mathjs/src/function/probability/multinomial.js

'use strict'

const deepForEach = require('../../utils/collection/deepForEach')

function factory (type, config, load, typed) {
  const add = load(require('../arithmetic/add'))
  const multiply = load(require('../arithmetic/multiply'))
  const divide = load(require('../arithmetic/divide'))
  const factorial = load(require('../probability/factorial'))
  const isInteger = load(require('../utils/isInteger'))
  const isPositive = load(require('../utils/isPositive'))

  /**
   * 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) {
      let sum = 0
      let denom = 1

      deepForEach(a, function (ai) {
        if (!isInteger(ai) || !isPositive(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