https://github.com/stdlib-js/stats-incr-pcorrmat
Compute a sample Pearson product-moment correlation matrix incrementally.
https://github.com/stdlib-js/stats-incr-pcorrmat
anticorrelation correlated correlation covariance dispersion javascript math mathematics matrix node node-js nodejs sample-covariance standard-deviation statistics stats stdlib unbiased var variance
Last synced: 5 months ago
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Compute a sample Pearson product-moment correlation matrix incrementally.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-incr-pcorrmat
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T19:01:59.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-03-31T00:49:04.000Z (6 months ago)
- Last Synced: 2025-04-12T17:57:32.655Z (6 months ago)
- Topics: anticorrelation, correlated, correlation, covariance, dispersion, javascript, math, mathematics, matrix, node, node-js, nodejs, sample-covariance, standard-deviation, statistics, stats, stdlib, unbiased, var, variance
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 2.35 MB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# incrpcorrmat
[![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 matrix][pearson-correlation] incrementally.
A [Pearson product-moment correlation matrix][pearson-correlation] is an M-by-M matrix whose elements specified by indices `j` and `k` are the [Pearson product-moment correlation coefficients][pearson-correlation] between the jth and kth data variables. The [Pearson product-moment correlation coefficient][pearson-correlation] between random variables `X` and `Y` is defined as
```math
\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}
```
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
```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}}
```
## Installation
```bash
npm install @stdlib/stats-incr-pcorrmat
```
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 incrpcorrmat = require( '@stdlib/stats-incr-pcorrmat' );
```
#### incrpcorrmat( out\[, means] )
Returns an accumulator `function` which incrementally computes a [sample Pearson product-moment correlation matrix][pearson-correlation].
```javascript
// Create an accumulator for computing a 2-dimensional correlation matrix:
var accumulator = incrpcorrmat( 2 );
```
The `out` argument may be either the order of the [correlation matrix][pearson-correlation] or a square 2-dimensional [`ndarray`][@stdlib/ndarray/ctor] for storing the [correlation 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 matrix:
var corr = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );
var accumulator = incrpcorrmat( corr );
```
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 = incrpcorrmat( 2, means );
```
#### accumulator( \[vector] )
If provided a data vector, the accumulator function returns an updated [sample Pearson product-moment correlation matrix][pearson-correlation]. If not provided a data vector, the accumulator function returns the current [sample Pearson product-moment correlation 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 corr = 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 = incrpcorrmat( corr );
vec.set( 0, 2.0 );
vec.set( 1, 1.0 );
var out = accumulator( vec );
// returns
var bool = ( out === corr );
// 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
```
## Examples
```javascript
var randu = require( '@stdlib/random-base-randu' );
var ndarray = require( '@stdlib/ndarray-ctor' );
var Float64Array = require( '@stdlib/array-float64' );
var incrpcorrmat = require( '@stdlib/stats-incr-pcorrmat' );
var corr;
var rxy;
var ryx;
var rx;
var ry;
var i;
// Initialize an accumulator for a 2-dimensional correlation matrix:
var accumulator = incrpcorrmat( 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 matrix...
for ( i = 0; i < 100; i++ ) {
vec.set( 0, randu()*100.0 );
vec.set( 1, randu()*100.0 );
corr = accumulator( vec );
rx = corr.get( 0, 0 ).toFixed( 4 );
ry = corr.get( 1, 1 ).toFixed( 4 );
rxy = corr.get( 0, 1 ).toFixed( 4 );
ryx = corr.get( 1, 0 ).toFixed( 4 );
console.log( '[ %d, %d\n %d, %d ]', rx, rxy, ryx, ry );
}
```
* * *
## See Also
- [`@stdlib/stats-incr/covmat`][@stdlib/stats/incr/covmat]: compute an unbiased sample covariance matrix incrementally.
- [`@stdlib/stats-incr/pcorr`][@stdlib/stats/incr/pcorr]: compute a sample Pearson product-moment correlation coefficient.
- [`@stdlib/stats-incr/pcorrdistmat`][@stdlib/stats/incr/pcorrdistmat]: compute a sample Pearson product-moment correlation distance 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-pcorrmat.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-pcorrmat
[test-image]: https://github.com/stdlib-js/stats-incr-pcorrmat/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-incr-pcorrmat/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-pcorrmat/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-pcorrmat?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-pcorrmat/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-incr-pcorrmat/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-incr-pcorrmat/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-incr-pcorrmat/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-incr-pcorrmat/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-incr-pcorrmat/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-incr-pcorrmat/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-pcorrmat/main/LICENSE
[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
[covariance]: https://en.wikipedia.org/wiki/Covariance
[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/ndarray-ctor
[@stdlib/stats/incr/covmat]: https://github.com/stdlib-js/stats-incr-covmat
[@stdlib/stats/incr/pcorr]: https://github.com/stdlib-js/stats-incr-pcorr
[@stdlib/stats/incr/pcorrdistmat]: https://github.com/stdlib-js/stats-incr-pcorrdistmat