Variance

Computes the variance.

The population variance (biased sample variance) is defined as

and the unbiased sample variance is defined as

where x_0, x_1,...,x_{N-1} are individual data values and N is the total number of values in the data set.

Installation

$ npm install compute-variance

For use in the browser, use browserify.

Usage

var variance = require( 'compute-variance' );

variance( x[, opts] )

Computes the variance. x may be either an array, typed array, or matrix.

var data, s2;

data = [ 2, 4, 5, 3, 4, 3, 1, 5, 6, 9 ];
s2 = variance( data );
// returns 5.067

data = new Int8Array( data );
s2 = variance( data );
// returns 5.067

For non-numeric arrays, provide an accessor function for accessing numeric array values.

var data = [
    {'x':2},
    {'x':4},
    {'x':5},
    {'x':3},
    {'x':4},
    {'x':3},
    {'x':1},
    {'x':5},
    {'x':6},
    {'x':9}
];

function getValue( d ) {
    return d.x;
}

var s2 = variance( data, {
	'accessor': getValue
});
// returns 5.067

By default, the function calculates the unbiased sample variance. To calculate the population variance (or a biased sample variance), set the bias option to true.

var data = [ 2, 4, 5, 3, 4, 3, 1, 5, 6, 9 ];

var sigma2 = variance( data, {
	'bias': true
});
// returns 4.56

If provided a matrix, the function accepts the following additional options:

• dim: dimension along which to compute the variance. Default: 2 (along the columns).
• dtype: output matrix data type. Default: float64.

By default, the function computes the variance along the columns (dim=2).

var matrix = require( 'dstructs-matrix' ),
	data,
	mat,
	s2,
	i;

data = new Int8Array( 25 );
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = i;
}
mat = matrix( data, [5,5], 'int8' );
/*
	[  0  1  2  3  4
	   5  6  7  8  9
	  10 11 12 13 14
	  15 16 17 18 19
	  20 21 22 23 24 ]
*/

s2 = variance( mat );
/*
	[  2.5
	   2.5
	   2.5
	   2.5
	   2.5 ]
*/

To compute the variance along the rows, set the dim option to 1.

s2 = variance( mat, {
	'dim': 1
});
/*
	[ 62.5, 62.5, 62.5, 62.5, 62.5 ]
*/

By default, the output matrix data type is float64. To specify a different output data type, set the dtype option.

s2 = variance( mat, {
	'dim': 1,
	'dtype': 'uint8'
});
/*
	[ 62.5, 62.5, 62.5, 62.5, 62.5 ]
*/

var dtype = s2.dtype;
// returns 'uint8'

If provided a matrix having either dimension equal to 1, the function treats the matrix as a typed array and returns a numeric value.

data = [ 2, 4, 5, 3, 4, 3, 1, 5, 6, 9  ];

// Row vector:
mat = matrix( new Int8Array( data ), [1,10], 'int8' );
s2 = variance( mat );
// returns 5.067

// Column vector:
mat = matrix( new Int8Array( data ), [10,1], 'int8' );
s2 = variance( mat );
// returns 5.067

If provided an empty array, typed array, or matrix, the function returns null.

s2 = variance( [] );
// returns null

s2 = variance( new Int8Array( [] ) );
// returns null

s2 = variance( matrix( [0,0] ) );
// returns null

s2 = variance( matrix( [0,10] ) );
// returns null

s2 = variance( matrix( [10,0] ) );
// returns null

Examples

var matrix = require( 'dstructs-matrix' ),
	variance = require( 'compute-variance' );

var data,
	mat,
	s2,
	i;

// Plain arrays...
var data = new Array( 100 );
for ( var i = 0; i < data.length; i++ ) {
	data[ i ] = Math.round( Math.random() * 10 + 1 );
}
s2 = variance( data );

// Object arrays (accessors)...
function getValue( d ) {
	return d.x;
}
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = {
		'x': data[ i ]
	};
}
s2 = variance( data, {
	'accessor': getValue
});

// Typed arrays...
data = new Int32Array( 100 );
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = Math.round( Math.random() * 10 + 1 );
}
s2 = variance( data );

// Matrices (along rows)...
mat = matrix( data, [10,10], 'int32' );
s2 = variance( mat, {
	'dim': 1
});

// Matrices (along columns)...
s2 = variance( mat, {
	'dim': 2
});

// Matrices (custom output data type)...
s2 = variance( mat, {
	'dtype': 'uint8'
});

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

License

MIT license.

Copyright

Copyright © 2014-2015. The Compute.io Authors.