mirror of
https://github.com/josdejong/mathjs.git
synced 2025-12-08 19:46:04 +00:00
ecbd877643
* fix(combinatorics): Improve precision of stirlingS2 Previously the computation of stirlingS2 used the closed form, which suffers numerically by dividing a sum of very large terms by a large factorial, causing roundoff errors for unnecessarily small inputs. This commit switches to using the recurrence relation for the stirling numbers of the second kind, and caching the partial results for future calls. This has the advantage that all intermediate results are smaller than the final value. Also adds tests for much larger values of the stirlingS2 function and of bellNumbers, whose computation depends on stirlingS2. Resolves #2508. * fix(stirlingS2): Correct lint errors.
52 lines
2.2 KiB
JavaScript
52 lines
2.2 KiB
JavaScript
import assert from 'assert'
|
|
import math from '../../../../src/defaultInstance.js'
|
|
const bellNumbers = math.bellNumbers
|
|
|
|
describe('bellNumbers', function () {
|
|
it('should calculate the number of partitions of a set', function () {
|
|
assert.strictEqual(bellNumbers(3), 5)
|
|
assert.strictEqual(bellNumbers(0), 1)
|
|
assert.strictEqual(bellNumbers(8), 4140)
|
|
assert.strictEqual(bellNumbers(17), 82864869804)
|
|
assert.strictEqual(bellNumbers(22), 4506715738447323)
|
|
// That's as large as we can go with number representation
|
|
})
|
|
|
|
it('should calculate the bellNumbers of n items with BigNumbers', function () {
|
|
const bn = math.bignumber
|
|
assert.deepStrictEqual(bellNumbers(bn(2)), bn(2))
|
|
assert.deepStrictEqual(bellNumbers(bn(3)), bn(5))
|
|
assert.deepStrictEqual(bellNumbers(bn(17)), bn(82864869804))
|
|
assert.deepStrictEqual(bellNumbers(bn(22)), bn(4506715738447323))
|
|
// and now we can go farther
|
|
assert.deepStrictEqual(bellNumbers(bn(26)), bn('49631246523618756274'))
|
|
assert.deepStrictEqual(bellNumbers(bn(50)),
|
|
bn('185724268771078270438257767181908917499221852770'))
|
|
})
|
|
|
|
it('should not work with non-integer and negative input', function () {
|
|
assert.throws(function () { bellNumbers(0.5) }, TypeError)
|
|
assert.throws(function () { bellNumbers(-1) }, TypeError)
|
|
assert.throws(function () { bellNumbers(math.bignumber(-3)) }, TypeError)
|
|
assert.throws(function () { bellNumbers(math.bignumber(3.5)) }, TypeError)
|
|
})
|
|
|
|
it('should throw an error in case of non-integer input', function () {
|
|
assert.throws(function () { bellNumbers(5.2) }, /Non-negative integer value expected/)
|
|
})
|
|
|
|
it('should throw an error in case of negative input', function () {
|
|
assert.throws(function () { bellNumbers(-2) }, /Non-negative integer value expected/)
|
|
})
|
|
|
|
it('should throw an error in case of wrong number or type of arguments', function () {
|
|
assert.throws(function () { bellNumbers(5, 3, 2) })
|
|
assert.throws(function () { bellNumbers(true, 'hello world') })
|
|
})
|
|
|
|
it('should LaTeX bellNumbers', function () {
|
|
const expression = math.parse('bellNumbers(3)')
|
|
assert.strictEqual(expression.toTex(), '\\mathrm{B}_{3}')
|
|
})
|
|
})
|