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incrcovmat

Compute an unbiased sample covariance matrix incrementally.

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

$${\mathrm{cov}}_{\mathrm{jkn}}=\frac{1}{n-1}\sum _{i=0}^{n-1}(x_{ij}-{\overline{x}}_{jn})(x_{ik}-{\overline{x}}_{kn})$$

For known population means, the unbiased sample covariance is defined as

$${\mathrm{cov}}_{\mathrm{jkn}}=\frac{1}{n}\sum _{i=0}^{n-1}(x_{ij}-{\mu }_j)(x_{ik}-{\mu }_k)$$

Installation

npm install @stdlib/stats-incr-covmat

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

incrcovmat( out[, means] )

Returns an accumulator function which incrementally computes an unbiased sample covariance matrix.

// 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 or a square 2-dimensional ndarray for storing the unbiased sample covariance matrix.

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 containing mean values.

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. If not provided a data vector, the accumulator function returns the current unbiased sample covariance matrix.

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>

Examples

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 );
}

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See Also

• @stdlib/stats-incr/covariance: compute an unbiased sample covariance incrementally.
• @stdlib/stats-incr/pcorrmat: compute a sample Pearson product-moment correlation matrix incrementally.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.