Variance
!NPM versionnpm-imagenpm-url !Build Statustravis-imagetravis-url !Coverage Statuscoveralls-imagecoveralls-url !Dependenciesdependencies-imagedependencies-urlComputes the variance.
The population variance (biased sample variance) is defined as
<img src="https://cdn.rawgit.com/compute-io/variance/2b812a7ecb17a847cc39ed5730f13114636553d4/docs/img/eqn2.svg" alt="Equation for the population (biased sample) variance.">
<br>and the unbiased sample variance is defined as
<img src="https://cdn.rawgit.com/compute-io/variance/bdaaeaeb1718476b61f462cf3e5252d7b4c0c585/docs/img/eqn.svg" alt="Equation for the unbiased sample variance.">
<br>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-varianceFor 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 5.067For 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 5.067By 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 4.56If 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
matrixdata 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 5.067If 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 nullExamples
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.jsTests
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 testAll 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-covIstanbul creates a
./reports/coverage directory. To access an HTML version of the report,$ make view-cov
