simple-squiggle

A restricted subset of Squiggle
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stirlingS2.js (3134B)

      1 "use strict";
      2 
      3 Object.defineProperty(exports, "__esModule", {
      4   value: true
      5 });
      6 exports.createStirlingS2 = void 0;
      7 
      8 var _factory = require("../../utils/factory.js");
      9 
     10 var _is = require("../../utils/is.js");
     11 
     12 var name = 'stirlingS2';
     13 var dependencies = ['typed', 'addScalar', 'subtract', 'multiplyScalar', 'divideScalar', 'pow', 'factorial', 'combinations', 'isNegative', 'isInteger', 'number', '?bignumber', 'larger'];
     14 var createStirlingS2 = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
     15   var typed = _ref.typed,
     16       addScalar = _ref.addScalar,
     17       subtract = _ref.subtract,
     18       multiplyScalar = _ref.multiplyScalar,
     19       divideScalar = _ref.divideScalar,
     20       pow = _ref.pow,
     21       factorial = _ref.factorial,
     22       combinations = _ref.combinations,
     23       isNegative = _ref.isNegative,
     24       isInteger = _ref.isInteger,
     25       number = _ref.number,
     26       bignumber = _ref.bignumber,
     27       larger = _ref.larger;
     28   var smallCache = [];
     29   var bigCache = [];
     30   /**
     31    * The Stirling numbers of the second kind, counts the number of ways to partition
     32    * a set of n labelled objects into k nonempty unlabelled subsets.
     33    * stirlingS2 only takes integer arguments.
     34    * The following condition must be enforced: k <= n.
     35    *
     36    *  If n = k or k = 1 <= n, then s(n,k) = 1
     37    *  If k = 0 < n, then s(n,k) = 0
     38    *
     39    * Note that if either n or k is supplied as a BigNumber, the result will be
     40    * as well.
     41    *
     42    * Syntax:
     43    *
     44    *   math.stirlingS2(n, k)
     45    *
     46    * Examples:
     47    *
     48    *    math.stirlingS2(5, 3) //returns 25
     49    *
     50    * See also:
     51    *
     52    *    bellNumbers
     53    *
     54    * @param {Number | BigNumber} n    Total number of objects in the set
     55    * @param {Number | BigNumber} k    Number of objects in the subset
     56    * @return {Number | BigNumber}     S(n,k)
     57    */
     58 
     59   return typed(name, {
     60     'number | BigNumber, number | BigNumber': function numberBigNumberNumberBigNumber(n, k) {
     61       if (!isInteger(n) || isNegative(n) || !isInteger(k) || isNegative(k)) {
     62         throw new TypeError('Non-negative integer value expected in function stirlingS2');
     63       } else if (larger(k, n)) {
     64         throw new TypeError('k must be less than or equal to n in function stirlingS2');
     65       }
     66 
     67       var big = !((0, _is.isNumber)(n) && (0, _is.isNumber)(k));
     68       var cache = big ? bigCache : smallCache;
     69       var make = big ? bignumber : number;
     70       var nn = number(n);
     71       var nk = number(k);
     72       /* See if we already have the value: */
     73 
     74       if (cache[nn] && cache[nn].length > nk) {
     75         return cache[nn][nk];
     76       }
     77       /* Fill the cache */
     78 
     79 
     80       for (var m = 0; m <= nn; ++m) {
     81         if (!cache[m]) {
     82           cache[m] = [m === 0 ? make(1) : make(0)];
     83         }
     84 
     85         if (m === 0) continue;
     86         var row = cache[m];
     87         var prev = cache[m - 1];
     88 
     89         for (var i = row.length; i <= m && i <= nk; ++i) {
     90           if (i === m) {
     91             row[i] = 1;
     92           } else {
     93             row[i] = addScalar(multiplyScalar(make(i), prev[i]), prev[i - 1]);
     94           }
     95         }
     96       }
     97 
     98       return cache[nn][nk];
     99     }
    100   });
    101 });
    102 exports.createStirlingS2 = createStirlingS2;