npm package: @stdlib/stats-incr-pcorrdistmat
Description: Compute a sample Pearson product-moment correlation distance matrix incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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# incrpcorrdistmat

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute a [sample Pearson product-moment correlation distance matrix][pearson-correlation] incrementally.

<section class="intro">

A [sample Pearson product-moment correlation distance matrix][pearson-correlation] is an M-by-M matrix whose elements specified by indices `j` and `k` are the [sample Pearson product-moment correlation distances][pearson-correlation] between the jth and kth data variables. The [sample Pearson product-moment correlation distance][pearson-correlation] is defined as

<!-- <equation class="equation" label="eq:pearson_distance" align="center" raw="d_{x,y} = 1 - r_{x,y} = 1 - \frac{\operatorname{cov_n(x,y)}}{\sigma_x \sigma_y}" alt="Equation for the Pearson product-moment correlation distance."> -->

<div class="equation" align="center" data-raw-text="d_{x,y} = 1 - r_{x,y} = 1 - \frac{\operatorname{cov_n(x,y)}}{\sigma_x \sigma_y}" data-equation="eq:pearson_distance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/pcorrdistmat/docs/img/equation_pearson_distance.svg" alt="Equation for the Pearson product-moment correlation distance.">
    <br>
</div>

<!-- </equation> -->

where `r` is the [sample Pearson product-moment correlation coefficient][pearson-correlation], `cov(x,y)` is the sample covariance, and `σ` corresponds to the sample standard deviation. As `r` resides on the interval `[-1,1]`, `d` resides on the interval `[0,2]`.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-pcorrdistmat
```

</section>

<section class="usage">

## Usage

```javascript
var incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );
```

#### incrpcorrdistmat( out\[, means] )

Returns an accumulator `function` which incrementally computes a [sample Pearson product-moment correlation distance matrix][pearson-correlation].

```javascript
// Create an accumulator for computing a 2-dimensional correlation distance matrix:
var accumulator = incrpcorrdistmat( 2 );
```

The `out` argument may be either the order of the [correlation distance matrix][pearson-correlation] or a square 2-dimensional [`ndarray`][@stdlib/ndarray/ctor] for storing the [correlation distance matrix][pearson-correlation].

```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 correlation distance matrix:
var dist = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

var accumulator = incrpcorrdistmat( dist );
```

When means are known, the function supports providing a 1-dimensional [`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 = incrpcorrdistmat( 2, means );
```

#### accumulator( \[vector] )

If provided a data vector, the accumulator function returns an updated [sample Pearson product-moment distance correlation matrix][pearson-correlation]. If not provided a data vector, the accumulator function returns the current [sample Pearson product-moment correlation distance matrix][pearson-correlation].

```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 dist = 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 = incrpcorrdistmat( dist );

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

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

var bool = ( out === dist );
// 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>
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Due to limitations inherent in representing numeric values using floating-point format (i.e., the inability to represent numeric values with infinite precision), the [correlation distance][pearson-correlation] between perfectly correlated random variables may **not** be `0` or `2`. In fact, the [correlation distance][pearson-correlation] is **not** guaranteed to be strictly on the interval `[0,2]`. Any computed distance should, however, be within floating-point roundoff error.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random-base-randu' );
var ndarray = require( '@stdlib/ndarray-ctor' );
var Float64Array = require( '@stdlib/array-float64' );
var incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );

var dist;
var dxy;
var dyx;
var dx;
var dy;
var i;

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

    dx = dist.get( 0, 0 ).toFixed( 4 );
    dy = dist.get( 1, 1 ).toFixed( 4 );
    dxy = dist.get( 0, 1 ).toFixed( 4 );
    dyx = dist.get( 1, 0 ).toFixed( 4 );

    console.log( '[ %d, %d\n  %d, %d ]', dx, dxy, dyx, dy );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-incr/pcorrdist`][@stdlib/stats/incr/pcorrdist]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation distance.</span>
-   <span class="package-name">[`@stdlib/stats-incr/pcorrmat`][@stdlib/stats/incr/pcorrmat]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation matrix incrementally.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

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