npm package: @stdlib/stats-incr-covmat
Description: Compute an unbiased sample covariance matrix incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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# incrcovmat

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

> Compute an [unbiased sample covariance matrix][covariance-matrix] incrementally.

<section class="intro">

A [covariance matrix][covariance-matrix] is an M-by-M matrix whose elements specified by indices `j` and `k` are the [covariances][covariance-matrix] between the jth and kth data variables. For unknown population means, the [unbiased sample covariance][covariance-matrix] is defined as

<!-- <equation class="equation" label="eq:unbiased_sample_covariance_unknown_means" align="center" raw="\operatorname{cov_{jkn}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_{ij} - \bar{x}_{jn})(x_{ik} - \bar{x}_{kn})" alt="Equation for the unbiased sample covariance for unknown population means."> -->

<div class="equation" align="center" data-raw-text="\operatorname{cov_{jkn}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_{ij} - \bar{x}_{jn})(x_{ik} - \bar{x}_{kn})" data-equation="eq:unbiased_sample_covariance_unknown_means">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/covmat/docs/img/equation_unbiased_sample_covariance_unknown_means.svg" alt="Equation for the unbiased sample covariance for unknown population means.">
    <br>
</div> -->

<!-- </equation> -->

For known population means, the [unbiased sample covariance][covariance-matrix] is defined as

<!-- <equation class="equation" label="eq:unbiased_sample_covariance_known_means" align="center" raw="\operatorname{cov_{jkn}} = \frac{1}{n} \sum_{i=0}^{n-1} (x_{ij} - \mu_{j})(x_{ik} - \mu_{k})" alt="Equation for the unbiased sample covariance for known population means."> -->

<!-- <div class="equation" align="center" data-raw-text="\operatorname{cov_{jkn}} = \frac{1}{n} \sum_{i=0}^{n-1} (x_{ij} - \mu_{j})(x_{ik} - \mu_{k})" data-equation="eq:unbiased_sample_covariance_known_means">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@566f739b0d9a5b720546f84f74de841b8d5e0c54/lib/node_modules/@stdlib/stats/incr/covmat/docs/img/equation_unbiased_sample_covariance_known_means.svg" alt="Equation for the unbiased sample covariance for known population means.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-covmat
```

</section>

<section class="usage">

## Usage

```javascript
var incrcovmat = require( '@stdlib/stats-incr-covmat' );
```

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

Returns an accumulator `function` which incrementally computes an [unbiased sample covariance matrix][covariance-matrix].

```javascript
// Create an accumulator for computing a 2-dimensional covariance matrix:
var accumulator = incrcovmat( 2 );
```

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

```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 covariance matrix:
var cov = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

var accumulator = incrcovmat( cov );
```

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 = incrcovmat( 2, means );
```

#### accumulator( \[vector] )

If provided a data vector, the accumulator function returns an updated [unbiased sample covariance matrix][covariance-matrix]. If not provided a data vector, the accumulator function returns the current [unbiased sample covariance matrix][covariance-matrix].

```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 cov = 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 = incrcovmat( cov );

vec.set( 0, 2.0 );
vec.set( 1, 1.0 );

var out = accumulator( vec );
// returns <ndarray>

var bool = ( out === cov );
// returns true

vec.set( 0, 1.0 );
vec.set( 1, -5.0 );

out = accumulator( vec );
// returns <ndarray>

vec.set( 0, 3.0 );
vec.set( 1, 3.14 );

out = accumulator( vec );
// returns <ndarray>

out = accumulator();
// returns <ndarray>
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random-base-randu' );
var ndarray = require( '@stdlib/ndarray-ctor' );
var Float64Array = require( '@stdlib/array-float64' );
var incrcovmat = require( '@stdlib/stats-incr-covmat' );

var cov;
var cxy;
var cyx;
var vx;
var vy;
var i;

// Initialize an accumulator for a 2-dimensional covariance matrix:
var accumulator = incrcovmat( 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 unbiased sample covariance matrix...
for ( i = 0; i < 100; i++ ) {
    vec.set( 0, randu()*100.0 );
    vec.set( 1, randu()*100.0 );
    cov = accumulator( vec );

    vx = cov.get( 0, 0 ).toFixed( 4 );
    vy = cov.get( 1, 1 ).toFixed( 4 );
    cxy = cov.get( 0, 1 ).toFixed( 4 );
    cyx = cov.get( 1, 0 ).toFixed( 4 );

    console.log( '[ %d, %d\n  %d, %d ]', vx, cxy, cyx, vy );
}
```

</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/covariance`][@stdlib/stats/incr/covariance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample covariance incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/pcorrmat`][@stdlib/stats/incr/pcorrmat]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation matrix incrementally.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[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-covmat/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-incr-covmat/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-covmat/main/LICENSE

[covariance-matrix]: https://en.wikipedia.org/wiki/Covariance_matrix

[@stdlib/ndarray/ctor]: https://www.npmjs.com/package/@stdlib/ndarray-ctor

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[@stdlib/stats/incr/covariance]: https://www.npmjs.com/package/@stdlib/stats-incr-covariance

[@stdlib/stats/incr/pcorrmat]: https://www.npmjs.com/package/@stdlib/stats-incr-pcorrmat

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</section>

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