// wink-statistics
// Fast and Numerically Stable Statistical Analysis Utilities.
//
// Copyright (C) GRAYPE Systems Private Limited
//
// This file is part of “wink-statistics”.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
// ## streaming
var getValidFD = require( './get-valid-fd.js' );
// ### cov (Covariance)
/**
*
* Covariance is computed incrementally with arrival of each pair of `x` and `y`
* values from a stream of data.
*
* The [`compute()`](https://winkjs.org/wink-statistics/Stream.html#compute) requires
* two numeric arguments `x` and `y`.
*
* The [`result()`](https://winkjs.org/wink-statistics/Stream.html#result) returns
* an object containing sample covariance `cov`, along with
* `meanX`, `meanY` and `size` of data i.e. number of x & y pairs. It also contains
* population covariance `covp`.
*
* @memberof streaming#
* @return {Stream} Object containing methods such as `compute()`, `result()` & `reset()`.
* @example
* var covariance = cov();
* covariance.compute( 10, 80 );
* covariance.compute( 15, 75 );
* covariance.compute( 16, 65 );
* covariance.compute( 18, 50 );
* covariance.compute( 21, 45 );
* covariance.compute( 30, 30 );
* covariance.compute( 36, 18 );
* covariance.compute( 40, 9 );
* covariance.result();
* // returns { size: 8,
* // meanX: 23.25,
* // meanY: 46.5,
* // cov: -275.8571,
* // covp: -241.375
* // }
*/
var covariance = function () {
var meanX = 0;
var meanY = 0;
var covXY = 0;
var items = 0;
// Returned!
var methods = Object.create( null );
methods.compute = function ( xi, yi ) {
var dx, dy;
items += 1;
dx = xi - meanX;
dy = yi - meanY;
meanX += dx / items;
meanY += dy / items;
covXY += dx * ( yi - meanY );
return undefined;
}; // compute()
// This returns the sample standard deviation.
methods.value = function ( fractionDigits ) {
var fd = getValidFD( fractionDigits );
return ( items > 1 ) ? +( covXY / ( items - 1 ) ).toFixed( fd ) : 0;
}; // value()
// This returns the sample covariance along with host of other statistics.
methods.result = function ( fractionDigits ) {
var obj = Object.create( null );
var fd = getValidFD( fractionDigits );
var cov = ( items > 1 ) ? ( covXY / ( items - 1 ) ) : 0;
var covp = ( items ) ? ( covXY / items ) : 0;
obj.size = items;
obj.meanX = +meanX.toFixed( fd );
obj.meanY = +meanY.toFixed( fd );
// Sample covariance.
obj.cov = +cov.toFixed( fd );
// Population covariance.
obj.covp = +covp.toFixed( fd );
return obj;
}; // result()
methods.reset = function () {
meanX = 0;
meanY = 0;
covXY = 0;
items = 0;
}; // reset()
return methods;
}; // covariance()
module.exports = covariance;
