Compute an unbiased sample covariance matrix incrementally.
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Compute an [unbiased sample covariance matrix][covariance-matrix] incrementally.
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 asmath
\mathop{\mathrm{cov_{jkn}}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_{ij} - \bar{x}_{jn})(x_{ik} - \bar{x}_{kn})
math
\mathop{\mathrm{cov_{jkn}}} = \frac{1}{n} \sum_{i=0}^{n-1} (x_{ij} - \mu_{j})(x_{ik} - \mu_{k})
bash
npm install @stdlib/stats-incr-covmat
script
tag without installation and bundlers, use the [ES Module][es-module] available on the [esm
][esm-url] branch (see [README][esm-readme]).deno
][deno-url] branch (see [README][deno-readme] for usage intructions).umd
][umd-url] branch (see [README][umd-readme]).javascript
var incrcovmat = require( '@stdlib/stats-incr-covmat' );
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 );
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 );
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 );
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>
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 );
}