simple-squiggle/node_modules/mathjs/lib/esm/function/combinatorics/stirlingS2.js

94 lines
2.7 KiB
JavaScript

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