feat: refactor and add protocol support to stats/base/variancepn

- Adds accessor arrays support.
- Refactors `stats/base/variancepn`.

Does this pull request have any related issues?

- No

Any questions for reviewers of this pull request?

- No.

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

- No.

Please ensure the following tasks are completed before submitting this pull request.

- [ ] Read, understood, and followed the contributing guidelines.

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Author: thefauxpastrouper

lib/node_modules/@stdlib/stats/base/variancepn/README.md

@@ -2,7 +2,7 @@
 
 @license Apache-2.0
 
-Copyright (c) 2020 The Stdlib Authors.
+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.
@@ -88,8 +88,10 @@ The use of the term `n-1` is commonly referred to as Bessel's correction. Note,
 
 </section>
 
+
 <!-- /.intro -->
 
+
 <section class="usage">
 
 ## Usage
@@ -98,7 +100,7 @@ The use of the term `n-1` is commonly referred to as Bessel's correction. Note,
 var variancepn = require( '@stdlib/stats/base/variancepn' );
 ```
 
-#### variancepn( N, correction, x, stride )
+#### variancepn( N, correction, x, strideX )
 
 Computes the [variance][variance] of a strided array `x` using a two-pass algorithm.
 
@@ -115,17 +117,14 @@ The function has the following parameters:
 -   **N**: number of indexed elements.
 -   **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
 -   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
--   **stride**: index increment for `x`.
+-   **strideX**: stride length for `x`.
 
-The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,
 
 ```javascript
-var floor = require( '@stdlib/math/base/special/floor' );
-
 var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
-var N = floor( x.length / 2 );
 
-var v = variancepn( N, 1, x, 2 );
+var v = variancepn( 4, 1, x, 2 );
 // returns 6.25
 ```
 
@@ -135,18 +134,15 @@ Note that indexing is relative to the first index. To introduce an offset, use [
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var floor = require( '@stdlib/math/base/special/floor' );
 
 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
-var N = floor( x0.length / 2 );
-
-var v = variancepn( N, 1, x1, 2 );
+var v = variancepn( 4, 1, x1, 2 );
 // returns 6.25
 ```
 
-#### variancepn.ndarray( N, correction, x, stride, offset )
+#### variancepn.ndarray( N, correction, x, strideX, offsetX )
 
 Computes the [variance][variance] of a strided array using a two-pass algorithm and alternative indexing semantics.
 
@@ -160,55 +156,52 @@ var v = variancepn.ndarray( N, 1, x, 1, 0 );
 
 The function has the following additional parameters:
 
--   **offset**: starting index for `x`.
+-   **offsetX**: starting index for `x`.
 
-While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [variance][variance] for every other value in `x` starting from the second value
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer , the offset parameters support indexing semantics based on starting indices. For example, to calculate the [variance][variance] for every other value in `x` starting from the second value
 
 ```javascript
-var floor = require( '@stdlib/math/base/special/floor' );
-
 var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
-var N = floor( x.length / 2 );
 
-var v = variancepn.ndarray( N, 1, x, 2, 1 );
+var v = variancepn.ndarray( 4, 1, x, 2, 1 );
 // returns 6.25
 ```
 
 </section>
 
+
 <!-- /.usage -->
 
+
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0`, both functions return `NaN`.
 -   If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.
 -   Depending on the environment, the typed versions ([`dvariancepn`][@stdlib/stats/base/dvariancepn], [`svariancepn`][@stdlib/stats/base/svariancepn], etc.) are likely to be significantly more performant.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
 
 </section>
 
+
 <!-- /.notes -->
 
+
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
-var randu = require( '@stdlib/random/base/randu' );
-var round = require( '@stdlib/math/base/special/round' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var Float64Array = require( '@stdlib/array/float64' );
 var variancepn = require( '@stdlib/stats/base/variancepn' );
 
-var x;
-var i;
-
-x = new Float64Array( 10 );
-for ( i = 0; i < x.length; i++ ) {
-    x[ i ] = round( (randu()*100.0) - 50.0 );
-}
+var x = uniform( 10, -50.0, 50.0, {
+    'dtype': 'float64'
+});
 console.log( x );
 
 var v = variancepn( x.length, 1, x, 1 );
@@ -217,6 +210,7 @@ console.log( v );
 
 </section>
 
+
 <!-- /.examples -->
 
 * * *
@@ -230,6 +224,7 @@ console.log( v );
 
 </section>
 
+
 <!-- /.references -->
 
 <!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
@@ -247,16 +242,21 @@ console.log( v );
 
 </section>
 
+
 <!-- /.related -->
 
 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
+
 <section class="links">
 
+
 [variance]: https://en.wikipedia.org/wiki/Variance
 
 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
 
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
 [@stdlib/stats/base/svariancepn]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/svariancepn
@@ -277,6 +277,8 @@ console.log( v );
 
 <!-- </related-links> -->
 
+
 </section>
 
+
 <!-- /.links -->

lib/node_modules/@stdlib/stats/base/variancepn/benchmark/benchmark.js

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2020 The Stdlib Authors.
+* 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.
@@ -21,13 +21,20 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var pkg = require( './../package.json' ).name;
 var variancepn = require( './../lib/variancepn.js' );
 
 
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
 // FUNCTIONS //
 
 /**
@@ -38,13 +45,7 @@ var variancepn = require( './../lib/variancepn.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = [];
-	for ( i = 0; i < len; i++ ) {
-		x.push( ( randu()*20.0 ) - 10.0 );
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/variancepn/benchmark/benchmark.ndarray.js

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2020 The Stdlib Authors.
+* 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.
@@ -21,13 +21,20 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var pkg = require( './../package.json' ).name;
 var variancepn = require( './../lib/ndarray.js' );
 
 
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
 // FUNCTIONS //
 
 /**
@@ -38,13 +45,7 @@ var variancepn = require( './../lib/ndarray.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = [];
-	for ( i = 0; i < len; i++ ) {
-		x.push( ( randu()*20.0 ) - 10.0 );
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/variancepn/docs/repl.txt

@@ -1,12 +1,12 @@
 
-{{alias}}( N, correction, x, stride )
-    Computes the variance of a strided array using a two-pass algorithm.
+{{alias}}( N, correction, x, strideX )
+    Computes the variance of a strided array (two-pass algorithm).
 
-    The `N` and `stride` parameters determine which elements in `x` are accessed
-    at runtime.
+    The `N` and stride parameters determine which elements in the
+    strided arrays are accessed at runtime.
 
-    Indexing is relative to the first index. To introduce an offset, use a typed
-    array view.
+    Indexing is relative to the first index. To introduce
+    an offset, use a typed array view.
 
     If `N <= 0`, the function returns `NaN`.
 
@@ -30,8 +30,8 @@
     x: Array<number>|TypedArray
         Input array.
 
-    stride: integer
-        Index increment.
+    strideX: integer
+        Stride length.
 
     Returns
     -------
@@ -43,24 +43,23 @@
     // Standard Usage:
     > var x = [ 1.0, -2.0, 2.0 ];
     > {{alias}}( x.length, 1, x, 1 )
-    ~4.3333
+    4.333333333333334
 
-    // Using `N` and `stride` parameters:
+    // Using `N` and `strideX` parameters:
     > x = [ -2.0, 1.0, 1.0, -5.0, 2.0, -1.0 ];
-    > var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
-    > var stride = 2;
-    > {{alias}}( N, 1, x, stride )
-    ~4.3333
+    > var strideX = 2;
+    > {{alias}}( 4, 1, x, strideX )
+    NaN
 
     // Using view offsets:
     > var x0 = new {{alias:@stdlib/array/float64}}( [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ] );
     > var x1 = new {{alias:@stdlib/array/float64}}( x0.buffer, x0.BYTES_PER_ELEMENT*1 );
-    > N = {{alias:@stdlib/math/base/special/floor}}( x0.length / 2 );
-    > stride = 2;
-    > {{alias}}( N, 1, x1, stride )
-    ~4.3333
+    > strideX = 2;
+    > {{alias}}( 4, 1, x1, strideX )
+    NaN
+
 
-{{alias}}.ndarray( N, correction, x, stride, offset )
+{{alias}}.ndarray( N, correction, x, strideX, offset )
     Computes the variance of a strided array using a two-pass algorithm and
     alternative indexing semantics.
 
@@ -88,8 +87,8 @@
     x: Array<number>|TypedArray
         Input array.
 
-    stride: integer
-        Index increment.
+    strideX: integer
+        Stride length.
 
     offset: integer
         Starting index.
@@ -108,10 +107,9 @@
 
     // Using offset parameter:
     > var x = [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ];
-    > var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
-    > {{alias}}.ndarray( N, 1, x, 2, 1 )
-    ~4.3333
+    > {{alias}}.ndarray( 4, 1, x, 2, 1 )
+    NaN
+
 
     See Also
     --------
-