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https://issues.apache.org/jira/browse/MATH-1169?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Rob Tompkins updated MATH-1169:
-------------------------------
    Fix Version/s: 4.X

> Faster Percentile
> -----------------
>
>                 Key: MATH-1169
>                 URL: https://issues.apache.org/jira/browse/MATH-1169
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Adam Stelmaszczyk
>            Priority: Minor
>             Fix For: 4.X
>
>         Attachments: FloydRivest.java, Main.java, PercentileFloydRivest.java
>
>
> Percentile class is now using Hoare selection algorithm (aka 
> [Quickselect|http://en.wikipedia.org/wiki/Quickselect]) with median of 3 for 
> choosing a pivot and caching pivots. Quickselect expected runtime is about 
> 3.4N + O(N).
> The constant can be improved to 1.5N by different pivot strategy involving 
> sampling, yielding the [Floyd–Rivest 
> algorithm|http://en.wikipedia.org/wiki/Floyd%E2%80%93Rivest_algorithm], which 
> has average complexity of 1.5N + O(N) for median, with other position 
> statistics even faster.
> For proof of concept I implemented Floyd–Rivest algorithm without caching 
> pivots following Wikipedia and benchmarked it with 
> [Caliper|https://code.google.com/p/caliper/].
> Array size - runtime for Floyd-Rivest - runtime for current Percentile - % 
> faster
> 100000 - 6.907 - 7.083 - 2.5% 
> [link|https://microbenchmarks.appspot.com/runs/a0d947ee-57fc-4636-b687-b4bc5170f1d7#r:scenario.benchmarkSpec.methodName]
> 1000000 - 70.3 - 75.4 - 6.8% 
> [link|https://microbenchmarks.appspot.com/runs/77291c2e-6dbb-4666-bf37-c174e4b53f2e#r:scenario.benchmarkSpec.methodName]
> 10000000 - 708 - 868 - 18.4% 
> [link|https://microbenchmarks.appspot.com/runs/c0f65e35-44c0-458e-b6e0-634b4e6fa68b#r:scenario.benchmarkSpec.methodName]
> In attachments:
> {{Main.java}} should be run to repeat experiments, it needs Caliper JAR: 
> https://code.google.com/p/caliper/downloads/detail?name=caliper-1.0-beta-1-all.jar
> Every call to evaluate() I'm filling the input double[] array with different 
> random numbers.
> {{FloydRivest.java}} contatins implementation of algorithm basing on 
> pseudocode from its Wikipedia page.
> {{PercentileFloydRivest.java}} is Percentile.java with modified evaluate(), 
> so it calls FloydRivest.select() instead of typical select(). pivotsHeap was 
> removed for simplicity (maybe it can improve efficiency even more).



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