feat: add incrnanmmeanvar (moving mean/variance with NaN skipping) (fixes #5592)

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

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+<!--
+
+@license Apache-2.0
+
+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.
+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.
+
+-->
+
+# incrnanmmeanvar
+
+> Compute a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance] incrementally, **skipping `NaN` values**.
+
+<section class="intro">
+
+For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as
+
+<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->
+
+```math
+\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@c8c3c87eeab590bfdff924ec0fb269fb33a7de2b/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+and the [unbiased sample variance][sample-variance] is defined as
+
+<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->
+
+```math
+s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2
+```
+
+<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@563a8587d936008c82db675be84f8ce1474fee27/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanmmeanvar = require( '@stdlib/stats/incr/nanmmeanvar' );
+```
+
+#### incrnanmmeanvar( \[out,] window )
+
+Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance] **while skipping `NaN` values**. The `window` parameter defines the maximum number of most recent **non-NaN** values used to compute the moving statistics.
+
+```javascript
+var accumulator = incrnanmmeanvar( 3 );
+```
+
+By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object. Unlike `incrmmeanvar`, this accumulator ignores (skips) any `NaN` values and does not allow them to propagate into the moving mean and variance.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var accumulator = incrnanmmeanvar( new Float64Array( 2 ), 3 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function updates and returns the current moving arithmetic mean and unbiased sample variance. If `x` is `NaN`, the value is ignored (i.e., it does not affect the window). If not provided an input value `x`, the accumulator function returns the current accumulated values without updating.
+
+```javascript
+var incrnanmmeanvar = require( '@stdlib/stats/incr/nanmmeanvar' );
+
+var accumulator = incrnanmmeanvar( 3 );
+
+var out = accumulator();
+// returns null
+
+// Fill the window (no NaNs yet)...
+out = accumulator( 2.0 ); // [2.0]
+// returns [ 2.0, 0.0 ]
+
+out = accumulator( NaN ); // NaN is ignored [2.0]
+// returns [ 2.0, 0.0 ]
+
+out = accumulator( 1.0 ); // [2.0, 1.0]
+// returns [ 1.5, 0.5 ]
+
+out = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
+// returns [ 2.0, 1.0 ]
+
+// Window begins sliding...
+out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
+// returns [ -1.0, 28.0 ]
+
+out = accumulator( NaN );  // NaN ignored [1.0, 3.0, -7.0]
+// returns [ -1.0, 28.0 ]
+
+out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
+// returns [ -3.0, 28.0 ]
+
+out = accumulator();
+// returns [ -3.0, 28.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If provided `NaN`, the value is ignored and does not affect the moving window or the accumulated statistics. If non-numeric inputs are possible, you are advised to type check and handle them **before** passing values to the accumulator function.
+-   As `W` valid (non-`NaN`) values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window has received `W` valid values, each returned value is calculated from all valid inputs seen so far.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var Float64Array = require( '@stdlib/array/float64' );
+var ArrayBuffer = require( '@stdlib/array/buffer' );
+var incrnanmmeanvar = require( '@stdlib/stats/incr/nanmmeanvar' );
+
+var offset;
+var acc;
+var buf;
+var out;
+var mv;
+var N;
+var v;
+var i;
+var j;
+
+// Define the number of accumulators:
+N = 5;
+
+// Create an array buffer for storing accumulator output:
+buf = new ArrayBuffer( N*2*8 );
+
+// Initialize accumulators:
+acc = [];
+for ( i = 0; i < N; i++ ) {
+    // Compute the byte offset for the i­th accumulator:
+    offset = i * 2 * 8;
+
+    // Create a typed array view over the correct section of the buffer:
+    out = new Float64Array( buf, offset, 2 );
+
+    // Create a moving mean/variance accumulator with window W = 5:
+    acc.push( incrnanmmeanvar( out, 5 ) );
+}
+
+// Simulate streaming data updates:
+for ( i = 0; i < 100; i++ ) {
+    for ( j = 0; j < N; j++ ) {
+
+        // Generate random values, but occasionally insert NaN.
+        // Any NaNs are ignored by the accumulator.
+        v = ( randu() > 0.1 ) ? randu() * 100 : NaN;
+
+        // Update accumulator j:
+        acc[ j ]( v );
+    }
+}
+
+// Display final moving means and variances:
+console.log( 'Mean\tVariance' );
+for ( i = 0; i < N; i++ ) {
+    mv = acc[ i ](); // Get the current result
+    console.log( mv[ 0 ].toFixed( 3 ) + '\t' + mv[ 1 ].toFixed( 3 ) );
+}
+```
+
+</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/mmeanvar`][@stdlib/stats/incr/mmeanvar]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean and unbiased sample variance incrementally (**propagates NaN values**).</span>
+-   <span class="package-name">[`@stdlib/stats/incr/meanvar`][@stdlib/stats/incr/meanvar]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean and unbiased sample variance incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mmean`][@stdlib/stats/incr/mmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mmeanstdev`][@stdlib/stats/incr/mmeanstdev]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean and corrected sample standard deviation incrementally.</span>
+-   <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>
+
+</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">
+
+[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
+
+[sample-variance]: https://en.wikipedia.org/wiki/Variance
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/mmeanvar]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmeanvar
+
+[@stdlib/stats/incr/meanvar]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/meanvar
+
+[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmean
+
+[@stdlib/stats/incr/mmeanstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmeanstdev
+
+[@stdlib/stats/incr/mvariance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mvariance
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* 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.
+* 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 incrnanmmeanvar = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanmmeanvar( (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 = incrnanmmeanvar( 5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v.length !== 2 ) {
+			b.fail( 'should contain two elements' );
+		}
+	}
+	b.toc();
+	if ( v[ 0 ] !== v[ 0 ] || v[ 1 ] !== v[ 1 ] ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});