simple-squiggle

A restricted subset of Squiggle
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stirlingS2.js (2721B)

      1 import { factory } from '../../utils/factory.js';
      2 import { isNumber } from '../../utils/is.js';
      3 var name = 'stirlingS2';
      4 var dependencies = ['typed', 'addScalar', 'subtract', 'multiplyScalar', 'divideScalar', 'pow', 'factorial', 'combinations', 'isNegative', 'isInteger', 'number', '?bignumber', 'larger'];
      5 export var createStirlingS2 = /* #__PURE__ */factory(name, dependencies, _ref => {
      6   var {
      7     typed,
      8     addScalar,
      9     subtract,
     10     multiplyScalar,
     11     divideScalar,
     12     pow,
     13     factorial,
     14     combinations,
     15     isNegative,
     16     isInteger,
     17     number,
     18     bignumber,
     19     larger
     20   } = _ref;
     21   var smallCache = [];
     22   var bigCache = [];
     23   /**
     24    * The Stirling numbers of the second kind, counts the number of ways to partition
     25    * a set of n labelled objects into k nonempty unlabelled subsets.
     26    * stirlingS2 only takes integer arguments.
     27    * The following condition must be enforced: k <= n.
     28    *
     29    *  If n = k or k = 1 <= n, then s(n,k) = 1
     30    *  If k = 0 < n, then s(n,k) = 0
     31    *
     32    * Note that if either n or k is supplied as a BigNumber, the result will be
     33    * as well.
     34    *
     35    * Syntax:
     36    *
     37    *   math.stirlingS2(n, k)
     38    *
     39    * Examples:
     40    *
     41    *    math.stirlingS2(5, 3) //returns 25
     42    *
     43    * See also:
     44    *
     45    *    bellNumbers
     46    *
     47    * @param {Number | BigNumber} n    Total number of objects in the set
     48    * @param {Number | BigNumber} k    Number of objects in the subset
     49    * @return {Number | BigNumber}     S(n,k)
     50    */
     51 
     52   return typed(name, {
     53     'number | BigNumber, number | BigNumber': function numberBigNumberNumberBigNumber(n, k) {
     54       if (!isInteger(n) || isNegative(n) || !isInteger(k) || isNegative(k)) {
     55         throw new TypeError('Non-negative integer value expected in function stirlingS2');
     56       } else if (larger(k, n)) {
     57         throw new TypeError('k must be less than or equal to n in function stirlingS2');
     58       }
     59 
     60       var big = !(isNumber(n) && isNumber(k));
     61       var cache = big ? bigCache : smallCache;
     62       var make = big ? bignumber : number;
     63       var nn = number(n);
     64       var nk = number(k);
     65       /* See if we already have the value: */
     66 
     67       if (cache[nn] && cache[nn].length > nk) {
     68         return cache[nn][nk];
     69       }
     70       /* Fill the cache */
     71 
     72 
     73       for (var m = 0; m <= nn; ++m) {
     74         if (!cache[m]) {
     75           cache[m] = [m === 0 ? make(1) : make(0)];
     76         }
     77 
     78         if (m === 0) continue;
     79         var row = cache[m];
     80         var prev = cache[m - 1];
     81 
     82         for (var i = row.length; i <= m && i <= nk; ++i) {
     83           if (i === m) {
     84             row[i] = 1;
     85           } else {
     86             row[i] = addScalar(multiplyScalar(make(i), prev[i]), prev[i - 1]);
     87           }
     88         }
     89       }
     90 
     91       return cache[nn][nk];
     92     }
     93   });
     94 });