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incrpcorrmat

Compute a sample Pearson product-moment correlation matrix incrementally.

A Pearson product-moment correlation matrix is an M-by-M matrix whose elements specified by indices j and k are the Pearson product-moment correlation coefficients between the jth and kth data variables. The Pearson product-moment correlation coefficient between random variables X and Y is defined as

$$\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}$$

where the numerator is the covariance and the denominator is the product of the respective standard deviations.

For a sample of size n, the sample Pearson product-moment correlation coefficient is defined as

$$r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}$$

Installation

npm install @stdlib/stats-incr-pcorrmat

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 incrpcorrmat = require( '@stdlib/stats-incr-pcorrmat' );

incrpcorrmat( out[, means] )

Returns an accumulator function which incrementally computes a sample Pearson product-moment correlation matrix.

// Create an accumulator for computing a 2-dimensional correlation matrix:
var accumulator = incrpcorrmat( 2 );

The out argument may be either the order of the correlation matrix or a square 2-dimensional ndarray for storing the correlation 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 correlation matrix:
var corr = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

var accumulator = incrpcorrmat( corr );

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 = incrpcorrmat( 2, means );

accumulator( [vector] )

If provided a data vector, the accumulator function returns an updated sample Pearson product-moment correlation matrix. If not provided a data vector, the accumulator function returns the current sample Pearson product-moment correlation 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 corr = 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 = incrpcorrmat( corr );

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

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

var bool = ( out === corr );
// 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 incrpcorrmat = require( '@stdlib/stats-incr-pcorrmat' );

var corr;
var rxy;
var ryx;
var rx;
var ry;
var i;

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

    rx = corr.get( 0, 0 ).toFixed( 4 );
    ry = corr.get( 1, 1 ).toFixed( 4 );
    rxy = corr.get( 0, 1 ).toFixed( 4 );
    ryx = corr.get( 1, 0 ).toFixed( 4 );

    console.log( '[ %d, %d\n  %d, %d ]', rx, rxy, ryx, ry );
}

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See Also

• @stdlib/stats-incr/covmat: compute an unbiased sample covariance matrix incrementally.
• @stdlib/stats-incr/pcorr: compute a sample Pearson product-moment correlation coefficient.
• @stdlib/stats-incr/pcorrdistmat: compute a sample Pearson product-moment correlation distance 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 © 2016-2024. The Stdlib Authors.