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https://github.com/stdlib-js/stats-incr-pcorrdistmat

Compute a sample Pearson product-moment correlation distance matrix incrementally.
https://github.com/stdlib-js/stats-incr-pcorrdistmat

anticorrelation corr correlated correlation covariance dist distance javascript math mathematics matrix node node-js nodejs pearson product-moment sample-covariance statistics stats stdlib

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Compute a sample Pearson product-moment correlation distance matrix incrementally.

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README 

        



  

    About stdlib...

  

  
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# incrpcorrdistmat



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Compute a [sample Pearson product-moment correlation distance matrix][pearson-correlation] incrementally.



A [sample Pearson product-moment correlation distance matrix][pearson-correlation] is an M-by-M matrix whose elements specified by indices `j` and `k` are the [sample Pearson product-moment correlation distances][pearson-correlation] between the jth and kth data variables. The [sample Pearson product-moment correlation distance][pearson-correlation] is defined as



```math

d_{x,y} = 1 - r_{x,y} = 1 - \frac{\mathop{\mathrm{cov_n(x,y)}}}{\sigma_x \sigma_y}

```



where `r` is the [sample Pearson product-moment correlation coefficient][pearson-correlation], `cov(x,y)` is the sample covariance, and `σ` corresponds to the sample standard deviation. As `r` resides on the interval `[-1,1]`, `d` resides on the interval `[0,2]`.



## Installation



```bash

npm install @stdlib/stats-incr-pcorrdistmat

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

var incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );

```



#### incrpcorrdistmat( out\[, means] )



Returns an accumulator `function` which incrementally computes a [sample Pearson product-moment correlation distance matrix][pearson-correlation].



```javascript

// Create an accumulator for computing a 2-dimensional correlation distance matrix:

var accumulator = incrpcorrdistmat( 2 );

```



The `out` argument may be either the order of the [correlation distance matrix][pearson-correlation] or a square 2-dimensional [`ndarray`][@stdlib/ndarray/ctor] for storing the [correlation distance matrix][pearson-correlation].



```javascript

var Float64Array = require( '@stdlib/array-float64' );

var ndarray = require( '@stdlib/ndarray-ctor' );



var buffer = new Float64Array( 4 );

var shape = [ 2, 2 ];

var strides = [ 2, 1 ];



// Create a 2-dimensional output correlation distance matrix:

var dist = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );



var accumulator = incrpcorrdistmat( dist );

```



When means are known, the function supports providing a 1-dimensional [`ndarray`][@stdlib/ndarray/ctor] containing mean values.



```javascript

var Float64Array = require( '@stdlib/array-float64' );

var ndarray = require( '@stdlib/ndarray-ctor' );



var buffer = new Float64Array( 2 );

var shape = [ 2 ];

var strides = [ 1 ];



var means = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );



means.set( 0, 3.0 );

means.set( 1, -5.5 );



var accumulator = incrpcorrdistmat( 2, means );

```



#### accumulator( \[vector] )



If provided a data vector, the accumulator function returns an updated [sample Pearson product-moment distance correlation matrix][pearson-correlation]. If not provided a data vector, the accumulator function returns the current [sample Pearson product-moment correlation distance matrix][pearson-correlation].



```javascript

var Float64Array = require( '@stdlib/array-float64' );

var ndarray = require( '@stdlib/ndarray-ctor' );



var buffer = new Float64Array( 4 );

var shape = [ 2, 2 ];

var strides = [ 2, 1 ];

var dist = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );



buffer = new Float64Array( 2 );

shape = [ 2 ];

strides = [ 1 ];

var vec = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );



var accumulator = incrpcorrdistmat( dist );



vec.set( 0, 2.0 );

vec.set( 1, 1.0 );



var out = accumulator( vec );

// returns 



var bool = ( out === dist );

// returns true



vec.set( 0, 1.0 );

vec.set( 1, -5.0 );



out = accumulator( vec );

// returns 



vec.set( 0, 3.0 );

vec.set( 1, 3.14 );



out = accumulator( vec );

// returns 



out = accumulator();

// returns 

```



## Notes



-   Due to limitations inherent in representing numeric values using floating-point format (i.e., the inability to represent numeric values with infinite precision), the [correlation distance][pearson-correlation] between perfectly correlated random variables may **not** be `0` or `2`. In fact, the [correlation distance][pearson-correlation] is **not** guaranteed to be strictly on the interval `[0,2]`. Any computed distance should, however, be within floating-point roundoff error.



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var ndarray = require( '@stdlib/ndarray-ctor' );

var Float64Array = require( '@stdlib/array-float64' );

var incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );



var dist;

var dxy;

var dyx;

var dx;

var dy;

var i;



// Initialize an accumulator for a 2-dimensional correlation distance matrix:

var accumulator = incrpcorrdistmat( 2 );



// Create a 1-dimensional data vector:

var buffer = new Float64Array( 2 );

var shape = [ 2 ];

var strides = [ 1 ];



var vec = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );



// For each simulated data vector, update the sample correlation distance matrix...

for ( i = 0; i < 100; i++ ) {

    vec.set( 0, randu()*100.0 );

    vec.set( 1, randu()*100.0 );

    dist = accumulator( vec );



    dx = dist.get( 0, 0 ).toFixed( 4 );

    dy = dist.get( 1, 1 ).toFixed( 4 );

    dxy = dist.get( 0, 1 ).toFixed( 4 );

    dyx = dist.get( 1, 0 ).toFixed( 4 );



    console.log( '[ %d, %d\n  %d, %d ]', dx, dxy, dyx, dy );

}

```



* * *



## See Also



-   [`@stdlib/stats-incr/pcorrdist`][@stdlib/stats/incr/pcorrdist]: compute a sample Pearson product-moment correlation distance.

-   [`@stdlib/stats-incr/pcorrmat`][@stdlib/stats/incr/pcorrmat]: compute a sample Pearson product-moment correlation matrix incrementally.



* * *



## Notice



This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.



For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-pcorrdistmat.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-pcorrdistmat



[test-image]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-pcorrdistmat/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-pcorrdistmat?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-incr-pcorrdistmat/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-pcorrdistmat/main/LICENSE



[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient



[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/ndarray-ctor



[@stdlib/stats/incr/pcorrdist]: https://github.com/stdlib-js/stats-incr-pcorrdist



[@stdlib/stats/incr/pcorrmat]: https://github.com/stdlib-js/stats-incr-pcorrmat