* ```
*
* - The weighted variance is obtained by normalizing
*
* ```tex
* \sigma_n^2 = \frac{S_n}{W_n}
* ```
*
* - The weighted mean is updated incrementally according to
*
* ```tex
* \mu_n = \mu_{n-1} + \frac{w_n}{W_n}(x_n - \mu_{n-1})
* ```
*
* - Using this update, the unnormalized variance accumulator satisfies
*
* ```tex
* S_n = S_{n-1} + w_n (x_n - \mu_{n-1})(x_n - \mu_n)
* ```
*
* which yields a numerically stable, one-pass algorithm for computing the
* weighted variance.
*
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrwvariance();
*
* var s2 = accumulator();
* // returns null
*
* s2 = accumulator( 2.0, 1.0 );
* // returns 0.0
*
* s2 = accumulator( 2.0, 0.5 );
* // returns 0.0
*
* s2 = accumulator( 3.0, 1.5 );
* // returns 0.25
*
* s2 = accumulator();
* // returns 0.25
*/
function incrwvariance() {
var poisoned;
var mu;
var W;
var S;
var N;
N = 0;
W = 0.0;
S = 0.0;
mu = 0.0;
poisoned = false;
return accumulator;
/**
* If provided arguments, the accumulator function returns an updated weighted variance. If not provided arguments, the accumulator function returns the current weighted variance.
*
* @private
* @param {number} [x] - value
* @param {number} [w] - weight
* @returns {(number|null)} weighted variance or null
*/
function accumulator( x, w ) {
var muprev;
if ( poisoned ) {
return NaN;
}
if ( arguments.length === 0 ) {
if ( N === 0 ) {
return null;
}
return S / W;
}
if ( arguments.length !== 2 ) {
poisoned = true;
return NaN;
}
if ( isnan( x ) || isnan( w ) ) {
poisoned = true;
return NaN;
}
N += 1;
W += w;
muprev = mu;
mu += ( w / W ) * ( x - mu );
S += w * ( x - muprev ) * ( x - mu );
if ( N === 1 ) {
return 0.0;
}
return S / W;
}
}
// EXPORTS //
module.exports = incrwvariance;
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