verify

Author: jalajk3004

lib/node_modules/@stdlib/stats/incr/cv/lib/main.js

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2025 The Stdlib Authors.
+* Copyright (c) 2018 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.
@@ -20,51 +20,142 @@
 
 // MODULES //
 
-var isnan = require('@stdlib/math/base/assert/is-nan');
-var incrcv = require('./../../cv/lib/main');
+var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var format = require( '@stdlib/string/format' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
 
 
 // MAIN //
 
 /**
-* Returns an accumulator function which incrementally computes the coefficient of variation (CV), ignoring NaN values.
+* Returns an accumulator function which incrementally computes the coefficient of variation (CV).
 *
+* ## Method
+*
+* -   This implementation uses [Welford's method][algorithms-variance] for efficient computation, which can be derived as follows. Let
+*
+*     ```tex
+*     \begin{align*}
+*     S_n &= n \sigma_n^2 \\
+*         &= \sum_{i=1}^{n} (x_i - \mu_n)^2 \\
+*         &= \biggl(\sum_{i=1}^{n} x_i^2 \biggr) - n\mu_n^2
+*     \end{align*}
+*     ```
+*
+*     Accordingly,
+*
+*     ```tex
+*     \begin{align*}
+*     S_n - S_{n-1} &= \sum_{i=1}^{n} x_i^2 - n\mu_n^2 - \sum_{i=1}^{n-1} x_i^2 + (n-1)\mu_{n-1}^2 \\
+*                   &= x_n^2 - n\mu_n^2 + (n-1)\mu_{n-1}^2 \\
+*                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1}^2 - \mu_n^2) \\
+*                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1} - \mu_n)(\mu_{n-1} + \mu_n) \\
+*                   &= x_n^2 - \mu_{n-1}^2 + (\mu_{n-1} - x_n)(\mu_{n-1} + \mu_n) \\
+*                   &= x_n^2 - \mu_{n-1}^2 + \mu_{n-1}^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
+*                   &= x_n^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
+*                   &= (x_n - \mu_{n-1})(x_n - \mu_n) \\
+*                   &= S_{n-1} + (x_n - \mu_{n-1})(x_n - \mu_n)
+*     \end{align*}
+*     ```
+*
+*     where we use the identity
+*
+*     ```tex
+*     x_n - \mu_{n-1} = n (\mu_n - \mu_{n-1})
+*     ```
+*
+* [algorithms-variance]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
+*
+* @param {number} [mean] - mean value
+* @throws {TypeError} must provide a number primitive
 * @returns {Function} accumulator function
 *
 * @example
-* var accumulator = incrnancv();
+* var accumulator = incrcv();
 *
 * var cv = accumulator();
 * // returns null
 *
-* cv = accumulator(2.0);
-* // returns 0.0
-*
-* cv = accumulator(NaN);
+* cv = accumulator( 2.0 );
 * // returns 0.0
 *
-* cv = accumulator(1.0);
+* cv = accumulator( 1.0 );
 * // returns ~0.47
 *
 * cv = accumulator();
 * // returns ~0.47
+*
+* @example
+* var accumulator = incrcv( 3.14 );
 */
-function incrnancv() {
-	var cv = incrcv();
-	function accumulator(x) {
-		if (arguments.length === 0) {
-			return cv();
+function incrcv( mean ) {
+	var delta;
+	var mu;
+	var M2;
+	var N;
+
+	M2 = 0.0;
+	N = 0;
+	if ( arguments.length ) {
+		if ( !isNumber( mean ) ) {
+			throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
 		}
-		if (isnan(x)) {
-			return cv();
+		mu = mean;
+		return accumulator2;
+	}
+	mu = 0.0;
+	return accumulator1;
+
+	/**
+	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
+	*
+	* @private
+	* @param {number} [x] - new value
+	* @returns {(number|null)} accumulated value or null
+	*/
+	function accumulator1( x ) {
+		if ( arguments.length === 0 ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			if ( N === 1 ) {
+				return ( isnan( M2 ) ) ? NaN : 0.0/mu;
+			}
+			return sqrt( M2/(N-1) ) / mu;
+		}
+		N += 1;
+		delta = x - mu;
+		mu += delta / N;
+		M2 += delta * ( x - mu );
+		if ( N < 2 ) {
+			return ( isnan( M2 ) ) ? NaN : 0.0/mu;
 		}
-		return cv(x);
+		return sqrt( M2/(N-1) ) / mu;
 	}
 
-    return accumulator;
+	/**
+	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
+	*
+	* @private
+	* @param {number} [x] - new value
+	* @returns {(number|null)} accumulated value or null
+	*/
+	function accumulator2( x ) {
+		if ( arguments.length === 0 ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			return sqrt( M2/N ) / mu;
+		}
+		N += 1;
+		delta = x - mu;
+		M2 += delta * delta;
+		return sqrt( M2/N ) / mu;
+	}
 }
 
 
 // EXPORTS //
 
-module.exports = incrnancv;
+module.exports = incrcv;