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Add ability to sample elements from openArray according to a weight array (#10072)

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* Add the ability to sample elements from an openArray according to a parallel
array of weights/unnormalized probabilities (any sort of histogram, basically).
Also add a non-thread safe version for convenience.

* Address Araq comments on https://github.com/nim-lang/Nim/pull/10072

* import at top of file and space after '#'.

* Put in a check for non-zero total weight.

* Clarify constraint on `w`.

* Rename `rand(openArray[T])` to `sample(openArray[T])` to `sample`, deprecating
old name and name new (openArray[T], openArray[U]) variants `sample`.

* Rename caller-provided state version of rand(openArray[T]) and also clean
up doc comments.

* Add test for new non-uniform array sampler.  3 sd bound makes it 99% likely
that it will still pass in the future if the random number generator changes.
We cannot both have a tight bound to check distribution *and* loose check to
ensure resilience to RNG changes.  (We cannot *guarantee* resilience, anyway.
There's always a small chance any test hits a legitimate random fluctuation.)
This commit is contained in:
c-blake
2018-12-23 07:23:20 -05:00
committed by Dominik Picheta
parent d407af565f
commit e1d5356ae9
2 changed files with 62 additions and 3 deletions
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28
tests/stdlib/tmath.nim
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@@ -4,6 +4,8 @@ discard """
[Suite] random float
[Suite] random sample
[Suite] ^
'''
@@ -11,7 +13,7 @@ discard """
import math, random, os
import unittest
import sets
import sets, tables
suite "random int":
test "there might be some randomness":
@@ -72,6 +74,30 @@ suite "random float":
var rand2:float = random(1000000.0)
check rand1 != rand2
suite "random sample":
test "non-uniform array sample":
let values = [ 10, 20, 30, 40, 50 ] # values
let weight = [ 4, 3, 2, 1, 0 ] # weights aka unnormalized probabilities
let weightSum = 10.0 # sum of weights
var histo = initCountTable[int]()
for v in sample(values, weight, 5000):
histo.inc(v)
check histo.len == 4 # number of non-zero in `weight`
# Any one bin is a binomial random var for n samples, each with prob p of
# adding a count to k; E[k]=p*n, Var k=p*(1-p)*n, approximately Normal for
# big n. So, P(abs(k - p*n)/sqrt(p*(1-p)*n))>3.0) =~ 0.0027, while
# P(wholeTestFails) =~ 1 - P(binPasses)^4 =~ 1 - (1-0.0027)^4 =~ 0.01.
for i, w in weight:
if w == 0:
check values[i] notin histo
continue
let p = float(w) / float(weightSum)
let n = 5000.0
let expected = p * n
let stdDev = sqrt(n * p * (1.0 - p))
check abs(float(histo[values[i]]) - expected) <= 3.0 * stdDev
suite "^":
test "compiles for valid types":
check: compiles(5 ^ 2)