# 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

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

## 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 );
}