mathjs/lib/function/probability/multinomial.js

'use strict';

var isPositiveInteger = require('../../util/bignumber').isPositiveInteger; // FIXME: this disables using bellNumbers without loading BigNumbers

function factory (type, config, load, typed) {
  var collection = load(require('../../type/matrix/collection'));
  var add = load(require('../arithmetic/add'));
  var multiply = load(require('../arithmetic/multiply'));
  var divide = load(require('../arithmetic/divide'));
  var factorial = load(require('../probability/factorial'));

  /**
   * Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities.
   *
   * multinomial takes one array of integers as an argument.
   * The following condition must be enforced: every ai <= 0
   *
   * Syntax:
   *
   *     math.multinomial(a) // a is an array type
   *
   * Examples:
   *
   *    math.multinomial([1,2,1]); // returns 12
   *
   * See also:
   *
   *    combinations, factorial
   *
   * @param {number[] | BigNumber[]} a    Integer numbers of objects in the subset
   * @return {Number | BigNumber}         Multinomial coefficient.
   */
  return typed('multinomial', {
    'Array | Matrix': function (a) {
      var sum = 0;
      var denom = 1;

      collection.deepForEach(a, function(ai) {
        if(!isPositiveInteger(ai)) {
          throw new TypeError('Positive integer value expected in function multinomial');
        }
        sum = add(sum, ai);
        denom = multiply(denom, factorial(ai));
      });

      return divide(factorial(sum), denom);
    }
  });
}

exports.name = 'multinomial';
exports.factory = factory;