Compute a moving unbiased sample covariance incrementally.
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Compute a moving [unbiased sample covariance][covariance] incrementally.
n of size W is defined asmath
\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=j}^{j+W-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)j specifies the index of the value at which the window begins. For example, for a trailing (i.e., non-centered) window using zero-based indexing and j greater than or equal to W, j is the n-Wth value with n being the number of values thus analyzed.n of size W is defined asmath
\mathop{\mathrm{cov_n}} = \frac{1}{n} \sum_{i=j}^{j+W-1} (x_i - \mu_x)(y_i - \mu_y)bash
npm install @stdlib/stats-incr-mcovariancescript 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 incrmcovariance = require( '@stdlib/stats-incr-mcovariance' );function which incrementally computes a moving [unbiased sample covariance][covariance]. The window parameter defines the number of values over which to compute the moving [unbiased sample covariance][covariance].javascript
var accumulator = incrmcovariance( 3 );mx and my arguments.javascript
var accumulator = incrmcovariance( 3, 5.0, -3.14 );x and y, the accumulator function returns an updated [unbiased sample covariance][covariance]. If not provided input values x and y, the accumulator function returns the current [unbiased sample covariance][covariance].javascript
var accumulator = incrmcovariance( 3 );
var v = accumulator();
// returns null
// Fill the window...
v = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 0.0
v = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~-7.49
v = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns -8.35
// Window begins sliding...
v = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns -29.42
v = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns -24.5
v = accumulator();
// returns -24.5NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for at least W-1 future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.W (x,y) pairs are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.javascript
var randu = require( '@stdlib/random-base-randu' );
var incrmcovariance = require( '@stdlib/stats-incr-mcovariance' );
var accumulator;
var x;
var y;
var i;
// Initialize an accumulator:
accumulator = incrmcovariance( 5 );
// For each simulated datum, update the moving unbiased sample covariance...
for ( i = 0; i < 100; i++ ) {
x = randu() * 100.0;
y = randu() * 100.0;
accumulator( x, y );
}
console.log( accumulator() );
