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# incrpcorrdistmat

> 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.rawgit.com/stdlib-js/stdlib/27e2a43c70db648bb5bbc3fd0cdee050c25adc0b/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="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 class="links">

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

[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/ndarray-ctor

</section>

<!-- /.links -->
