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7ac1fc81fd
* Resolve things raised in https://github.com/nim-lang/Nim/issues/10081 ? CDF is a standard ident in all things related to random numbers/sampling, and full words "cumulativeDistributionFunction" would be silly long, in this case, IMO. We use lowercase `cdf` to make it not look like a type, remove all looping from `sample` letting callers do it. Besides just side-stepping any `sampleSize` name choice, callers may want to filter out samples anyway which this makes slightly simpler. Also add two variants of `cumsum`, value return and in-place update distinguished by the var-ness of the first argument. Add tests for `int` and `float` for both `cumsum` and the new `sample`. (The sample tests exercise the value return mode of `cumsum`.) Functionality pre-this-PR `sample(a, w)` is now the almost as simple `for i in 0..<n: sample(a, w.cumsum)`, but this new code factoring is almost surely better. The statistical tests pass, as before. * Address Araq comment in https://github.com/nim-lang/Nim/pull/10084 We can always add in some `var` version later if desired to save memory, but this change now at least firms up the `sample` interface. * Rename `cumsum` -> `cumsummed` to honor NEP1 style. Re-instate `cumsum` as the in-place transformation. Test both in `tests/stdlib/tmath.nim` and use `cumsummed` in the example code for sample since that's a simpler example. * Fix requests from https://github.com/nim-lang/Nim/pull/10084 : example in lib/pure/math.nim and comment whitespace in lib/pure/random.nim
147 lines
4.1 KiB
Nim
147 lines
4.1 KiB
Nim
discard """
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action: run
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output: '''[Suite] random int
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[Suite] random float
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[Suite] cumsum
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[Suite] random sample
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[Suite] ^
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'''
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"""
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import math, random, os
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import unittest
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import sets, tables
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suite "random int":
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test "there might be some randomness":
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var set = initSet[int](128)
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randomize()
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for i in 1..1000:
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incl(set, random(high(int)))
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check len(set) == 1000
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test "single number bounds work":
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randomize()
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var rand: int
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for i in 1..1000:
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rand = random(1000)
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check rand < 1000
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check rand > -1
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test "slice bounds work":
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randomize()
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var rand: int
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for i in 1..1000:
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rand = random(100..1000)
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check rand < 1000
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check rand >= 100
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test "randomize() again gives new numbers":
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randomize()
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var rand1 = random(1000000)
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os.sleep(200)
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randomize()
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var rand2 = random(1000000)
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check rand1 != rand2
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suite "random float":
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test "there might be some randomness":
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var set = initSet[float](128)
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randomize()
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for i in 1..100:
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incl(set, random(1.0))
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check len(set) == 100
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test "single number bounds work":
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randomize()
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var rand: float
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for i in 1..1000:
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rand = random(1000.0)
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check rand < 1000.0
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check rand > -1.0
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test "slice bounds work":
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randomize()
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var rand: float
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for i in 1..1000:
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rand = random(100.0..1000.0)
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check rand < 1000.0
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check rand >= 100.0
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test "randomize() again gives new numbers":
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randomize()
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var rand1:float = random(1000000.0)
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os.sleep(200)
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randomize()
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var rand2:float = random(1000000.0)
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check rand1 != rand2
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suite "cumsum":
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test "cumsum int seq return":
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let counts = [ 1, 2, 3, 4 ]
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check counts.cumsummed == [ 1, 3, 6, 10 ]
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test "cumsum float seq return":
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let counts = [ 1.0, 2.0, 3.0, 4.0 ]
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check counts.cumsummed == [ 1.0, 3.0, 6.0, 10.0 ]
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test "cumsum int in-place":
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var counts = [ 1, 2, 3, 4 ]
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counts.cumsum
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check counts == [ 1, 3, 6, 10 ]
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test "cumsum float in-place":
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var counts = [ 1.0, 2.0, 3.0, 4.0 ]
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counts.cumsum
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check counts == [ 1.0, 3.0, 6.0, 10.0 ]
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suite "random sample":
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test "non-uniform array sample unnormalized int CDF":
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let values = [ 10, 20, 30, 40, 50 ] # values
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let counts = [ 4, 3, 2, 1, 0 ] # weights aka unnormalized probabilities
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var histo = initCountTable[int]()
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let cdf = counts.cumsummed # unnormalized CDF
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for i in 0 ..< 5000:
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histo.inc(sample(values, cdf))
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check histo.len == 4 # number of non-zero in `counts`
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# Any one bin is a binomial random var for n samples, each with prob p of
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# adding a count to k; E[k]=p*n, Var k=p*(1-p)*n, approximately Normal for
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# big n. So, P(abs(k - p*n)/sqrt(p*(1-p)*n))>3.0) =~ 0.0027, while
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# P(wholeTestFails) =~ 1 - P(binPasses)^4 =~ 1 - (1-0.0027)^4 =~ 0.01.
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for i, c in counts:
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if c == 0:
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check values[i] notin histo
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continue
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let p = float(c) / float(cdf[^1])
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let n = 5000.0
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let expected = p * n
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let stdDev = sqrt(n * p * (1.0 - p))
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check abs(float(histo[values[i]]) - expected) <= 3.0 * stdDev
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test "non-uniform array sample normalized float CDF":
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let values = [ 10, 20, 30, 40, 50 ] # values
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let counts = [ 0.4, 0.3, 0.2, 0.1, 0 ] # probabilities
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var histo = initCountTable[int]()
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let cdf = counts.cumsummed # normalized CDF
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for i in 0 ..< 5000:
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histo.inc(sample(values, cdf))
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check histo.len == 4 # number of non-zero in ``counts``
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for i, c in counts:
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if c == 0:
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check values[i] notin histo
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continue
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let p = float(c) / float(cdf[^1])
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let n = 5000.0
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let expected = p * n
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let stdDev = sqrt(n * p * (1.0 - p))
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# NOTE: like unnormalized int CDF test, P(wholeTestFails) =~ 0.01.
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check abs(float(histo[values[i]]) - expected) <= 3.0 * stdDev
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suite "^":
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test "compiles for valid types":
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check: compiles(5 ^ 2)
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check: compiles(5.5 ^ 2)
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check: compiles(5.5 ^ 2.int8)
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check: compiles(5.5 ^ 2.uint)
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check: compiles(5.5 ^ 2.uint8)
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check: not compiles(5.5 ^ 2.2) |