build: Add incremental absolute Pearson correlation function ignoring NaN

lib/node_modules/@stdlib/stats/incr/nanapcorr/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.
+
+-->
+
+# incrnanapcorr
+
+> Compute a sample absolute [Pearson product-moment correlation coefficient][pearson-correlation] incrementally.
+
+<section class="intro">
+
+The [Pearson product-moment correlation coefficient][pearson-correlation] between random variables `X` and `Y` is defined as
+
+<!-- <equation class="equation" label="eq:pearson_correlation_coefficient" align="center" raw="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" alt="Equation for the Pearson product-moment correlation coefficient."> -->
+
+```math
+\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" data-equation="eq:pearson_correlation_coefficient">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@80f96253bf726f33bc71d8eb68037ab203ae4cf9/lib/node_modules/@stdlib/stats/incr/nanapcorr/docs/img/equation_pearson_correlation_coefficient.svg" alt="Equation for the Pearson product-moment correlation coefficient.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations.
+
+For a sample of size `n`, the sample [Pearson product-moment correlation coefficient][pearson-correlation] is defined as
+
+<!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
+
+```math
+r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@80f96253bf726f33bc71d8eb68037ab203ae4cf9/lib/node_modules/@stdlib/stats/incr/nanapcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+The sample **absolute** [Pearson product-moment correlation coefficient][pearson-correlation] is thus defined as the absolute value of the sample [Pearson product-moment correlation coefficient][pearson-correlation].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanapcorr = require( '@stdlib/stats/incr/nanapcorr' );
+```
+
+#### incrnanapcorr( \[mx, my] )
+
+Returns an accumulator `function` which incrementally computes a sample absolute [Pearson product-moment correlation coefficient][pearson-correlation].
+
+```javascript
+var accumulator = incrnanapcorr();
+```
+
+If the means are already known, provide `mx` and `my` arguments.
+
+```javascript
+var accumulator = incrnanapcorr( 3.0, -5.5 );
+```
+
+#### accumulator( \[x, y] )
+
+If provided input value `x` and `y`, the accumulator function returns an updated accumulated value. If not provided input values `x` and `y`, the accumulator function returns the current accumulated value.
+
+```javascript
+var accumulator = incrnanapcorr();
+
+var v = accumulator( 2.0, 1.0 );
+// returns 0.0
+
+var v = accumulator( NaN, 1.0 ); //ignore NaN
+// returns 0.0
+
+v = accumulator( 1.0, -5.0 );
+// returns 1.0
+
+v = accumulator( 3.0, 3.14 );
+// returns ~0.965
+
+v = accumulator( 3.0, NaN ); //ignore NaN
+// returns ~0.965
+
+v = accumulator();
+// returns ~0.965
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, then it will be Ignored but you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+-   In comparison to the sample [Pearson product-moment correlation coefficient][pearson-correlation], the sample absolute [Pearson product-moment correlation coefficient][pearson-correlation] is useful when only concerned with the strength of the correlation and not the direction.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanapcorr = require( '@stdlib/stats/incr/nanapcorr' );
+
+var accumulator;
+var x;
+var y;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanapcorr();
+
+// For each simulated datum, update the sample absolute correlation coefficient...
+for ( i = 0; i < 100; i++ ) {
+
+    x = (randu() < 0.2) ? NaN : randu() * 100.0; // 20% of the time, generate a NaN
+    y = (randu() < 0.1) ? NaN : randu() * 100.0; // 10% of the time, generate a NaN
+
+    ar = accumulator( x, y );
+    console.log( '%d\t%d\t%d', isnan(x) ? 'NaN' : x.toFixed( 4 ), isnan(y) ? 'NaN' : y.toFixed( 4 ), ar.toFixed( 4 ) );
+}
+```
+
+</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/mapcorr`][@stdlib/stats/incr/mapcorr]</span><span class="delimiter">: </span><span class="description">compute a moving sample absolute Pearson product-moment correlation coefficient incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/pcorr`][@stdlib/stats/incr/pcorr]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation coefficient.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/pcorr2`][@stdlib/stats/incr/pcorr2]</span><span class="delimiter">: </span><span class="description">compute a squared sample Pearson product-moment correlation coefficient.</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">
+
+[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+
+[covariance]: https://en.wikipedia.org/wiki/Covariance
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/mapcorr]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mapcorr
+
+[@stdlib/stats/incr/pcorr]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/pcorr
+
+[@stdlib/stats/incr/pcorr2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/pcorr2
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/nanapcorr/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 incrnanapcorr = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanapcorr();
+		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 = incrnanapcorr();
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu(), 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,known_means', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanapcorr( 3.0, -2.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu(), 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();
+});