mathjs/lib/function/probability/kldivergence.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict';

function factory(type, config, load, typed) {
  var matrix = load(require('../../type/matrix/function/matrix'));
  var divide = load(require('../arithmetic/divide'));
  var sum = load(require('../statistics/sum'));
  var multiply = load(require('../arithmetic/multiply'));
  var dotDivide = load(require('../arithmetic/dotDivide'));
  var log = load(require('../arithmetic/log'));
  var isNumeric = load(require('../utils/isNumeric'));
  /**
     * Calculate the Kullback-Leibler (KL) divergence  between two distributions
     *
     * Syntax:
     *
     *     math.kldivergence(x, y)
     *
     * Examples:
     *
     *     math.kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])   //returns 0.24376698773121153
     *
     *
     * @param  {Array | Matrix} q    First vector
     * @param  {Array | Matrix} p    Second vector
     * @return {number}              Returns distance between q and p
     */

  var kldivergence = typed('kldivergence', {
    'Array, Array': function ArrayArray(q, p) {
      return _kldiv(matrix(q), matrix(p));
    },
    'Matrix, Array': function MatrixArray(q, p) {
      return _kldiv(q, matrix(p));
    },
    'Array, Matrix': function ArrayMatrix(q, p) {
      return _kldiv(matrix(q), p);
    },
    'Matrix, Matrix': function MatrixMatrix(q, p) {
      return _kldiv(q, p);
    }
  });

  function _kldiv(q, p) {
    var plength = p.size().length;
    var qlength = q.size().length;

    if (plength > 1) {
      throw new Error('first object must be one dimensional');
    }

    if (qlength > 1) {
      throw new Error('second object must be one dimensional');
    }

    if (plength !== qlength) {
      throw new Error('Length of two vectors must be equal');
    } // Before calculation, apply normalization


    var sumq = sum(q);

    if (sumq === 0) {
      throw new Error('Sum of elements in first object must be non zero');
    }

    var sump = sum(p);

    if (sump === 0) {
      throw new Error('Sum of elements in second object must be non zero');
    }

    var qnorm = divide(q, sum(q));
    var pnorm = divide(p, sum(p));
    var result = sum(multiply(qnorm, log(dotDivide(qnorm, pnorm))));

    if (isNumeric(result)) {
      return result;
    } else {
      return Number.NaN;
    }
  }

  return kldivergence;
}

exports.name = 'kldivergence';
exports.factory = factory;