feat: add stats/incr/nanmvariance

lib/node_modules/@stdlib/stats/incr/nanmvariance/README.md

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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.
+
+-->
+
+# nanmvariance
+
+> Compute a moving [unbiased sample variance][sample-variance] incrementally, ignoring `NaN` values.
+
+<section class="intro">
+
+For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
+
+<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->
+
+```math
+s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2
+```
+
+<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mvariance/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `n` is the number of non-`NaN` values in the window, and `\bar{x}` is the arithmetic mean of the non-`NaN` values.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
+```
+
+#### incrnanmvariance( window\[, mean] )
+
+Returns an accumulator `function` which incrementally computes a moving [unbiased sample variance][sample-variance], ignoring `NaN` values. The `window` parameter defines the number of values over which to compute the moving [unbiased sample variance][sample-variance].
+
+```javascript
+var accumulator = incrnanmvariance( 3 );
+```
+
+If the mean is already known, provide a `mean` argument.
+
+```javascript
+var accumulator = incrnanmvariance( 3, 5.0 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated [unbiased sample variance][sample-variance]. If not provided an input value `x`, the accumulator function returns the current [unbiased sample variance][sample-variance].
+
+```javascript
+var accumulator = incrnanmvariance( 3 );
+
+var s2 = accumulator();
+// returns null
+
+// Fill the window...
+s2 = accumulator( 2.0 ); // [2.0]
+// returns 0.0
+
+s2 = accumulator( NaN ); // [2.0, NaN]
+// returns 0.0
+
+s2 = accumulator( -5.0 ); // [2.0, NaN, -5.0]
+// returns 24.5
+
+// Window begins sliding...
+s2 = accumulator( 3.0 ); // [NaN, -5.0, 3.0]
+// returns 19.0
+
+s2 = accumulator( NaN ); // [-5.0, 3.0, NaN]
+// returns 19.0
+
+s2 = accumulator();
+// returns 19.0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+-   NaN input values are ignored. If the window contains only NaN values, the variance is calculated as if the window were empty.
+-   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided non-NaN values.
+-   The implementation uses [Welford's algorithm][welford-algorithm].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmvariance( 5 );
+
+// For each simulated datum, update the moving unbiased sample variance...
+console.log( '\nValue\tSample Variance\n' );
+for ( i = 0; i < 100; i++ ) {
+    if ( randu() < 0.2 ) {
+        v = NaN;
+    } else {
+        v = randu() * 100.0;
+    }
+    console.log( '%d\t%d', v.toFixed( 4 ), accumulator( v ).toFixed( 4 ) );
+}
+console.log( '\nFinal variance: %d\n', accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/stats/incr/mvariance`][@stdlib/stats/incr/mvariance]</span><span class="delimiter">: </span><span class="description">compute a moving unbiased sample variance incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/nanmmean`][@stdlib/stats/incr/nanmmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally, ignoring NaN values.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/nanmstdev`][@stdlib/stats/incr/nanmstdev]</span><span class="delimiter">: </span><span class="description">compute a moving corrected sample standard deviation incrementally, ignoring NaN values.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/nanvariance`][@stdlib/stats/incr/nanvariance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample variance incrementally, ignoring NaN values.</span>
+
+</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">
+
+[sample-variance]: https://en.wikipedia.org/wiki/Variance
+[welford-algorithm]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/mvariance]: https://github.com/stdlib-js/stats-incr-mvariance
+
+[@stdlib/stats/incr/nanmmean]: https://github.com/stdlib-js/stats-incr-nanmmean
+
+[@stdlib/stats/incr/nanmstdev]: https://github.com/stdlib-js/stats-incr-nanmstdev
+
+[@stdlib/stats/incr/nanvariance]: https://github.com/stdlib-js/stats-incr-nanvariance
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/nanmvariance/benchmark/benchmark.js

@@ -0,0 +1,113 @@
+/**
+* @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 bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanmvariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanmvariance( (i%5)+1 );
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanmvariance( 5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator,NaN', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanmvariance( 5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( NaN );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanmvariance( 5, 0.5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});