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From "Adam Stelmaszczyk (JIRA)" <j...@apache.org>
Subject [jira] [Issue Comment Deleted] (MATH-1169) Faster Percentile
Date Thu, 13 Nov 2014 23:08:33 GMT

     [ https://issues.apache.org/jira/browse/MATH-1169?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Adam Stelmaszczyk updated MATH-1169:
------------------------------------
    Comment: was deleted

(was: {{Main.java}} should be run, 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 creating a new double[] array filled 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).)

> 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
>         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 k being 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 in seconds 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 creating a new double[] array filled 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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