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
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
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 );
}