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Posted to issues@commons.apache.org by "Alex Herbert (Jira)" <ji...@apache.org> on 2021/09/28 11:31:00 UTC
[jira] [Reopened] (RNG-160) Performance of modified Ziggurat
samplers
[ https://issues.apache.org/jira/browse/RNG-160?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Alex Herbert reopened RNG-160:
------------------------------
Assignee: Alex Herbert
Reopened to add updated benchmark results
> Performance of modified Ziggurat samplers
> -----------------------------------------
>
> Key: RNG-160
> URL: https://issues.apache.org/jira/browse/RNG-160
> Project: Commons RNG
> Issue Type: Improvement
> Components: sampling
> Affects Versions: 1.4
> Reporter: Alex Herbert
> Assignee: Alex Herbert
> Priority: Minor
> Fix For: 1.4
>
> Attachments: Exp.jpg, Gaussian.jpg
>
>
> The modified ziggurat algorithm implemented in RNG-151 has a variation for sampling from the overhang regions at the ziggurat edges, region A below:
> {noformat}
> \
> ----------+\
> | \
> B |A \
> -------------+\
> | \
> {noformat}
> Note: Region B is the ziggurat layer which is entirely within the distribution PDF.
> These overhangs can be convex, concave or an inflection (change from convex to concave). Samples from the region A must be below the distribution density curve (PDF). When sampling from region A, the sampler will create a random point (x,y) uniformly within the rectangle. This is tested to determine if it is below the curve. Convex and concave curves can use a fast method that knows the largest possible triangle that fits above or below the curve. If a sampled point (x,y) is within these triangles then the actual curve position (pdf( x)) for the point x does not need to be computed. This can save time if the pdf is computationally expensive. In the case of exponential (exp(-x)) or Gaussian (exp(-0.5 * x * x)) this involves a call to Math.exp.
> The current sampler implements the fast look-up method. The alternative is to always compute pdf( x) and determine if y is below the curve. This is known as 'simple overhangs'.
> Investigate the use of simple overhangs on the performance of the sampler.
> Note: The Marsaglia version of the ziggurat sampler uses the 'simple overhangs' method.
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