mathjs/lib/function/combinatorics/bellNumbers.js

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.createBellNumbers = void 0;

var _factory = require("../../utils/factory");

var name = 'bellNumbers';
var dependencies = ['typed', 'addScalar', 'isNegative', 'isInteger', 'stirlingS2'];
var createBellNumbers = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
  var typed = _ref.typed,
      addScalar = _ref.addScalar,
      isNegative = _ref.isNegative,
      isInteger = _ref.isInteger,
      stirlingS2 = _ref.stirlingS2;

  /**
   * 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 takes integer arguments.
   * The following condition must be enforced: n >= 0
   *
   * Syntax:
   *
   *   math.bellNumbers(n)
   *
   * Examples:
   *
   *    math.bellNumbers(3) // returns 5
   *    math.bellNumbers(8) // returns 4140
   *
   * See also:
   *
   *    stirlingS2
   *
   * @param {Number | BigNumber} n    Total number of objects in the set
   * @return {Number | BigNumber}     B(n)
   */
  return typed(name, {
    'number | BigNumber': function numberBigNumber(n) {
      if (!isInteger(n) || isNegative(n)) {
        throw new TypeError('Non-negative integer value expected in function bellNumbers');
      } // Sum (k=0, n) S(n,k).


      var result = 0;

      for (var i = 0; i <= n; i++) {
        result = addScalar(result, stirlingS2(n, i));
      }

      return result;
    }
  });
});
exports.createBellNumbers = createBellNumbers;