92 lines
2.8 KiB
JavaScript
92 lines
2.8 KiB
JavaScript
"use strict";
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Object.defineProperty(exports, "__esModule", {
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value: true
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});
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exports.createStirlingS2 = void 0;
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var _factory = require("../../utils/factory.js");
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var _is = require("../../utils/is.js");
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const name = 'stirlingS2';
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const dependencies = ['typed', 'addScalar', 'subtractScalar', 'multiplyScalar', 'divideScalar', 'pow', 'factorial', 'combinations', 'isNegative', 'isInteger', 'number', '?bignumber', 'larger'];
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const createStirlingS2 = exports.createStirlingS2 = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
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let {
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typed,
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addScalar,
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subtractScalar,
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multiplyScalar,
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divideScalar,
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pow,
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factorial,
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combinations,
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isNegative,
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isInteger,
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number,
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bignumber,
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larger
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} = _ref;
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const smallCache = [];
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const bigCache = [];
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/**
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* The Stirling numbers of the second kind, counts the number of ways to partition
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* a set of n labelled objects into k nonempty unlabelled subsets.
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* stirlingS2 only takes integer arguments.
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* The following condition must be enforced: k <= n.
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*
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* If n = k or k = 1 <= n, then s(n,k) = 1
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* If k = 0 < n, then s(n,k) = 0
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*
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* Note that if either n or k is supplied as a BigNumber, the result will be
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* as well.
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*
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* Syntax:
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*
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* math.stirlingS2(n, k)
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*
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* Examples:
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*
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* math.stirlingS2(5, 3) //returns 25
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*
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* See also:
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*
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* bellNumbers
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*
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* @param {Number | BigNumber} n Total number of objects in the set
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* @param {Number | BigNumber} k Number of objects in the subset
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* @return {Number | BigNumber} S(n,k)
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*/
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return typed(name, {
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'number | BigNumber, number | BigNumber': function (n, k) {
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if (!isInteger(n) || isNegative(n) || !isInteger(k) || isNegative(k)) {
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throw new TypeError('Non-negative integer value expected in function stirlingS2');
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} else if (larger(k, n)) {
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throw new TypeError('k must be less than or equal to n in function stirlingS2');
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}
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const big = !((0, _is.isNumber)(n) && (0, _is.isNumber)(k));
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const cache = big ? bigCache : smallCache;
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const make = big ? bignumber : number;
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const nn = number(n);
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const nk = number(k);
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/* See if we already have the value: */
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if (cache[nn] && cache[nn].length > nk) {
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return cache[nn][nk];
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}
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/* Fill the cache */
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for (let m = 0; m <= nn; ++m) {
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if (!cache[m]) {
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cache[m] = [m === 0 ? make(1) : make(0)];
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}
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if (m === 0) continue;
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const row = cache[m];
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const prev = cache[m - 1];
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for (let i = row.length; i <= m && i <= nk; ++i) {
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if (i === m) {
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row[i] = 1;
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} else {
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row[i] = addScalar(multiplyScalar(make(i), prev[i]), prev[i - 1]);
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}
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}
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}
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return cache[nn][nk];
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}
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});
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}); |