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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';
// MODULES //
var isNonNegativeNumber = require( '@stdlib/assert/is-nonnegative-number' ).isPrimitive;
var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var format = require( '@stdlib/string/format' );
// MAIN //
/**
* Returns an accumulator function which incrementally computes a weighted sample standard deviation.
*
* ## Method
*
* - The weighted sample standard deviation is defined as
*
* ```tex
* \sigma = \sqrt{\frac{\sum_{i=0}^{n-1} w_i (x_i - \mu)^2}{\sum_{i=0}^{n-1} w_i}}
* ```
*
* where \\( w_i \\) are the weights and \\( \mu \\) is the weighted arithmetic mean.
*
* - To derive an incremental formula for computing a weighted sample standard deviation, let:
*
* ```tex
* W_n = \sum_{i=1}^{n} w_i
* ```
*
* - Accordingly:
*
* ```tex
* \begin{align*}
* \sigma^2 &= \frac{1}{W_n} \sum_{i=1}^{n} w_i (x_i - \mu)^2 \\
* &= \frac{1}{W_n} \sum_{i=1}^{n} w_i x_i^2 - \mu^2
* \end{align*}
* ```
*
* - Let:
*
* ```tex
* M2_n = W_n \sigma^2_n = \sum_{i=1}^{n} w_i x_i^2 - W_n \mu_n^2
* ```
*
* - To compute the incremental update for \\(M2_n\\):
*
* ```tex
* \begin{align*}
* M2_n - M2_{n-1} &= \sum_{i=1}^{n} w_i x_i^2 - W_n \mu_n^2 - \sum_{i=1}^{n-1} w_i x_i^2 + W_{n-1} \mu_{n-1}^2 \\
* &= w_n x_n^2 - W_n \mu_n^2 + W_{n-1} \mu_{n-1}^2 \\
* &= w_n x_n^2 - W_n \mu_n^2 + (W_n - w_n) \mu_{n-1}^2 \\
* &= w_n (x_n^2 - \mu_{n-1}^2) + W_n (\mu_{n-1}^2 - \mu_n^2)
* \end{align*}
* ```
*
* - Simplify further:
*
* ```tex
* \begin{align*}
* M2_n - M2_{n-1} &= w_n (x_n - \mu_{n-1}) (x_n - \mu_n) \\
* M2_n &= M2_{n-1} + w_n (x_n - \mu_{n-1}) (x_n - \mu_n)
* \end{align*}
* ```
*
* - Finally, compute the weighted sample standard deviation:
*
* ```tex
* \sigma_n = \sqrt{\frac{M2_n}{W_n}}
* ```
*
* - Incrementally updating the weighted sample mean:
*
* ```tex
* \begin{align*}
* \mu_n &= \mu_{n-1} + \frac{w_n}{W_n} (x_n - \mu_{n-1})
* \end{align*}
* ```
*
* @param {number} [mean] - mean value
* @throws {TypeError} must provide a number primitive
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrwstdev();
*
* var s = accumulator();
* // returns null
*
* s = accumulator( 2.0, 1.0 );
* // returns 0.0
*
* s = accumulator( 3.0, 2.0 );
* // returns ~0.471
*
* s = accumulator( 2.0, 0.1 );
* // returns ~0.478
*
* s = accumulator();
* // returns ~0.478
*
* @example
* var accumulator = incrwstdev( 3.0 );
*/
function incrwstdev( mean ) {
var delta;
var wsum;
var FLG;
var M2;
var mu;
wsum = 0.0;
M2 = 0.0;
if ( arguments.length ) {
if ( !isNumber( mean ) ) {
throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
}
mu = mean;
return accumulator2;
}
mu = 0.0;
return accumulator1;
/**
* If provided a value, the accumulator function returns an updated weighted sample standard deviation. If not provided a value, the accumulator function returns the current weighted sample standard deviation.
*
* @private
* @param {number} [x] - value
* @param {NonNegativeNumber} [w] - weight
* @throws {TypeError} second argument must be a nonnegative number
* @returns {(number|null)} weighted sample standard deviation or null
*/
function accumulator1( x, w ) {
if ( arguments.length === 0 ) {
if ( FLG === void 0 ) {
return null;
}
return sqrt( M2 / wsum );
}
if ( !isNonNegativeNumber( w ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a nonnegative number. Value: `%s`.', w ) );
}
if ( w === 0.0 ) {
return ( FLG === void 0 ) ? null : sqrt( M2 / wsum );
}
FLG = true;
delta = x - mu;
wsum += w;
mu += ( w / wsum ) * delta;
M2 += w * delta * ( x - mu );
return sqrt( M2 / wsum );
}
/**
* If provided a value, the accumulator function returns an updated weighted sample standard deviation. If not provided a value, the accumulator function returns the current weighted sample standard deviation.
*
* @private
* @param {number} [x] - value
* @param {NonNegativeNumber} [w] - weight
* @throws {TypeError} second argument must be a nonnegative number
* @returns {(number|null)} weighted sample standard deviation or null
*/
function accumulator2( x, w ) {
if ( arguments.length === 0 ) {
if ( FLG === void 0 ) {
return null;
}
return sqrt( M2 / wsum );
}
if ( !isNonNegativeNumber( w ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a nonnegative number. Value: `%s`.', w ) );
}
if ( w === 0.0 ) {
return ( FLG === void 0 ) ? null : sqrt( M2 / wsum );
}
FLG = true;
delta = x - mu;
wsum += w;
M2 += w * delta * delta;
return sqrt( M2 / wsum );
}
}
// EXPORTS //
module.exports = incrwstdev;
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