mathjs/lib/function/combinatorics/bellNumbers.js

'use strict';

module.exports = function (math) {
  var util = require('../../util/index'),

  BigNumber = math.type.BigNumber,
  collection = math.collection,

  isNumber = util.number.isNumber,
  isInteger = util.number.isInteger;

  /**
  * The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S.

  * bellNumbers only take integer arguments.
  * The following condition must be enforced: n >= 0
  *
  * Syntax:
  *
  *   math.bellNumbers(n)
  *
  * Examples:
  *
  *    math.bellNumbers(4, 3); //returns 10
  *
  *
  * @param {Number | BigNumber} n    Total number of objects in the set
  * @return {Number | BigNumber}     B(n)
  */

  math.bellNumbers = function bellNumbers (n) {
    var result = 0;
    var arity = arguments.length;
    if (arity != 1) {
      throw new math.error.ArgumentsError('bellNumbers', arguments.length, 1);
    }

    if (isNumber(n) || n instanceof BigNumber) {

      if (!isInteger(n) || n < 0) {
        throw new TypeError('Positive integer value expected in function bellNumbers');
      }

      // Sum (k=0, n) S(n,k).
      for(var i = 0; i <= n; i++) {
        result = math.add(result, math.stirlingS2(n,i));
      }
      return result;
    }
    throw new math.error.UnsupportedTypeError('bellNumbers', math['typeof'](n));
  }



  /**
   * Test whether BigNumber n is a positive integer
   * @param {BigNumber} n
   * @returns {boolean} isPositiveInteger
   */
   var isPositiveInteger = function(n) {
     return n.isInteger() && n.gte(0);
   };
 };