Add pkg to incrementally compute an exponentially weighted moving variance

Author: kgryte

lib/node_modules/@stdlib/stats/incr/ewvariance/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.
+
+-->
+
+# increwvariance
+
+> Compute an [exponentially weighted variance][moving-average] incrementally.
+
+<section class="intro">
+
+An [exponentially weighted variance][moving-average] can be defined recursively as
+
+<!-- <equation class="equation" label="eq:exponentially_weighted_variance" align="center" raw="S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}" alt="Recursive definition for computing an exponentially weighted variance."> -->
+
+<div class="equation" align="center" data-raw-text="S_n = \begin{cases} 0 &amp; \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) &amp; \textrm{if}\ n &gt; 0 \end{cases}" data-equation="eq:exponentially_weighted_variance">
+    <img src="" alt="Recursive definition for computing an exponentially weighted variance.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var increwvariance = require( '@stdlib/stats/incr/ewvariance' );
+```
+
+#### increwvariance( alpha )
+
+Returns an accumulator `function` which incrementally computes an [exponentially weighted variance][moving-average], where `alpha` is a smoothing factor between `0` and `1`.
+
+```javascript
+var accumulator = increwvariance( 0.5 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated variance. If not provided an input value `x`, the accumulator function returns the current variance.
+
+```javascript
+var accumulator = increwvariance( 0.5 );
+
+var v = accumulator();
+// returns null
+
+v = accumulator( 2.0 );
+// returns 0.0
+
+v = accumulator( 1.0 );
+// returns 0.25
+
+v = accumulator( 3.0 );
+// returns 0.6875
+
+v = accumulator();
+// returns 0.6875
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var increwvariance = require( '@stdlib/stats/incr/ewvariance' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = increwvariance( 0.5 );
+
+// For each simulated datum, update the exponentially weighted variance...
+for ( i = 0; i < 100; i++ ) {
+    v = randu() * 100.0;
+    accumulator( v );
+}
+console.log( accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[moving-average]: https://en.wikipedia.org/wiki/Moving_average
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/ewvariance/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 increwvariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = increwvariance( 0.5 );
+		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 = increwvariance( 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();
+});

lib/node_modules/@stdlib/stats/incr/ewvariance/docs/img/equation_exponentially_weighted_variance.svg

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+
+{{alias}}( α )
+    Returns an accumulator function which incrementally computes an
+    exponentially weighted variance, where α is a smoothing factor between 0 and
+    1.
+
+    If provided a value, the accumulator function returns an updated variance.
+    If not provided a value, the accumulator function returns the current
+    variance.
+
+    If provided `NaN` or a value which, when used in computations, results in
+    `NaN`, the accumulated value is `NaN` for all future invocations.
+
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+
+    Examples
+    --------
+    > var accumulator = {{alias}}( 0.5 );
+    > var v = accumulator()
+    null
+    > v = accumulator( 2.0 )
+    0.0
+    > v = accumulator( -5.0 )
+    12.25
+    > v = accumulator()
+    12.25
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/incr/ewvariance/docs/repl.txt

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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';
+
+var randu = require( '@stdlib/random/base/randu' );
+var increwvariance = require( './../lib' );
+
+var accumulator;
+var s2;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = increwvariance( 0.5 );
+
+// For each simulated datum, update the exponentially weighted variance...
+console.log( '\nValue\tVariance\n' );
+for ( i = 0; i < 100; i++ ) {
+	v = randu() * 100.0;
+	s2 = accumulator( v );
+	console.log( '%d\t%d', v.toFixed( 4 ), s2.toFixed( 4 ) );
+}
+console.log( '\nFinal variance: %d\n', accumulator() );