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feat: add incremental Pearson correlation coefficient accumulator that ignores NaN values
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‎lib/node_modules/@stdlib/stats/incr/nanpcorr/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# incrnanpcorr
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> Compute a [sample Pearson product-moment correlation coefficient][pearson-correlation] incrementally.
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<section class="intro">
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The [Pearson product-moment correlation coefficient][pearson-correlation] between random variables `X` and `Y` is defined as
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<!-- <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."> -->
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```math
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\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}
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```
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<!-- <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">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/nanpcorr/docs/img/equation_pearson_correlation_coefficient.svg" alt="Equation for the Pearson product-moment correlation coefficient.">
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<br>
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</div> -->
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<!-- </equation> -->
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where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations.
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For a sample of size `n`, the [sample Pearson product-moment correlation coefficient][pearson-correlation] is defined as
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<!-- <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."> -->
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```math
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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}}
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```
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<!-- <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">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/nanpcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var incrnanpcorr = require( '@stdlib/stats/incr/nanpcorr' );
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```
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#### incrnanpcorr( \[mx, my] )
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Returns an accumulator `function` which incrementally computes a [sample Pearson product-moment correlation coefficient][pearson-correlation].
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```javascript
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var accumulator = incrnanpcorr();
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```
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If the means are already known, provide `mx` and `my` arguments.
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```javascript
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var accumulator = incrnanpcorr( 3.0, -5.5 );
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```
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#### accumulator( \[x, y] )
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If provided input value `x` and `y`, the accumulator function returns an updated [sample correlation coefficient][pearson-correlation]. If not provided input values `x` and `y`, the accumulator function returns the current [sample correlation coefficient][pearson-correlation].
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```javascript
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var accumulator = incrnanpcorr();
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var v = accumulator( 2.0, 1.0 );
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// returns 0.0
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var v = accumulator( NaN, 1.0 );
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// returns 0.0
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v = accumulator( 1.0, -5.0 );
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// returns 1.0
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v = accumulator( 1.0, NaN );
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// returns 1.0
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v = accumulator( 3.0, 3.14 );
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// returns ~0.965
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v = accumulator();
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// returns ~0.965
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, it will be ignored but you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var incrnanpcorr = require( './../lib' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var accumulator;
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var r;
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var x;
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var y;
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var i;
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// Initialize an accumulator:
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accumulator = incrnanpcorr();
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// For each simulated datum, update the sample Pearson correlation coefficient...
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console.log( '\nx\ty\tCorrelation Coefficient\n' );
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for ( i = 0; i < 100; i++ ) {
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x = (randu() < 0.2) ? NaN : randu()*100.0; // ~20% NaN values assigned to `x`
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y = (randu() < 0.2) ? NaN : randu()*100.0; // ~20% NaN values assigned to `y`
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r = accumulator( x, y );
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}
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console.log( accumulator() );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/stats/incr/covariance`][@stdlib/stats/incr/covariance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample covariance incrementally.</span>
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- <span class="package-name">[`@stdlib/stats/incr/mpcorr`][@stdlib/stats/incr/mpcorr]</span><span class="delimiter">: </span><span class="description">compute a moving sample Pearson product-moment correlation coefficient incrementally.</span>
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- <span class="package-name">[`@stdlib/stats/incr/summary`][@stdlib/stats/incr/summary]</span><span class="delimiter">: </span><span class="description">compute a statistical summary incrementally.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
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[covariance]: https://en.wikipedia.org/wiki/Covariance
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<!-- <related-links> -->
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[@stdlib/stats/incr/covariance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/covariance
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[@stdlib/stats/incr/mpcorr]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mpcorr
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[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/summary
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var pkg = require( './../package.json' ).name;
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var incrnanpcorr = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var f;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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f = incrnanpcorr();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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}
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b.toc();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::accumulator', function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanpcorr();
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( randu(), randu() );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::accumulator,known_means', function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanpcorr( 3.0, -2.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( randu(), randu() );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/stats/incr/nanpcorr/docs/img/equation_pearson_correlation_coefficient.svg‎

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